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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 163 records · Page 9
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NASA NTRS1972

Decay of homogeneous turbulence from a specified state

The homogeneous turbulence problem is formulated by first specifying the multipoint velocity correlations or their spectral equivalents at an initial time. Those quantities, together with the correlation or spectral equations, are then used to calculate initial time derivatives of correlations or spectra. The derivatives in turn are used in time series to calculate the evolution of turbulence quantities with time. When the problem is treated in this way, the correlation equations are closed by the initial specification of the turbulence and no closure assumption is necessary. An exponential series which is an iterative solution of the Navier stokes equations gave much better results than a Taylor power series when used with the limited available initial data. In general, the agreement between theory and experiment was good.

Deissler, R. G.↗
NASA NTRS1972

Application of Contraction Mappings to the Control of Nonlinear Systems

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Killingsworth, W. R., Jr.↗
NASA NTRS1969

Determination of the temperature profile in an atmosphere from its outgoing radiation

A highly convergent relaxation method for the inversion of the full radiative transfer equation was developed. The results of the iterative solution indicate that convergence can be achieved over a wide range of initial guesses, enabling the temperature profile of a relatively unknown atmosphere to be unambiguously determined. The method is illustrated by examples for the outgoing radiance in the earth's atmosphere for the region of the 4.3 microns CO2 band, but can be similarly applied in other frequency ranges.

Chahine, M. T.↗
NASA NTRS1972

The optical properties of platinum and gold in the vacuum ultraviolet

The optical constants of platinum and gold thin films have been determined in the spectral region of 40 to 200 nm by reflection measurements. The highly polarized continuum of synchrotron radiation emitted by the 240-MeV electron storage ring at the Physical Sciences Laboratory of the University of Wisconsin was used as a light source for the spectrum below 120 nm, while a windowless discharge lamp coupled to a normal incidence monochromator provided a source for the longer wavelengths. Optical constants were determined by a computer program based on iterative solutions to the Fresnel equations for reflection as a function of the angle of incidence.

Linton, R. C.↗
NASA NTRS1972

Nonlinear actuator disk theory.

Results obtained from a recent investigation of the flowfield induced by a heavily loaded actuator disk. First, the governing nonlinear integral equations are formulated from two different points of view, and the iterative solution is briefly outlined. Calculated flow patterns are presented for representative advance ratios and blade circulation distributions. For the static condition, the experimentally observed lingering of the tip vortices in the propeller plane, and the insensitivity of the streamline pattern to thrust coefficient are both accounted for, and a 'dividing streamline' - apparently not previously discussed in the literature, is predicted for the nonstatic case. Finally, the relationship between the actuator disk flow and the zero harmonic of the flowfield induced by a finite-bladed propeller is considered.

Greenberg, M. D.↗
NASA NTRS1973

Computer programs for the solution of systems of linear algebraic equations

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Sequi, W. T.↗
NASA NTRS1975

DYNGEN: A program for calculating steady-state and transient performance of turbojet and turbofan engines

The DYNGEN, a digital computer program for analyzing the steady state and transient performance of turbojet and turbofan engines, is described. The DYNGEN is based on earlier computer codes (SMOTE, GENENG, and GENENG 2) which are capable of calculating the steady state performance of turbojet and turbofan engines at design and off-design operating conditions. The DYNGEN has the combined capabilities of GENENG and GENENG 2 for calculating steady state performance; to these the further capability for calculating transient performance was added. The DYNGEN can be used to analyze one- and two-spool turbojet engines or two- and three-spool turbofan engines without modification to the basic program. A modified Euler method is used by DYNGEN to solve the differential equations which model the dynamics of the engine. This new method frees the programmer from having to minimize the number of equations which require iterative solution. As a result, some of the approximations normally used in transient engine simulations can be eliminated. This tends to produce better agreement when answers are compared with those from purely steady state simulations. The modified Euler method also permits the user to specify large time steps (about 0.10 sec) to be used in the solution of the differential equations. This saves computer execution time when long transients are run. Examples of the use of the program are included, and program results are compared with those from an existing hybrid-computer simulation of a two-spool turbofan.

Sellers, J. F.↗
NASA NTRS1975

Transonic airfoil flowfield analysis using Cartesian coordinates

A numerical technique for analyzing transonic airfoils is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that Cartesian coordinates are used rather than a grid which fits the airfoil, such as the conformal circle-plane or 'sheared parabolic' coordinates which were used previously. Comparison with previous results shows that it is not necessary to match the computational grid to the airfoil surface, and that accurate results can be obtained with a Cartesian grid for lifting supercritical airfoils.

Carlson, L. A.↗
NASA NTRS1975

A method for the dynamic and thermal stress analysis of space shuttle surface insulation

The thermal protection system of the space shuttle consists of thousands of separate insulation tiles bonded to the orbiter's surface through a soft strain-isolation layer. The individual tiles are relatively thick and possess nonuniform properties. Therefore, each is idealized by finite-element assemblages containing up to 2500 degrees of freedom. Since the tiles affixed to a given structural panel will, in general, interact with one another, application of the standard direct-stiffness method would require equation systems involving excessive numbers of unknowns. This paper presents a method which overcomes this problem through an efficient iterative procedure which requires treatment of only a single tile at any given time. Results of associated static, dynamic, and thermal stress analyses and sufficient conditions for convergence of the iterative solution method are given.

Ojalvo, I. U.↗
NASA NTRS1975

Contribution of the National Aeronautics and Space Administration Langley Research Center

As part of a special international effort, three nozzles were designed and tested on single nacelle models in wind tunnels of several nations belonging to the North Atlantic Treaty Organization. All three of these nozzles were investigated in the Langley 16-foot transonic wind tunnel at the National Aeronautics and Space Administration's Langley Research Center. Langley Research Center also contributed theoretical calculations of the jet plume boundary and afterbody pressures. The calculations were obtained using an iterative solution which combined the inviscid Douglas Neumann method for the external flow with the method of characteristics for the flow in the jet plume. For the investigation, the nozzles were mounted on a single nacelle model 15.24 centimeters in diameter and 162.56 centimeters long. Tests were made at free stream Mach number from 0.4 to 1.2, and at Reynolds numbers per meter from 7.38 million to 13.78 million depending on the Mach number. Four types of data were recorded: afterbody pressure data, afterbody force data, model boundary layer data, and tunnel wall pressure data. The ratio of jet total pressure to free stream static pressure ranged up to 8.5. A description of the wind tunnel, model, and test procedure is included.

Compton, W. B., III↗
NASA NTRS1976

Transonic airfoil design using Cartesian coordinates

A numerical technique for designing transonic airfoils having a prescribed pressure distribution (the inverse problem) is presented. The method employs the basic features of Jameson's iterative solution for the full potential equation, except that inverse boundary conditions and Cartesian coordinates are used. The method is a direct-inverse approach that controls trailing-edge closure. Examples show the application of the method to design aft-cambered and other airfoils specifically for transonic flight.

Carlson, L. A.↗
NASA NTRS1976

Transformation of apparent ocean wave spectra observed from an aircraft sensor platform

The problem considered was transformation of a unidirectional apparent ocean wave spectrum observed from an aircraft sensor platform into the true spectrum that would be observed from a stationary platform. Spectral transformation equations were developed in terms of the linear wave dispersion relationship and the wave group speed. An iterative solution to the equations was outlined and used to transform reference theoretical apparent spectra for several assumed values of average water depth. Results show that changing the average water depth leads to a redistribution of energy density among the various frequency bands of the transformed spectrum. This redistribution is most severe when much of the energy density is expected, a priori, to reside at relatively low true frequencies.

Poole, L. R.↗
NASA NTRS1976

Accelerated iterative calculation of transonic nacelle flowfields

A method is presented for the calculation of inviscid, supercritical flowfields about axisymmetric inlet cowls. A finite-difference calculation is performed in a simple, rectangular domain obtained from the nacelle geometry by a nearly-conformal mapping procedure. Type-dependent finite-differences are constructed using a coordinate-independent, 'rotated' differencing scheme. Methods of accelerating convergence of the iterative solution are demonstrated including a hybrid fast-Poisson-solver/relaxation scheme and an extrapolated relaxation procedure. Calculated pressure distributions are compared with experimental data for a variety of Mach numbers and mass-flow ratios, and show generally good agreement.

Caughey, D. A.↗
NASA NTRS1976

Influence of nonconservative differencing on transonic streamline shapes

A computer program recently developed by South and Brandt (1976) which contained the Murman (1973) conservative finite-difference scheme is easily modified to use the Garabedian and Korn (1971) nonconservative finite difference scheme. This program solves the transonic small disturbance equation for only symmetric flow, but incorporates several iterative solution techniques. Results are presented for the case where the equally spaced computational grid extended to infinity in both the streamwise and normal directions. Streamline shapes are obtained along several grid lines by a streamwise integration of the normal component of the perturbation velocity. Comparison cases are run for a 10% thick parabolic arc airfoil at zero incidence for freestream Mach numbers of 0, 0.70, 0.84, and 0.95. It is shown that the use of a nonconservative finite-difference scheme in transonic flow calculations destroys the global mass balance when shocks are present. This lack of mass balance may prove to be more crucial in the case of an unconfined external flow.

Newman, P. A.↗
NASA NTRS1975

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗
NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗
NASA NTRS1977

Fast methods incorporating direct elliptic solvers for nonlinear applications in fluid dynamics

Semidirect methods are discussed, their present role, as well as some developments for their application in computational fluid dynamics. A semidirect method is a computational scheme that uses a fast, direct, elliptic solver as the driving algorithm for the iterative solution of finite difference equations. Specific subtopics include: (1) direct Cauchy Riemann solvers for first order elliptic equations; (2) application of the semidirect method to the mixed elliptic hyperbolic problem of steady, inviscid transonic flow; and (3) the treatment of interior conditions, such as those on an airfoil or wing, in semidirect methods.

Martin, E. D.↗
NASA NTRS1979

Crack propagation in aluminum sheets reinforced with boron-epoxy

An analysis was developed to predict both the crack growth and debond growth in a reinforced system. The analysis was based on the use of complex variable Green's functions for cracked, isotropic sheets and uncracked, orthotropic sheets to calculate inplane and interlaminar stresses, stress intensities, and strain-energy-release rates. An iterative solution was developed that used the stress intensities and strain-energy-release rates to predict crack and debond growths, respectively, on a cycle-by-cycle basis. A parametric study was made of the effects of boron-epoxy composite reinforcement on crack propagation in aluminum sheets. Results show that the size of the debond area has a significant effect on the crack propagation in the aluminum. For small debond areas, the crack propagation rate is reduced significantly, but these small debonds have a strong tendency to enlarge. Debond growth is most likely to occur in reinforced systems that have a cracked metal sheet reinforced with a relatively thin composite sheet.

Roderick, G. L.↗