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At least 1,315 records · Page 73

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NASA NTRS1972

Plasticity - Theory and finite element applications.

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Armen, H., Jr.↗

NASA NTRS1974

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.

Curry, D. M.↗

NASA NTRS1974

The application of Riegels' rule and time-like damping to transonic flow calculations

Finite difference relaxation solutions of the nonlinear small perturbation equations have proven reliable and successful in determining the transonic flowfields about thin airfoils. However, application of the small perturbation approach to thick airfoils usually results in an accuracy less than desirable. The incorporation of Riegels' Rule and time-like damping into the small perturbation approach and their application to thick and thin airfoils in transonic flow are discussed. Studies for thick and thin airfoils are presented. It is concluded that Riegels' Rule and damping should both be included in small perturbation transonic flow calculations.

Herron, D. L.↗

NASA NTRS1974

A numerical calculation of outward propagation of solar disturbances

The responses of the solar atmosphere due to an outward propagation shock are examined by employing the Lax-Wendroff method to solve the set of nonlinear partial differential equations in the model of the solar atmosphere. It is found that this theoretical model can be used to explain the solar phenomena of surge and spray. A criterion to discriminate the surge and spray is established and detailed information concerning the density, velocity, and temperature distribution with respect to the height and time is presented. The complete computer program is also included.

Wu, S. T.↗

NASA NTRS1974

Theoretical investigations on plasma processes in the Kaufman thruster

An analysis of the sputtering of metal surfaces and grids by ions of medium energies is given and it is shown that an exact, nonlinear, hyperbolic wave equation for the temperature field describes the transient transport of heat in metals. Quantum statistical and perturbation theoretical analysis of surface sputtering by low energy ions are used to develop the same expression for the sputtering rate. A transport model is formulated for the deposition of sputtered atoms on system components. Theoretical efforts in determining the potential distribution and the particle velocity distributions in low pressure discharges are briefly discussed.

Wilhelm, H. E.↗

NASA NTRS1975

Time-dependent transonic flow solutions for axial turbomachinery

Three-dimensional unsteady transonic flow through an axial turbomachine stage is described in terms of a pair of two-dimensional formulations pertaining to orthogonal surfaces, namely, a blade-to-blade surface and a hub-to-casing surface. The resulting systems of nonlinear, inviscid, compressible equations of motion are solved by an explicit finite-difference technique. The blade-to-blade program includes the periodic interaction between rotor and stator blade rows. Treatment of the boundary conditions and of the blade slipstream motion by a characteristic type procedure is discussed in detail. Harmonic analysis of the acoustic far field produced by the blade row interaction, including an arbitrary initial transient, is outlined. Results from the blade-to-blade program are compared with experimental measurements of the rotating pressure field at the tip of a high-speed fan. The hub-to-casing program determines circumferentially averaged flow properties on a meridional plane. Blade row interactions are neglected in this formulation, but the force distributions over the entire blade surface for both the rotor and stator are obtained. Results from the hub-to-casing program are compared with a relaxation method solution for a subsonic rotor. Results are also presented for a quiet fan stage which includes transonic flow in both the rotor and stator and a normal shock in the stator.

Erdos, J.↗

NASA NTRS1975

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.

Martin, E. D.↗

NASA NTRS1976

Mathematical model of one-man air revitalization system

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

Source record↗

NASA NTRS1975

Remote sensing applied to numerical modelling

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

Sengupta, S.↗

NASA NTRS1976

Pseudopotentials of Estabrook and Wahlquist, the geometry of solitons, and the theory of connections

The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property - linked to the existence of an SL(2,R) connection - is proved for the solutions of the Korteweg-de Vries equation.

Hermann, R.↗

NASA NTRS1976

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

Martin, E. D.↗

NASA NTRS1976

Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders

The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions.

Ghandour, N. N.↗

NASA NTRS1976

Operations research investigations of satellite power stations

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

Cole, J. W.↗

NASA NTRS1977

Aeroelastic stability of coupled flap-lag-torsional motion of helicopter rotor blades in forward flight

A set of coupled periodic nonlinear differential flap-lag-torsional equations of blade motion is described which can simulate a blade having a precone, twist, distributed torsion, root torsion, torque offset, blade-root offsets, and offsets among the elastic axis, the aerodynamic center, and the blade cross-sectional center of mass. It is noted that the aerodynamic loads derived for these equations are applicable to cases of both hover and forward flight. The aeroelastic stability of a hingeless helicopter blade is investigated by linearizing the nonlinear differential equations of motion about a time-dependent equilibrium position of the helicopter in forward flight, using propulsion and moment trim procedures. A comparison of the results with those obtained previously for coupled flap-lag-torsional boundaries in hover indicates that aeroelastic-stability margins are degraded due to forward flight.

Friedmann, P.↗

NASA NTRS1976

An efficient procedure for computing partial ionization of a gas in numerical fluid dynamics

A numerical procedure is described that allows efficient solution for the three nonlinear and implicit equations of state relating the equilibrium properties of a partially (and singly) ionized neutral gas. In the computation, the values for the intensive variables, that is pressure, temperature and ionization coefficient, are iteratively obtained with a given accuracy starting from assigned values for energy and volume per unit mass. Iterative computation is performed only when the value for the ionization coefficient lies within the lower and the upper bounds fixed by the required number of significant digits; otherwise the two explicit equations of state for nonionized or for fully ionized gases are employed.

Garribba, S.↗

NASA NTRS1978

Analysis of turbulent free jet hydrogen-air diffusion flames with finite chemical reaction rates

The nonequilibrium flow field resulting from the turbulent mixing and combustion of a supersonic axisymmetric hydrogen jet in a supersonic parallel coflowing air stream is analyzed. Effective turbulent transport properties are determined using the (K-epsilon) model. The finite-rate chemistry model considers eight reactions between six chemical species, H, O, H2O, OH, O2, and H2. The governing set of nonlinear partial differential equations is solved by an implicit finite-difference procedure. Radial distributions are obtained at two downstream locations of variables such as turbulent kinetic energy, turbulent dissipation rate, turbulent scale length, and viscosity. The results show that these variables attain peak values at the axis of symmetry. Computed distributions of velocity, temperature, and mass fraction are also given. A direct analytical approach to account for the effect of species concentration fluctuations on the mean production rate of species (the phenomenon of unmixedness) is also presented. However, the use of the method does not seem justified in view of the excessive computer time required to solve the resulting system of equations.

Sislian, J. P.↗

NASA NTRS1978

Galactic civilizations: Population dynamics and interstellar diffusion

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

Newman, W. I.↗

NASA NTRS1979

A regression technique for evaluation and quantification for water quality parameters from remote sensing data

The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

Whitlock, C. H.↗