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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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NASA NTRS1984

Ground-state-energy theorem and the virial theorem of a many-particle system in d dimensions

The equivalence of Pauli's ground-state-energy theorem and the virial theorem is demonstrated for a many-particle system interacting with an interparticle potential in d dimensions at zero and finite temperatures. Pauli's theorem has an integral form in which the variable is the coupling constant e-squared, while the virial theorem has a differential form in which the variable has the number density n. The essence of the equivalence proof consists in changing the variable from n to e-squared by noting the dependence of the excess free energy on dimensionless quantities for zero-temperature and classical cases.

Iwamoto, N.↗

NASA NTRS1985

On the design derivatives of eigenvalues and eigenvectors for distributed parameter systems

In this paper, analytic expressions are obtained for the design derivatives of eigenvalues and eigenfunctions of self-adjoint linear distributed parameter systems. Explicit treatment of boundary conditions is avoided by casting the eigenvalue equation into integral form. Results are expressed in terms of the linear operators defining the eigenvalue problem, and are therefore quite general. Sufficiency conditions appropriate to structural optimization of eigenvalues are obtained.

Reiss, R.↗

NASA NTRS1985

Picard iterations of boundary-layer equations

A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.

Ardema, M. D.↗

NASA NTRS1986

ALESEP. Part 2: A computer program for the analysis of leading edge separation bubbles on infinite swept wings

A program called ALESEP is presented for the analysis of the inviscid-viscous interaction which occurs due to the presence of a closed laminar-transitional separation bubble on an airfoil or infinite swept wing. The ALESEP code provides an iterative solution of the boundary layer equations expressed in an inverse formulation coupled to a Cauchy integral representation of the inviscid flow. This interaction analysis is treated as a local perturbation to a known solution obtained from a global airfoil analysis; hence, part of the required input to the ALESEP code are the reference displacement thickness and tangential velocity distributions. Special windward differencing may be used in the reversed flow regions of the separation bubble to accurately account for the flow direction in the discretization of the streamwise convection of momentum. The ALESEP code contains a forced transition model based on a streamwise intermittency function, a natural transition model based on a solution of the integral form of the turbulent kinetic energy equation, and an empirical natural transition model.

Davis, R. L.↗

NASA NTRS1986

Overview of the NASA SETI Program

The NASA Search of Extraterrestrial Intelligence (SETI) program plan is to scan the microwave window from 1 to 10 GHz with existing radio telescopes and sophisticated signal processing equipment looking for narrow band features that might represent artificial signals. A microwave spectrometer was built and is being field tested. A pattern recognition computer to search for drifting continuous wave signals and pulse trains in the output spectra is being designed. Equipment to characterize the radio frequency interference environment was also built. The plan is to complete the hardware and software by FY-88. Then, with increased funding, this equipment will be replicated in Very Large Scale Integration form. Observations, both a complete sky survey and a search fo nearby solar type stars, will begin in about 1990. The hypothesis that very powerful signals exist or that signals are being beamed at us will be tested. To detect the kinds of signals radiated at distances of 100 light years will require a collecting area kilometers in diameter.

Oliver, B. M.↗

NASA NTRS1987

An evaluation of higher-order model methods for calculating transient structural response

A higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method is evaluated. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force-derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗

NASA NTRS1987

A finite volume Euler calculation of the aerodynamics of transonic airfoil-vortex interaction

Unsteady inviscid transonic airfoil-vortex interaction is numerically analyzed by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables is used to form the numerical dissipation terms to stabilize the scheme. A velocity decomposition technique is applied to alleviate the problem of vortex diffusion by the numerical dissipation terms and to treat the interaction of a Rankine vortex with an airfoil accurately. Results obtained are compared with available numerical data.

Damodaran, Murali↗

NASA NTRS1987

An evaluation of higher-order modal methods for calculating transient structural response

The present study evaluates a higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗

NASA NTRS1988

Finite volume computation of unsteady inviscid rotational transonic flows past airfoils in rigid body motion

Unsteady inviscid transonic flow over airfoils in arbitrary rigid body motion is analyzed numerically by solving the two-dimensional unsteady Euler equations in integral form using a finite volume scheme. The solution procedure is based on an explicit Runge-Kutta time-stepping scheme wherein the spatial terms are central-differenced and a combination of second- and fourth-differences in the flow variables are used to form the numerical dissipation terms to stabilize the scheme. Unsteady calculations are started from converged steady-state solutions as initial conditions. Nonreflective boundary conditions are imposed on the far-field boundaries. Results are presented and, where possible, validated against available numerical and experimental data for airfoils subjected to a step change in angle of attack, airfoils oscillating and plunging in transonic flow, and airfoils immersed in a time-varying free stream.

Damodaran, Murali↗

NASA NTRS1988

Attitude control of an object commonly held by multiple robot arms - A Lyapunov approach

Multiple robot arms moving a commonly held object can be viewed as complex actuators whose purpose is to provide net forces and moments to the object. These forces and moments can be used to control the orientation, or attitude, of the object via the Euler equation describing attitude evolution in response to applied moments at the mass center. In contrast to the common approach that feedback-linearizes the attitude dynamics to a double integrator form with respect to some three-parameter local representation of orientation, the authors control the object using a globally nonsingular representation. Using an energy-motivated Liapunov function, globally stable control of attitude is shown.

Kreutz, Kenneth↗

NASA NTRS1989

Transonic flutter calculations using the Euler equations

In transonic flutter problems where shock motion plays an important part, it is believed that accurate predictions of the flutter boundaries will require the use of codes based on the Euler equations. Only Euler codes can obtain the correct shock location and shock strength, and the crucially important shock excursion amplitude and phase lag. The present study is based on the finite volume scheme developed by Jameson and Venkatakrishnan for the 2-D unsteady Euler equations. The equations are solved in integral form on a moving grid. The variable are pressure, density, Cartesian velocity components, and total energy.

Bendiksen, Oddvar O.↗

NASA NTRS1989

Analysis of low Reynolds number separation bubbles using semiempirical methods

The formation and growth of transitional separation bubbles can significantly affect boundary-layer development on airfoils operating at low chord Reynolds numbers. Of primary concern is the change in boundary-layer thickness between laminar separation and turbulent reattachment. This can be estimated using semiempirical methods, such as the one devised by Horton (1968), which are based on solutions to the integral forms of the boundary-layer equations. The applicability of these methods at low Reynolds numbers was investigated using hot-wire measurements of bubbles formed on an NACA 66(3)-018 airfoil at chord Reynolds numbers of 50,000-200,000. The momentum thickness growth between separation and transition was found to be similar to that predicted for a laminar half-jet and appears to be influenced by the momentum thickness Reynolds number at separation. This parameter also was found to have a noticeable effect on the Reynolds number based on the length of a bubble's laminar portion.

Schmidt, Gordon S.↗

NASA NTRS1990

On unstructured grids and solvers

The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.

Barth, T. J.↗

NASA NTRS1990

Vorticity-dilatation boundary conditions for viscous compressible flows

The theoretical generalization, synthesis, and classification of various relevant formulations of the vorticity-dilatation conditioning problem is presented. Kinematic and dynamic conditions as well as differential and integral forms are considered. The possibility of using various variables that relate directly to vorticity and dilatation to construct the desired boundary conditions is examined. Some new formulations are given and previously proposed ones are located properly in the classification, and their interrelations are clarified.

Wu, J. Z.↗

NASA NTRS1990

Thermal compensating mount

The main objective is to provide a device for maintaining the alignment integrity of an alignment sensitive component over a wide range of temperatures. A thermal compensating mount is presented. A cylindrical extension is integrally formed to the alignment sensitive component. Both the extension and component share the same coefficient of thermal expansion. The cylindrical extension is placed into a mounting structure which has a diameter greater than that of the extension. An adhesive secures the cylindrical extension to the mount. The difference between the diameters of the cylindrical extension and the cylindrical receptacle is such that the differential thermal expansion across the extension and the receptacle edges is exactly compensated for by the thermal compensation of the adhesive between them. Accordingly, the alignment sensitive component does not change position when subjected to temperature variations. One application of this invention is laser optical-path folding prisms, which are fixed to the mounting surface by a small amount of epoxy adhesive.

Jalink, Antony, Jr.↗

NASA NTRS1991

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Walker, K. P.↗

NASA NTRS1991

Gain in computational efficiency by vectorization in the dynamic simulation of multi-body systems

An improved technique for the identification and extraction of the exact quantities associated with the degrees of freedom at the element as well as the flexible body level is presented. It is implemented in the dynamic equations of motions based on the recursive formulation of Kane et al. (1987) and presented in a matrix form, integrating the concepts of strain energy, the finite-element approach, modal analysis, and reduction of equations. This technique eliminates the CPU intensive matrix multiplication operations in the code's hot spots for the dynamic simulation of the interconnected rigid and flexible bodies. A study of a simple robot with flexible links is presented by comparing the execution times on a scalar machine and a vector-processor with and without vector options. Performance figures demonstrating the substantial gains achieved by the technique are plotted.

Amirouche, F. M. L.↗

NASA NTRS1991

On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

A complete potential based framework using internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive while the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, i.e., the Compliance operator, is defined which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached, is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the used forms, to restore the complete potential structure.

Arnold, S. M.↗