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NASA NTRS1982

Scattering and collapse of Langmuir waves driven by a weak electron beam

Wave-wave interactions are examined, particularly for significance in relation to Langmuir turbulence associated with type III solar radio emissions. The Zakharov equations are considered as two coupled nonlinear partial differential equations for the low-frequency density and the Langmuir envelope, and the electron and ion temperatures are regarded as equal. The Zhakharov equations are solved in one dimension, and display no collapse of a driven broadband pump, indicating that scattering instabilities are important in the saturation of a beam-plasma instability. A two-dimensional numerical simulation is developed to interpret the role of parametric instabilities, and it is concluded that the distortion of a wave packet is due to scattering instability, and not a change in the physics of direct collapse due to an artificial numerical damping. Further discussions are presented for comparisons of models of Langmuir turbulence in type III bursts.

Hafizi, B.↗

NASA NTRS1982

Analysis and design of steady transonic flow over airfoils by the method of parametric differentiation

The results reported here are based on applying the method of parametric differentiation (MPD) to transform the nonlinear differential equation governing small-disturbance transonic flow to a linear equation. Implicit approximate factorization and monotone methods were used to accelerate convergence of the linear problem by an order of magnitude over successive line over-relaxation. The relative merits of using MPD are discussed in comparison to conventional small-disturbance applications. Several MPD analyses are performed on an array of airfoils. A design procedure utilizing MPD is discussed and demonstrated for two nonlifting cases.

Halt, D. W.↗

NASA NTRS1982

Finite element analysis for bearingless rotor blade aeroelasticity

A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.

Sivaneri, N. T.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

Manro, M. E.↗

NASA NTRS1983

Solitons in semiconductors with a superlattice

The nonlinear parabolic equation describing the propagation of the electromagnetic wave in a semiconductor with the superlattice is analyzed. The possibility of the existence of the solitary waves is proved both for a small amplitude of the electrical field and the latter moderate values.

Tetervov, A. P.↗

NASA NTRS1983

Finite element analysis of moisture effects in graphite-epoxy composites

A numerical analysis procedure is developed for the micro-mechanical investigation of moisture effects on graphite-epoxy composites. The procedure employs a nonlinear constitutive relationship in a finite element formulation. A quasi-Newton method is used to solve the resulting nonlinear algebraic equations. The results presented indicate that the stresses at the graphite-epoxy interface have a strong dependence on moisture content, fiber spacing, and applied load.

Tobing, F. E. L.↗

NASA NTRS1982

Nonlinear modal analysis of penetrative convection

It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies.

Zahn, J.-P.↗

NASA NTRS1983

Prediction of a propellant tank pressure history using state space methods

An analysis of the time response of a propellant supply system operating in the blowdown mode is presented. The supply system is part of a pump-fed propulsion system intended for use on interplanetary spacecraft. As such, the supply system must provide the pump with propellant at sufficient pressure to avoid pump cavitation. The system, consisting of the tank, the liquid propellant, the pressurant gas and propellant vapor mixture, and a film layer separating the liquid and vapor phases, is analyzed using the principles of mass and energy conservation. The resulting set of ordinary, coupled, nonlinear differential equations for the thermodynamic state variables is integrated as an initial value problem. The resulting histories of total pressure, propellant vapor pressure, propellant liquid temperature, film layer temperature, propellant vapor/pressurant gas temperature, propellant vapor mass, and propellant liquid mass enable the calculation of the net positive suction head available at the pump which determines the viability of the pump-fed system concept when operated in the blowdown mode.

Estey, P. N.↗

NASA NTRS1983

Ignition of a combustible half space

A half space of combustible material is subjected to an arbitrary energy flux at the boundary where convection heat loss is also allowed. An asymptotic analysis of the temperature growth reveals two conditions necessary for ignition to occur. Cases of both large and order unity Lewis number are shown to lead to a nonlinear integral equation governing the thermal runaway. Some global and asymptotic properties of the integral equation are obtained.

Olmstead, W. E.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1984

A computer program for predicting nonlinear uniaxial material responses using viscoplastic models

A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.

Chang, T. Y.↗

NASA NTRS1983

Weak cubic Langmuir turbulence

The cubically nonlinear Schroedinger equation model of Langmuir turbulence is solved in the weak turbulence limit. Steady-state power-law solutions for the energy spectra are found in arbitrary dimensionality. In one spatial dimension, the theory incorrectly predicts that no spectrum evolves in time. In three spatial dimensions, numerical solutions are obtained for the undriven, undamped, initial value problem and for the driven, damped, initial value problem.

Hansen, P. J.↗

NASA NTRS1984

Nonlinear mode coupling theory of the lower-hybrid-drift instability

A nonlinear mode coupling theory of the lower-hybrid-drift instability is presented. A two-dimensional nonlinear wave equation is derived which describes lower-hybrid drift wave turbulence in the plane transverse to B (k.B = 0), and which is valid for finite beta, collisional and collisionless plasmas. The instability saturates by transferring energy from growing, long wavelength modes to damped, short wavelength modes. Detailed numerical results are presented which compare favorably to both recent computer simulations and experimental observations. Applications of this theory to space plasmas, the earth's magnetotail and the equatorial F region ionosphere, are discussed. Previously announced in STAR as N84-17734

Drake, J. F.↗

NASA NTRS1986

Predicting the Dynamic Behavior of High-Speed Roller Bearings

Computer program developed for solving nonlinear differential equations of motion of high-speed, lightly loaded, cylindrical roller bearing. Program organized into three major parts: Main program, controls input and output; differential equation solver; and subroutines, used to evaluate vector function. Program has capability of performing either twodimensional or three-dimensional simulation.

Conry, T. F.↗

NASA NTRS1984

Chemoviscosity modeling for thermosetting resins - I

A new analytical model for chemoviscosity variation during cure of thermosetting resins was developed. This model is derived by modifying the widely used WLF (Williams-Landel-Ferry) Theory in polymer rheology. Major assumptions involved are that the rate of reaction is diffusion controlled and is linearly inversely proportional to the viscosity of the medium over the entire cure cycle. The resultant first order nonlinear differential equation is solved numerically, and the model predictions compare favorably with experimental data of EPON 828/Agent U obtained on a Rheometrics System 4 Rheometer. The model describes chemoviscosity up to a range of six orders of magnitude under isothermal curing conditions. The extremely non-linear chemoviscosity profile for a dynamic heating cure cycle is predicted as well. The model is also shown to predict changes of glass transition temperature for the thermosetting resin during cure. The physical significance of this prediction is unclear at the present time, however, and further research is required. From the chemoviscosity simulation point of view, the technique of establishing an analytical model as described here is easily applied to any thermosetting resin. The model thus obtained is used in real-time process controls for fabricating composite materials.

Hou, T. H.↗

NASA NTRS1984

Nonlinear evolution of astrophysical Alfven waves

Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.

Spangler, S. R.↗

NASA NTRS1985

Contributions on the Subject of Longitudinal Movements of Aircraft in Wind Shears

The effect of downburst-type wind shears on the longitudinal dynamic behavior of an unguided aircraft is simulated numerically on the basis of published meteorological data and the flight characteristics of an A300-B passenger jet. The nonlinear differential equations of the aircraft motion are linearized by conventional methods, and the wind effects are introduced via the linear derivatives of the wind components referred to the wind gradients to obtain simplified technical models of the longitudinal response to all possible types of constant-gradient wind shears during the first 20-60 sec. Graphs, maps, and diagrams are provided, and a number of accidents presumed to have involved wind shears are analyzed in detail.

Krauspe, P.↗