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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Solution of complex nonlinear problems by a generalized application of the method of base and comparison solutions with applications to aerodynamics problems

A theory for obtaining approximate solutions to nonlinear problems whose exact solutions require the use of large computational procedures is described. The technique represents in some respects a generalization of the method of base and comparison solutions for flows depending on a parameter. For the generalized problem, the input variable is no longer a parameter but a function that is incremented over its entire domain. After performing calculations for a base configuration and a small number of variations of it, solutions for a large class of configurations can be obtained by forming linear combinations of the solution increments. For a restricted class of problems, approximate solutions can be obtained for general variations of a base configuration by using a function-space derivative estimate obtained from a base solution and a single variation.

Barger, R. L.↗
NASA NTRS1973

Thermodynamic properties of gases dissolved in electrolyte solutions.

A method based on perturbation theory for mixtures is applied to the prediction of thermodynamic properties of gases dissolved in electrolyte solutions. The theory is compared with experimental data for the dependence of the solute activity coefficient on concentration, temperature, and pressure; calculations are included for partial molal enthalpy and volume of the dissolved gas. The theory is also compared with previous theories for salt effects and found to be superior. The calculations are best for salting-out systems. The qualitative feature of salting-in is predicted by the theory, but quantitative predictions are not satisfactory for such systems; this is attributed to approximations made in evaluating the perturbation terms.

Tiepel, E. W.↗
NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗
NASA NTRS2007

Quasi-Static Analysis of LaRC THUNDER Actuators

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Campbell, Joel F.↗
NASA NTRS2007

Quasi-Static Analysis of Round LaRC THUNDER Actuators

An analytic approach is developed to predict the shape and displacement with voltage in the quasi-static limit of round LaRC Thunder Actuators. The problem is treated with classical lamination theory and Von Karman non-linear analysis. In the case of classical lamination theory exact analytic solutions are found. It is shown that classical lamination theory is insufficient to describe the physical situation for large actuators but is sufficient for very small actuators. Numerical results are presented for the non-linear analysis and compared with experimental measurements. Snap-through behavior, bifurcation, and stability are presented and discussed.

Campbell, Joel F.↗
NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

Ghosh, Amitabha↗
NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

Ghosh, Amitabha↗
NASA NTRS1991

Homogeneous freezing nucleation of stratospheric solution droplets

The classical theory of homogeneous nucleation was used to calculate the freezing rate of sulfuric acid solution aerosols under stratospheric conditions. The freezing of stratospheric aerosols would be important for the nucleation of nitric acid trihydrate particles in the Arctic and Antarctic stratospheres. In addition, the rate of heterogeneous chemical reactions on stratospheric aerosols may be very sensitive to their state. The calculations indicate that homogeneous freezing nucleation of pure water ice in the stratospheric solution droplets would occur at temperatures below about 192 K. However, the physical properties of H2SO4 solution at such low temperatures are not well known, and it is possible that sulfuric acid aerosols will freeze out at temperatures ranging from about 180 to 195 K. It is also shown that the temperature at which the aerosols freeze is nearly independent of their size.

Jensen, Eric J.↗
NASA NTRS1991

Transient scattering analysis for a circular disk

The backscattered fields of a perfectly conducting circular disk are analyzed from a transient signature viewpoint. The significant dominant scattering mechanisms are identified for both principal polarizations at a variety of angles. Particular attention is given to the edge wave. The backscattered field behavior due to an incident plane wave on a perfectly conducting disk is presented. Good agreement was obtained between the eigenfunction and geometric theory of diffraction solutions. The expected mechanisms from first-, second-, and third-order diffractions with an accurate edge wave representation are demonstrated through the use of transient signatures. The most significant error in the geometric theory of diffraction (GTD) solution occurs in time where the nonprincipal plane double diffraction term exists.

Dominek, Allen K.↗
NASA NTRS1973

On the improper neglect of certain terms in random function theory

This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.

Lerche, I.↗
NASA NTRS1980

Assessment of analytic methods for the prediction of aerodynamic characteristics of arbitrary bodies at supersonic speeds

Trends toward the automation of the design process for airplanes and missiles accentuate the need for analytic techniques for the prediction of aerodynamic characteristics. A number of computer codes have been developed or are under development which show promise of significantly improving the estimation of aerodynamic characteristics for arbitrarily-shaped bodies at supersonic speeds. The programs considered range in complexity from a simple linearized solution employing slender body theory to an exact finite difference solution of the Euler equations. The results from five computer codes are compared with experimental data to determine the accuracy, range of applicability, ease of use, and computer time and cost of the programs. The results provide a useful guide for selecting the appropriate method for treating bodies at the various levels of an automated design process.

Landrum, E. J.↗
NASA NTRS1990

Interfacial wave theory of dendrite growth - Global mode solution and quantum condition

The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.

Xu, Jian-Jun↗
NASA NTRS1983

High frequency scattering by a thin lossless dielectric slab

A high frequency solution for scattering from a thin dielectric slab is developed, based on a modification of the uniform geometrical theory of diffraction solution for a half-plane, with the intention of developing a model for a windshield of a small private aircraft. Results of the theory are compared with experimental measurements and moment method calculations showing good agreement. Application of the solution is also addressed.

Burnside, W. D.↗