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NASA NTRS1977

Aerodynamic loads near cranks, apexes, and tips of thin, lifting wings in incompressible flow

The calculation of the incompressible and irrotational flow in the vicinity of tips and corners of thin, lifting wings is considered. It is shown that the important characteristics of the flow are governed by an eigenvalue problem, which is nonlinear at the trailing edge because of the shed wake (assumed to be in the wing plane). A new solution method was devised because either the existing methods were not valid for the trailing edge case or they would have required excessive amounts of computer time. The new method, which is fundamentally different than the previous ones, was used to calculate solutions for a number of cases, including some for which correct answers had not previously been obtained. Two of these solutions were used to determine the validity of drag and leading-edge-suction distributions near the tips of a delta wing and a swept wing as calculated by using both the vortex lattice method and a kernel function method. The calculations for the swept wing resolved the question of whether or not the induced drag should be zero at the wing tip.

Medan, R. T.↗

NASA NTRS1976

Some applications of the NASTRAN level 16 subsonic flutter analysis capability

The Level 16 flutter analysis capability was applied to an aspect-ratio-6.8 subsonic transport type wing, an aspect-ratio-1.7 arrow wing, and an aspect-ratio-1.3 all movable horizontal tail with a geared elevator. The transport wing and arrow wing results are compared with experimental results obtained in the Langley transonic dynamic tunnel and with other calculated results obtained using subsonic lifting surface (kernel function) unsteady aerodynamic theory.

Doggett, R. V., Jr.↗

NASA NTRS1977

Analysis of H-alpha flare spectra

Spectrographs of the H-alpha line taken at 15 second intervals from the event of 5 Sept. 1973 were interpreted by comparison with synthetic profiles. A sequence of 27 high resolution H alpha profiles was obtained from the second brightest flare kernel. The profiles were generally self reversed with a maximum peak intensity of 1.16 x continuum and a maximum central intensity of .91 x continuum. The line characteristics such as red and violet peak intensities and positions, center shifts and wing intensities were tabulated. Synthetic H-alpha profiles were generated from a finite layer assuming simple parameteric forms for the source function and velocity field. The velocity chosen always decreased with optical depth and had the same sign. For absorption profiles, bisector shifts were calculated for a variety of velocities. The velocity field and source function were derived as a function of optical depth and time.

Kulander, J. L.↗

NASA NTRS1976

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.

Edge, E. R.↗

NASA NTRS1976

A comparison of positions and sizes of sources of centimeter and X-ray bursts

Results are reported for a parallel study of three centimeter-wave radio bursts observed on August 9, 1973, with the NRAO three-element interferometer at 3.7 and 11.1 cm and the associated X-ray flares observed with the S-054 telescope aboard Skylab. Within the errors of the measurements, the radio and X-ray events are cospatial. Good agreement is found between the size of the X-ray kernel and that of the core of the centimeter burst, but there is evidence that much of the impulsive radio flux was produced in a larger area.

Kundu, M. R.↗

NASA NTRS1976

The temperature and density structures of an X-ray flare during the decay phase

The X-ray flare of 9 August 1973 was characterized by a spatially small kernel structure which persisted throughout its duration. The decay phase of this flare was observed in the objective grating mode of the X-ray telescope aboard the Skylab. Data analysis was carried out by scanning the images with a microdensitometer, converting the density arrays to energy using laboratory film calibration data and taking cross sections of the energy images. The 9 August flare shows two distinct periods in its decay phase, involving both cooling and material loss. The objective grating observations reveal that the two phenomena are separated in time. During the earlier phase of the flare decay, the distribution of emission measure as a function of temperature is changing, the high temperature component of the distribution being depleted relative to the cooler body of plasma. As the decay continues, the emission measure distribution stabilizes and the flux diminishes as the amount of material at X-ray emitting temperatures decreases.

Silk, J. K.↗

NASA NTRS1977

Some experimental and theoretical flutter characteristics of an arrow-wing configuration

Experimental and theoretical flutter results are presented for a simplified 1/50-size wind-tunnel model of an arrow-wing configuration. Transonic flutter characteristics are presented for three configurations - wing without engine nacelles, wing with flow-through nacelles, and wing with pencil nacelles (thin, streamline bodies). Experimental results are correlated with analytical results obtained from kernel-function and doublet-lattice unsteady aerodynamic theories. Theoretical results are presented that show the effects on flutter of systematic changes in structural stiffness and mass.

Doggett, R. V., Jr.↗

NASA NTRS1976

A higher order panel method for general analysis and design applications in subsonic flow

A higher-order panel method is described for numerical solution of boundary-value problems relating to steady inviscid irrotational incompressible subsonic fluid flow in a domain. Both Neumann and Dirichlet boundary conditions are treated; two types of auxiliary conditions are used to remove the degrees of freedom that arise from specifying only the derivative of the perturbation velocity potential. Four general network types and two expansions of the induced potential kernel are employed in the numerical solution. Some results are presented which illustrate the modeling options and numerical characteristics of the method.

Johnson, F. T.↗

NASA NTRS1976

A jet engine control problem for evaluating minimal design software

The problem of designing feedforward and feedback compensators to achieve a specified closed loop performance matrix is shown to reduce to a minimal design problem. Existing results for the F100 turbofan engine can be interpreted to yield the closed loop specifications for the associated control problem - and also a possible solution. All possible solutions can be enumerated by computing the kernel of a polynomial matrix. It is shown how this matrix can be obtained from the formulation of the minimal design problem.

Gejji, R. R.↗

NASA NTRS1977

The resolvent of singular integral equations

The investigation reported is concerned with the construction of the resolvent for any given kernel function. In problems with ill-behaved inhomogeneous terms as, for instance, in the aerodynamic problem of flow over a flapped airfoil, direct numerical methods become very difficult. A description is presented of a solution method by resolvent which can be employed in such problems.

Williams, M. H.↗

NASA NTRS1977

The problem of internal and edge cracks in an orthotropic strip

The plane elastostatic problem of internal and edge cracks in an infinite orthotropic strip is considered. The problems for the material types I and II are formulated in terms of singular integral equations. For the symmetric case the stress-intensity factors are calculated and are compared with the isotropic results. The results show that because of the dependence of the Fredholm kernels on the elastic constants in the strip (unlike the crack problem for an infinite plane) the stress-intensity factors are dependent on the elastic constants and are generally different from the corresponding isotropic results

Delale, F.↗

NASA NTRS1977

An extension to the Chahine method of inverting the radiative transfer equation

An extension of the Chahine relaxation method (1970) for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward. A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.

Twomey, S.↗

NASA NTRS1978

The matching of biological and technical elements and systems

The conditions necessary for matching the input-output relationships of nonlinear dynamic systems without memory and with image memory are discussed. A structural representation is provided for the input-output relationships of matched elements and systems with distributed kernels.

Zozulya, Y. I.↗

NASA NTRS1978

User's Guide for a Modular Flutter Analysis Software System (Fast Version 1.0)

The use and operation of a group of computer programs to perform a flutter analysis of a single planar wing are described. This system of programs is called FAST for Flutter Analysis System, and consists of five programs. Each program performs certain portions of a flutter analysis and can be run sequentially as a job step or individually. FAST uses natural vibration modes as input data and performs a conventional V-g type of solution. The unsteady aerodynamics programs in FAST are based on the subsonic kernel function lifting-surface theory although other aerodynamic programs can be used. Application of the programs is illustrated by a sample case of a complete flutter calculation that exercises each program.

Desmarais, R. N.↗

NASA NTRS1978

Analysis of preflutter and postflutter characteristics with motion-matched aerodynamic forces

The development of the equations of dynamic equilibrium for a lifting surface from Lagrange's equation is reviewed and restated for general exponential growing and decaying oscillatory motion. Aerodynamic forces for this motion are obtained from the three-dimensional supersonic kernel function that is newly generalized to complex reduced frequencies. Illustrative calculations were made for two flutter models at supersonic Mach numbers. Preflutter and postflutter motion isodecrement curves were obtained. This type of analysis can be used to predict preflutter behavior during flutter testing and to predict postflutter behavior for use in the design of flutter suppression systems.

Cunningham, H. J.↗

NASA NTRS1978

Mixed boundary-value problems in mechanics

Definitions in the case of multiple series equations and multiple integral equations are examined. In considering the solution of a given mixed boundary value problem perhaps the simplest technique is the direct application of the method of complex potentials provided the problem admits such potentials and the domain and the boundary conditions are suitable for such an application. The direct application of complex potentials is described with the aid of examples, taking into account a problem in potential theory, the case of periodic cuts, and an elasticity problem for a nonhomogeneous plane. The reduction to singular integral equations is discussed along with the numerical solution of singular integral equations of the first kind, integral equations with generalized Cauchy kernels, and singular integral equations of the second kind.

Erdogan, F.↗

NASA NTRS1978

Advanced panel-type influence coefficient methods applied to unsteady three dimensional potential flows

A panel method for solving unsteady, subsonic wind-body-tail flow problems is formulated and partially verified. The method is applicable to general aircraft configurations consisting of arbitrary arrangements of wings, bodies, tails, and nacelles. The wake may be located arbitrarily and the unsteady, transverse component of vorticity in the wake may be assigned any covection velocity. The wake in the unsteady flow problem, therefore, can be given the location and convection velocity of the wake produced by a steady flow which is the mean flow of the unsteady flow problem. The panel method has been used as a basis for expanding the unsteady kernel function in a power series to obtain panel influence coefficients which can be integrated in closed form.

Dusto, A. R.↗

NASA NTRS1980

Interfering surfaces in subsonic, transonic, and supersonic flow

Computer program provides analysis method based on kernel-function technique that uses assumed pressure functions with unknown coefficients. With technique, generalized forces are calculated in unsteady flow, and pressure distributions are obtained in steady and unsteady flow.

Cunningham, A. M., Jr.↗