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At least 937 records · Page 52

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NASA NTRS1977

Computation of the inviscid supersonic flow about cones at large angles of attack by a floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow shock, and vortical singularity in the leeward symmetry plane are treated as floating discontinuities in a fixed computational mesh. Where possible, the flowfield is partitioned into windward, shoulder, and leeward regions with each region computed separately to achieve maximum computational efficiency. An alternative shock fitting technique which treats the bow shock as a computational boundary is developed and compared with the floating-fitting approach. Several surface boundary condition schemes are also analyzed.

Daywitt, J.↗

NASA NTRS1977

Unsteady supersonic aerodynamic theory for interfering surfaces by the method of potential gradient

A generalized solution of the hyperbolic wave equation was further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals were evaluated in closed form, with numerical integration methods for more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient. Streamwise integrals were performed analytically, and spanwise integrals were neccessary only on element leading and trailing sides. All integrands vanish on the Mach cone. Pressure distribution on a double delta wing and generalized aerodynamic coefficients for three AGARD planforms were calculated and compared with available results.

Jones, W. P.↗

NASA NTRS1976

Viscid-inviscid interaction of incompressible separated flows

A flow model has been devised to deal with the viscid-inviscid interaction of a class of two-dimensional incompressible separated flow problems. It is suggested that the corresponding inviscid flow of these problems is described by the free streamline theory with few unspecified parameters and their values are, in turn, determined by the viscous flow considerations. The problem of a flow past a backward facing step is selected for study in detail. The viscous flow components of turbulent jet mixing, recompression, and reattachment are delineated and studied individually. When they are later combined, it is found that the point of reattachment behaves as a saddle-point-type singularity in the system of differential equations describing the viscous flow process. This feature is employed to the determination of the aforementioned free parameters and thus the establishment of the overall corresponding inviscid flow field. The resulting base pressure coefficient for the specific case agrees reasonably well with the available experimental data.

Chow, W. L.↗

NASA NTRS1976

Time-dependent perturbation of a two-state quantum system by a sinusoidal field

Different methods for solving the 'two-level problem' are discussed, namely, the problem of what happens to a material system having only two nondegenerate energy levels when it is perturbed by an electromagnetic field that varies with time in a monochromatic sinusoidal fashion. The various methods discussed include: (1) the Sen Gupta technique using nondegenerate Rayleigh-Schroedinger perturbation theory, (2) the Salwen-Winter-Shirley partitioning perturbation technique, (3) the Shirley and series degenerate Rayleigh-Schroedinger expansion, (4) the degenerate Rayleigh-Schroedinger technique for considering high frequency fields, and (5) the singular perturbation expansion technique.

Dion, D. R.↗

NASA NTRS1977

Unsteady supersonic aerodynamic theory by the method of potential gradient

A generalized solution of the hyperbolic wave equation has been derived. The method used has been further developed to relate the velocity components at a field point to the potential gradient distribution in the dependence domain. Singular integrals have been evaluated in closed form, while numerical integration methods are suggested for treating more complex but analytic functions. Idealization of the lifting surfaces by trapezoidal elements with two sides parallel to the streamlines is computationally efficient because line integrations along the other two sides need only be considered. Furthermore, all the integrands vanish on the Mach cone and the need for determining the hyperbolic curves of intersection of the cone with the lifting surface is avoided. Generalized aerodynamic coefficients for three AGARD planforms have been calculated and compared with the available results.

Jones, W. P.↗

NASA NTRS1976

Numerical solutions of the triple-deck equations for laminar trailing-edge stall

The problem of determining the effect of laminar boundary layers on the lift of thin wings in subsonic flow at high Reynolds numbers is considered. The boundary value problem is formulated in the framework of the triple-deck theory of Brown and Stewartson. The resulting fourth-order boundary value was solved by an iterative finite-difference technique. An inverse iteration procedure provides proper treatment of the trailing-edge singularity, and asymptotic far-field expansions and coordinate stretchings are used to deal with the problem of the slow algebraic decay of the solution.

Chow, R.↗

NASA NTRS1976

Effect of friction in wedging of elastic solids

In this paper the contact problem for an elastic wedge of arbitrary angle is considered. It is assumed that the external load is applied to the medium through a rigid wedge and the coefficient of friction between the loading wedge and the elastic solid is constant. The problem is reduced to a singular integral equation of the second kind with the contact pressure as the unknown function. An effective numerical solution of the integral equation is described and the results of three examples are presented. The comparison of these results with those obtained from the frictionless wedge problem indicates that generally friction has the tendency of reducing the peak values of the stress intensity factors calculated at the wedge apex and at the end points of the contact area.

Erdogan, F.↗

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 NTRS1976

Stress intensity factors for long, deep surface flaws in plates under extensional fields

Using a singular solution for a part circular crack by Smith, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors (SIFs) from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50, and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the 'equivalent' semi-elliptical flaw for correlating the part circular flaw results with semi-elliptical flaw results was not valid for a/2c much less than 0.20. Best overall agreement for the moderate (a/t about 0.5) to deep flaws (a/t about 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory due to Newman when compared on the basis of equivalent flaw depth and area. The Smith theory, when correlated on the basis of flaw depth and area, appears to yield reasonable estimates (within 10%) of the SIF for flat bottomed flaws for the geometries studied here.

Harms, A. E.↗

NASA NTRS1977

Large-scale inhomogeneity of the Universe - Spherically symmetric models

Dust-filled Tolman-Bondi (1934, 1947) spherically symmetric cosmological models are studied with application to superclustering of galaxies. Asymptotic expressions are given for the density and curvature contrast, valid near the singularity and at long times. The density profile of infalling material is expressed in terms of a single arbitrary function (the distribution of total energy per unit mass). Measurement of the distribution of excess galaxy counts and deviations from the Hubble flow in the vicinity of a supercluster could provide a determination of the cosmological deceleration parameter.

Silk, J.↗

NASA NTRS1977

Role of condensed phase details in the oscillatory combustion of composite propellants

The response functions of composite propellants are theoretically derived, including explicitly the pressure-dependent degradation term in the condensed phase, hypothesizing that the overall rate-limiting reactions are in the relatively low temperature condensed phase. The method of 'inner' and 'outer' expansions with the reduced activation energy as the singular perturbation parameter has been employed. The results cover subsurface reactions with and without surface reactions, adiabatic and uniform-combustion models for the quasi-steady gas phase processes. The response functions display several experimentally observed features like dependence on mean pressure and the instability behavior of some 'zero-n' propellants.

Kumar, R. N.↗

NASA NTRS1976

Characteristics of the boundary-layer equations of the minimum time-to-climb problem

In many singular perturbation solutions of optimal control problems, the most difficult numerical task is to solve the boundary-layer equations. However, these equations have a special structure that may often be used to expedite their solution. This paper begins by noting the general nature of the boundary-layer equations for optimal control problems. These results are then applied to the aircraft minimum time-to-climb problem. A specific numerical example is considered to illustrate the characteristics of the solution of the boundary-layer equations for this problem.

Ardema, M. D.↗

NASA NTRS1977

Image restoration consequences of the lack of a two variable fundamental theorem of algebra

It has been shown that, at least for one pair of otherwise attractive spaces of images and operators, singular convolution operators do not necessarily have nonsingular neighbors. This result is a nuisance in image restoration. It is suggested that this difficulty might be overcome if the following three conditions are satisfied: (1) a weaker constraint than absolute summability can be identified for useful operators: (2) if the z-transform of an operator has at most a finite number of zeros on the unit torus, then the inverse z-transform formula yields an inverse operator meeting the weaker constraint: and (3) operators whose z-transforms are zero in a set of real, closed curves on the unit torus have neighbors which are zero in only a finite set of points on the unit torus.

Kreznar, J. E.↗

NASA NTRS1977

To perform a gyro test of general relativity in a satellite and develop associated control technology

A satellite configuration having two gyroscopes with axes parallel to the boresight of a telescope and two at right angles to the telescope and approximately parallel and perpendicular to the earth's axis is proposed for measuring geodetic precessions due to the earth's motion about the sun, higher order geodetic terms calculated from the earth's quadrapole mass moment (0.010 arc-sec/year in a 400 nautical mile polar orbit), and deflection by the sun of the starlight signal for the reference telescope. Data from the experiment also contain large periodic signals due to the annual and orbital aberrations of starlight which are useful in providing a built in reference signal of known amplitude for scaling the relativity signals, and should yield a singularly precise measurement of the parallax of the reference star. The development of the gyroscope and its readout system are discussed, as well as signal integration, drag-free control, and attitude control.

Fairbank, W. M.↗

NASA NTRS1977

Aerodynamic interference effects on tilting proprotor aircraft

The Green's function method was used to study tilting proprotor aircraft aerodynamics with particular application to the problem of the mutual interference of the wing-fuselage-tail-rotor wake configuration. While the formulation is valid for fully unsteady rotor aerodynamics, attention was directed to steady state aerodynamics, which was achieved by replacing the rotor with the actuator disk approximation. The use of an actuator disk analysis introduced a mathematical singularity into the formulation; this problem was studied and resolved. The pressure distribution, lift, and pitching moment were obtained for an XV-15 wing-fuselage-tail rotor configuration at various flight conditions. For the flight configurations explored, the effects of the rotor wake interference on the XV-15 tilt rotor aircraft yielded a reduction in the total lift and an increase in the nose-down pitching moment. This method provides an analytical capability that is simple to apply and can be used to investigate fuselage-tail rotor wake interference as well as to explore other rotor design problem areas.

Soohoo, P.↗

NASA NTRS1978

Determination of optimal control using imbedding of the terminal conditions

The utility of a method to solve optimal control problems is discussed with emphasis placed on the solutions of singular optimal control problems. The method involves imbedding the optimization problem of interest in a family of optimization problems which are parameterized by their terminal conditions. The solution to the optimization problem is obtained by collapsing the terminal conditions of the family of problems onto those of the original problem, while appropriately modifying the control function to account for the changing terminal conditions. The utility of this method is illustrated by obtaining the solution to an aerial attack problem where the attacking vehicle must maneuver subject to control limitations so as to place the enemy in a certain relative position for launching a missile in the shortest possible time.

Montgomery, R. C.↗

NASA NTRS1977

Optimal solar sail planetocentric trajectories

The analysis of solar sail planetocentric optimal trajectory problem is described. A computer program was produced to calculate optimal trajectories for a limited performance analysis. A square sail model is included and some consideration is given to a heliogyro sail model. Orbit to a subescape point and orbit to orbit transfer are considered. Trajectories about the four inner planets can be calculated and shadowing, oblateness, and solar motion may be included. Equinoctial orbital elements are used to avoid the classical singularities, and the method of averaging is applied to increase computational speed. Solution of the two-point boundary value problem which arises from the application of optimization theory is accomplished with a Newton procedure. Time optimal trajectories are emphasized, but a penalty function has been considered to prevent trajectories which intersect a planet's surface.

Sackett, L. L.↗

NASA NTRS1978

The problem of an inclined crack in an orthotropic strip

The elastostatic problem for an infinite orthotropic strip containing crack was considered. It was assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack was located along an axis of orthotropy, hence, at an arbitrary angle with respect to the sides of the strip. The general problem was formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes 1 and 2 stress intensity factors were calculated for the strip having an internal or an edge crack with various lengths and angular orientations.

Delale, F.↗