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At least 721 records · Page 40

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NASA NTRS1971

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Rosenbaum, J. S.↗

NASA NTRS1974

Combustion instability with partial length acoustic liners

The development of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors is discussed. The studies involved nonlinear wave propagation effects and nonlinear combustion zone, liner, and nozzle responses. A second primary extension of the basic theory was directed at the inclusion of the effects of injector face baffles. Attention was restricted to the linear (small amplitude) problem, finite Mach numbers, three dimensional oscillations, and distributed combustion effects.

Mitchell, C. E.↗

NASA NTRS1975

Suppression of nonlinear oscillations in combustors with partial length acoustic liners

An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.

Espander, W. R.↗

NASA NTRS1975

Turbulent flow between a rotating disk and a parallel wall

A scalar effective viscosity method is used to calculate the incompressible flow in the gap between two infinite, parallel smooth disks, one of them rotating and the other stationary. The flow is calculated for two values of the gap Reynolds number omega(s squared)/nu, namely 296 and 2852, where omega is the disk angular velocity, s the gap width, and nu the kinematic viscosity of the fluid; and over a range of radial Reynolds number omega(r squared)/nu from 0 to 10 million, where r is the radius from the axis of rotation. A numerical shooting technique is used to match the two boundary-layer flows arising on the disk and wall. Gradual transition is assumed for radial Reynolds numbers from 160,000 to 250,000. The results are in good agreement with Daily and Nece's measurements of velocity profiles and disk friction drag for enclosed rotating disks, and at sufficiently large radius the local skin friction approaches that of turbulent Couette flow.

Cooper, P.↗

NASA NTRS1975

Finite element techniques applied to cracks interacting with selected singularities

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

Conway, J. C.↗

NASA NTRS1975

STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual

STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

Cooke, C. H.↗

NASA NTRS1976

Preheated, combustion-driven gasdynamic lasers

The effect of preheated nitrogen on the available laser specific energy is examined for two classes of combustion-driven gasdynamic lasers (GDLs). The analysis combines a nonequilibrium model of the relevant GDL processes with a simplified nondissociating combustion model handling a variety of candidate GDL fuels. For a more comprehensive evaluation of the capabilities of preheating, an optimization routine is added to the combined laser/combustion models. The effectiveness of preheating to enhance laser specific energy is demonstrated, although preheating may impose unacceptable hardware requirements. The application of numerical optimization techniques appears to offer a means to improve laser design.

Saunders, R. C., III↗

NASA NTRS1976

Laser beam scintillation beyond the turbulent atmosphere A numerical computation

The extended Huygens-Fresnel formulation for propagation through turbulence is used to examine scintillation of a finite laser beam. The method is demonstrated analytically for propagation beyond a weak Gaussian phase screen. A numerical integration technique is used to extend the results to a more realistic turbulence model. Results are compared with existing Gaussian beam propagation theory.

Bufton, J. L.↗

NASA NTRS1977

Solar generated quasi-biennial geomagnetic variation

The existence of highly correlated quasi-biennial variations in the geomagnetic field and in solar activity is demonstrated. The analysis uses a numerical filter technique applied to monthly averages of the geomagnetic horizontal component and of the Zurich relative sunspot number. Striking correlations are found between the quasi-biennial geomagnetic variations determined from several magnetic observatories located at widely different longitudes, indicating a worldwide nature of the obtained variation. The correlation coefficient between the filtered Dst index and the filtered relative sunspot number is found to be -0.79 at confidence level greater than 99% with a time-lag of 4 months, with solar activity preceding the Dst variation. The correlation between the unfiltered data of Dst and of the sunspot number is also high with a similar time-lag. Such a timelag has not been discussed in the literature, and a further study is required to establish the mode of sun-earth relationship that gives this time delay.

Sugiura, M.↗

NASA NTRS1976

Numerical optimization of gasdynamic lasers

A sophisticated numerical optimization procedure has been coupled to a detailed theoretical model of the carbon dioxide gasdynamic laser (GDL) for the purpose of systematically evaluating the performance of these systems. The integrated model was used to predict the performance of a wide variety of combustion-driven gasdynamic lasers and was then used to maximize the theoretical available specific energy of these lasers. Up to six design variables and three nonlinear constraints were used in these optimizations, although the method is not limited to this number. Results are presented to show the performance of typical lasers before and after optimization. Improvements approaching a factor of two in the available specific energy are found, suggesting that numerical optimization techniques are valuable in improving the design of gasdynamic lasers.

Saunders, R. C., III↗

NASA NTRS1977

Solar-generated quasi-biennial geomagnetic variation

The existence of highly correlated quasi-biennial variations in the geomagnetic field and in solar activity is demonstrated. The analysis uses a numerical filter technique applied to monthly averages of the geomagnetic horizontal component and of the Zurich relative sunspot number. Striking correlations are found between the quasi-biennial geomagnetic variations determined from several magnetic observatories located at widely different longitudes, indicating the worldwide nature of the obtained variation. The correlation coefficient between the filtered Dst index and the filtered relative sunspot number is found to be -0.79 at confidence level greater than 99% with a time lag of 4 months, solar activity preceding the Dst variation. The correlation between the unfiltered data of Dst and those of the sunspot number is also high with a similar time lag. Such a time lag has not been discussed in the literature, and a further study is required to establish the mode of sun-earth relationship that gives this time delay.

Sugiura, M.↗

NASA NTRS1978

Unsteady flow in a supersonic cascade with subsonic leading-edge locus

Linearized theory is used to predict the unsteady flow in a supersonic cascade with subsonic axial flow velocity. A closed-form analytical solution is obtained by using a double application of the Wiener-Hopf technique. Although numerical and semianalytical solutions of this problem have already appeared in the literature, this paper contains the first completely analytical solution. It has been stated in the literature that the blade source should vanish at the infinite duct resonance condition. The present analysis shows that this does not occur. This apparent discrepancy is explained in the paper.

Adamczyk, J. J.↗

NASA NTRS1980

Acid rain: Microphysical model

A microphysical model was used to simulate the case of a ground cloud without dilution by entrainment and without precipitation. The numerical integration techniques of the model are presented. The droplet size spectra versus time and the droplet molalities for each value of time are discussed.

Dingle, A. N.↗

NASA NTRS1979

Global Earth Response to Loading by Ocean Tide Models

Mathematical and programming techniques to numerically calculate Earth response to global semidiurnal and diurnal ocean tide models were developed. Global vertical crustal deformations were evaluated for M sub 2, S sub 2, N sub 2, K sub 2, K sub 1, O sub 1, and P sub 1 ocean tide loading, while horizontal deformations were evaluated for the M sub 2 tidal load. Tidal gravity calculations were performed for M sub 2 tidal loads, and strain tensor elements were evaluated for M sub 2 loads. The M sub 2 solution used for the ocean tide included the effects of self-gravitation and crustal loading.

Estes, R. H.↗

NASA NTRS1980

Calculation of the transient motion of elastic airfoils forced by control surface motion and gusts

The time-domain equations of motion of elastic airfoil sections forced by control surface motions and gusts were developed for the case of incompressible flow. Extensive use was made of special functions related to the inverse transform of Theodorsen's function. Approximations for the special cases of zero stream velocity, small time, large and time are given. A numerical solution technique for the solution of the general case is given. Examples of the exact transient response of an airfoil are presented.

Balakrishnan, A. V.↗

NASA NTRS1980

Reformulation of Possio's kernel with application to unsteady wind tunnel interference

An efficient method for computing the Possio kernel has remained elusive up to the present time. In this paper the Possio is reformulated so that it can be computed accurately using existing high precision numerical quadrature techniques. Convergence to the correct values is demonstrated and optimization of the integration procedures is discussed. Since more general kernels such as those associated with unsteady flows in ventilated wind tunnels are analytic perturbations of the Possio free air kernel, a more accurate evaluation of their collocation matrices results with an exponential improvement in convergence. An application to predicting frequency response of an airfoil-trailing edge control system in a wind tunnel compared with that in free air is given showing strong interference effects.

Fromme, J. A.↗

NASA NTRS1980

Stability of the stratifield cylindrical annulus flow

The linear stability analysis for the stratified flow between two rotating circular cylinders is formulated. Two approaches for the stability analysis are presented. The first approach results in an algebraic eigenvalue problem, while the second results in an initial value problem for the perturbation function. The advantages and disadvantages of both approaches are discussed and a preferable numerical solution technique is outlined.

Antar, B. N.↗

NASA NTRS1980

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

Steger, J. L.↗