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NASA NTRS1993

On the spectral stability of time integration algorithms for a class of constrained dynamics problems

Incomplete field formulations have recently been the subject of intense research because of their potential in coupled analysis of independently modeled substructures, adaptive refinement, domain decomposition, and parallel processing. This paper discusses the design and analysis of time-integration algorithms for these formulations and emphasizes the treatment of their inter-subdomain constraint equations. These constraints are shown to introduce a destabilizing effect in the dynamic system that can be analyzed by investigating the behavior of the time-integration algorithm at infinite and zero frequencies. Three different approaches for constructing penalty-free unconditionally stable second-order accurate solution procedures for this class of hybrid formulations are presented, discussed and illustrated with numerical examples. The theoretical results presented in this paper also apply to a large family of nonlinear multibody dynamics formulations. Some of the algorithms outlined herein are important alternatives to the popular technique consisting of transforming differential/algebraic equations into ordinary differential equations via the introduction of a stabilization term that depends on arbitrary constants and that influences the computed so1ution.

Farhat, Charbel↗

NASA NTRS1990

The effect of laser pulse tailored welding of Inconel 718

Pulse tailored laser welding has been applied to wrought, wrought grain grown, and cast Inconel 718 using a CO2 laser. Prior to welding, the material was characterized metallographically and the solid state transformation regions were identified using Differential Scanning Calorimetry and high temperature x-ray diffraction. Bead on plate welds (restrained and unrestrained) were then produced using a matrix of pulse duty cycles and pulsed average power. Subsequent characterization included heat affected zone width, penetration and underbead width, the presence of cracks, microfissures and porosity, fusion zone curvature, and precipitation and liquated region width. Pedigree welding on three selected processing conditions was shown by microstructural and dye penetrant analysis to produce no microfissures, a result which strongly indicates the viability of pulse tailored welding for microfissure free IN 718.

Mccay, T. Dwayne↗

NASA NTRS2011

The Effect of Dose Rate on Composite Durability When Exposed to a Simulated Long-Term Lunar Radiation Environment

Human exploration of space beyond low Earth orbit (LEO) requires a safe living and working environment for crew. Composite materials are one type of material being investigated by NASA as a multi-functional structural approach to habitats for long-term use in space or on planetary surfaces with limited magnetic fields and atmosphere. These materials provide high strength with the potential for decreased weight and increased radiation protection of crew and electronics when compared with conventional aluminum structures. However, these materials have not been evaluated in a harsh radiation environment, as would be experienced outside of LEO or on a planetary surface. Thus, NASA has been investigating the durability of select composite materials in a long-term radiation environment. Previously, NASA exposed composite samples to a simulated, accelerated 30-year radiation treatment and tensile stresses similar to those of a habitat pressure vessel. The results showed evidence of potential surface oxidation and enhanced cross-linking of the matrix. As a follow-on study, we performed the same accelerated exposure alongside an exposure with a decreased dose rate. The slower dose ]rate is comparable to a realistic scenario, although still accelerated. Strain measurements were collected during exposure and showed that with a fastdose rate, the strain decreased with time, but with a slow ]dose rate, the strain increased with time. After the radiation exposures, samples were characterized via tensile tests, flexure tests, Fourier Transform Infrared Spectroscopy (FTIR), and Differential Scanning Calorimetry (DSC). The results of these tests will be discussed.

Rojdev, Kristina↗

NASA NTRS1984

Nonlinear control of aircraft

Transformations of nonlinear systems were used to design automatic flight controllers for vertical and short takeoff aircraft. Under the assumption that a nonlinear system can be mapped to a controllable linear system, a method using partial differential equations was constructed to approximate transformations in cases where exact ones cannot be found. An application of the design theory to a rotorcraft, the UH-1H helicopter, was presented.

Hunt, L. R.↗

NASA NTRS2002

The Statistical Mechanics of Ideal Homogeneous Turbulence

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

Shebalin, John V.↗

NASA NTRS1967

Influence of concentrated effects on shallow shells

Fourier transform and theory of generalized functions to obtain differential equilibrium equations to determine concentrated bending and tangential forces on shallow shells

FOURIER TRANSFORM↗

NASA NTRS1980

Numerical solutions of transonic flows by parametric differentiation and integral equation techniques

The paper discusses results of an exploratory study of the advantages obtained by combining integral equation methods with the method of parametric differentiation in the treatment of transonic flow problems. In the proposed method, the nonlinear unsteady transonic flow equation for small perturbations is transformed into a linear equation by the use of the method of parametric differentiation. The linear equation is split into a pair of weakly coupled partial differential equations by writing the transformed perturbation potential as the sum of a steady component and an unsteady component. The solution of the steady equation as an integral equation is based on Ogana's treatment (1978). As a test case, the formulation is applied to predict the steady transonic flow over a nonlifting parabolic-arc airfoil.

Sivaneri, N. T.↗

NASA NTRS1967

Finite transform solution of the vibrating annular membrane.

Vibrating annular membrane problem, including load per unit area and asymmetry of load and vibration, using finite transform derivation

LOAD DISTRIBUTION↗

NASA NTRS1971

The spectrum of steady state turbulent convection.

Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Winterberg, F.↗

NASA NTRS1979

Maximum likelihood identification of aircraft parameters with unsteady aerodynamic modelling

A simplified aerodynamic force model based on the physical principle of Prandtl's lifting line theory and trailing vortex concept has been developed to account for unsteady aerodynamic effects in aircraft dynamics. Longitudinal equations of motion have been modified to include these effects. The presence of convolution integrals in the modified equations of motion led to a frequency domain analysis utilizing Fourier transforms. This reduces the integro-differential equations to relatively simple algebraic equations, thereby reducing computation time significantly. A parameter extraction program based on the maximum likelihood estimation technique is developed in the frequency domain. The extraction algorithm contains a new scheme for obtaining sensitivity functions by using numerical differentiation. The paper concludes with examples using computer generated and real flight data

Keskar, D. A.↗

NASA NTRS1983

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.↗

NASA NTRS1985

Unsteady Heat Transfer Due to Time-dependent Free Stream Velocity

The present work was undertaken in order to study the unsteady combined convection from a horizontal circular cylinder to a transverse flow. A coordinate perturbation method is used to transform the governing set of partial differential equations into a system of ordinary differential equations. The free stream time-dependent velocity was assumed to be sinusoidal and the boundary layer response due to both low as well as high frequencies of oscillation will be studied. Currently numerical solutions are being obtained for the distribution of the unsteady Nusselt number and the friction factor.

Gorla, R. S. R.↗

NASA NTRS1985

The general Lie group and similarity solutions for the one-dimensional Vlasov-Maxwell equations

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.

Roberts, D.↗

NASA NTRS1987

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗

NASA NTRS1992

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Chung, Chan-Hong↗

NASA NTRS1992

Modelling a single phase voltage controlled rectifier using Laplace transforms

The development of a 20 kHz, AC power system by NASA for large space projects has spurred a need to develop models for the equipment which will be used on these single phase systems. To date, models for the AC source (i.e., inverters) have been developed. It is the intent of this paper to develop a method to model the single phase voltage controlled rectifiers which will be attached to the AC power grid as an interface for connected loads. A modified version of EPRI's HARMFLO program is used as the shell for these models. The results obtained from the model developed in this paper are quite adequate for the analysis of problems such as voltage resonance. The unique technique presented in this paper uses the Laplace transforms to determine the harmonic content of the load current of the rectifier rather than a curve fitting technique. Laplace transforms yield the coefficient of the differential equations which model the line current to the rectifier directly.

Kraft, L. Alan↗

NASA NTRS1992

Fusible heat sink materials - Evaluation of alternate candidates

Fusible heat sinks are a possible source for thermal regulation of space suited astronauts. Materials with greater thermal storage capability than water could enable both an extension of time between recharging and/or a reduction in size and/or mass. An extensive literature search identified 1,215 candidates with a solid-liquid transformation within the temperature range of -13 C to 5 C. Based on data available in the literature, several candidates with a cooling capacity significantly greater than water were identified. Measurements of the transformation temperature and enthalpy of transformation were then undertaken with a differential scanning calorimeter in order to confirm the accuracy of the literature. Laboratory measurements have thus far not been able to corroborate the extremely high values found from the literature. This paper presents the approach for materials selection utilized in this study, the experimental procedure, and the results of the measurements thus far undertaken.

Selvaduray, Guna S.↗