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At least 1,243 records · Page 69

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NASA NTRS1979

Reduction of computer usage costs in predicting unsteady aerodynamic loadings caused by control surface motions: Analysis and results

Results of theoretical and numerical investigations conducted to develop economical computing procedures were applied to an existing computer program that predicts unsteady aerodynamic loadings caused by leading and trailing edge control surface motions in subsonic compressible flow. Large reductions in computing costs were achieved by removing the spanwise singularity of the downwash integrand and evaluating its effect separately in closed form. Additional reductions were obtained by modifying the incremental pressure term that account for downwash singularities at control surface edges. Accuracy of theoretical predictions of unsteady loading at high reduced frequencies was increased by applying new pressure expressions that exactly satisified the high frequency boundary conditions of an oscillating control surface. Comparative computer result indicated that the revised procedures provide more accurate predictions of unsteady loadings as well as providing reduction of 50 to 80 percent in computer usage costs.

Rowe, W. S.↗

NASA NTRS1979

Nonlinear effects on sound propagation through high subsonic Mach number flows in variable area ducts

A nonlinear theory for sound propagation in variable area ducts carrying a nearly sonic flow is presented. Linear acoustic theory is shown to be singular and the detailed nature of the singularity is used to develop the correct nonlinear theory. The theory is based on a quasi-one dimensional model. It is derived by the method of matched asymptotic expansions. In a nearly chocked flow, the theory indicates the following processes to be acting: a transonic trapping of upstream propagating sound causing an intensification of this sound in the throat region of the duct; generation of superharmonics and an acoustic streaming effect; development of shocks in the acoustic quantities near the throat. Several specific problems are solved analytically and numerical parameter studies are carried out. Results indicate that appreciable acoustic power is shifted to higher harmonics as shocked conditions are approached. The effect of the throat Mach number on the attenuation of upstream propagating sound excited by a fixed source is also determined.

Callegari, A. J.↗

NASA NTRS1979

Nonlinear wave choked inlets

The quasi-one dimensional flow program was modified in two ways. The Runge-Kutta subroutine was replaced with a subroutine which used a modified divided difference form of the Adams Pece method and the matrix inversion routine was replaced with a pseudo inverse routine. Calculations were run using both the original and modified programs. Comparison of the calculations showed that the original Runge-Kutta routine could not detect singularity near the throat and was integrating across it. The modified version was able to detect the singularity and therefore gave more valid calculations.

Source record↗

NASA NTRS1979

Flow patterns near a conical sonic line

A study is made in the physical plane of the flow properties near a conical cross flow sonic line. The shapes of the Mach lines at regular and singular sonic points are presented. Through a study of the jump conditions at a singular sonic point, the possibility of a double sonic line is discussed. The properties of bubbles of supersonic cross flow are examined. Numerical results are presented to support some of the theoretical observations.

Salas, M. D.↗

NASA NTRS1979

An elastic-plastic analysis of fatigue crack closure in modes I and II

In this paper, an efficient elastic-plastic finite element procedure to analyze crack-closure and, its effects on fatigue crack growth under general spectrum loading, is presented. A hybrid-displacement finite element procedure is used to properly treat the stress and strain singularities near the crack-tip; and crack-growth under cyclic loading is simulated by the translation of certain 'core' elements, near the crack-tip, in which proper stress and strain singularities were embedded. Both pure mode I and mode II types of cyclic loading are considered. In the mode I case, four types of cyclic loading, viz., constant amplitude block loading, high-to-low block loading, low-to-high block, and a single overload in an otherwise constant amplitude block loading are considered; whereas in mode II, only a constant amplitude block loading is considered. Detailed results are presented for the crack-closure and opening-stresses, crack-surface deformation profiles, etc., in each case. Certain observations, based on the present numerical results, concerning various factors that cause crack growth acceleration or retardation under general spectrum loading, are presented and discussed.

Nakagaki, M.↗

NASA NTRS1979

A computational fluid dynamic technique valid at the centerline for non-axisymmetric problems in cylindrical coordinates

A technique is described for the numerical solution of non-axisymmetric flow problems posed in cylindrical coordinates when the z-axis is included in the flowfield. The highlight of the technique is the manner in which the singularities at the centerline are handled. Specifically, the governing flowfield equations at r = 0 are put in a special form by applying L'Hospital's Rule. The required radial derivatives are evaluated using a one-sided, second-order accurate, first-difference. This leads to a smooth, convergent calculation of the flowfield at the centerline. This appears to be the first generally applicable numerical method for avoiding coordinate system singularities in the context of a finite-difference scheme, and could have application to many nonaxisymmetric flows. The technique is illustrated by specific results for the time-dependent flowfield inside an internal combustion engine.

Griffin, M. D.↗

NASA NTRS1979

Robustness of multiloop linear feedback systems

This paper presents a new approach to the frequency-domain analysis of multiloop linear feedback systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness.

Doyle, J. C.↗

NASA NTRS1979

Integral equations for flows in wind tunnels

This paper surveys recent work on the use of integral equations for the calculation of wind tunnel interference. Due to the large number of possible physical situations, the discussion is limited to two-dimensional subsonic and transonic flows. In the subsonic case, the governing boundary value problems are shown to reduce to a class of Cauchy singular equations generalizing the classical airfoil equation. The theory and numerical solution are developed in some detail. For transonic flows nonlinear singular equations result, and a brief discussion of the work of Kraft and Kraft and Lo on their numerical solution is given. Some typical numerical results are presented and directions for future research are indicated.

Fromme, J. A.↗

NASA NTRS1980

Stresses in a three-dimensional unidirectional composite containing broken fibers

An approximate solution is developed for the determination of the interlaminar normal and shear stresses in the vicinity of a crack in a three dimensional composite containing unidirectional linearly elastic fibers in an infinite linearly elastic matrix. In order to reduce the complexity of the formulation, certain assumptions are made as to the physically significant stresses to be retained. These simplifications reduce the partial differential equations of elasticity to differential-difference equations which are tractable using Fourier transform techniques. This 'material modeling' approach is in contrast with solutions developed by considering each lamina as a homogeneous, orthotropic layer. The resulting solution does not contain the classical singular stress field for the fibers and the influence of broken fibers on unbroken fibers is felt by a change in stress concentration factors. The matrix stresses however, are unbounded as the fiber spacing vanishes and an equivalent fiber-matrix geometry is proposed which gives the correct singular behavior. The numerical solution is considered in detail and several specific examples are presented. The potential for damaged or debonded zones to be generated by an embedded crack is discussed, and stress concentration factors for fibers near the crack are given. Detailed comparisons are made between the present solution, the analogous two-dimensional problem, and corresponding shear-lag models.

Goree, J. G.↗

NASA NTRS1980

A magnetohydrodynamic model for corotating interplanetary structures

A model is developed which treats interplanetary structures as a small-scale incompressible Alfvenic fluctuation superposed on a large-scale background flow, and uses the complete magnetohydrodynamic equations and the full energy equation to describe the interplanetary structures. For steady-state corotating structures the model assumes the background flow to be field aligned, and the nonlinear system is treated as being composed of two subsets: one dealing with the expansion of the solar wind in stream tubes, the other with the interaction between neighboring stream tubes. The expansion subset has a singularity at Parker's critical radius, and the interaction subset has a singularity at the Alfvenic point. Concerning the region where the flow velocity is super-Alfvenic, the characteristic equation is derived, and a general method of numerical solution for the three-dimensional problems based on the characteristics theory is discussed. In addition, a viscous WKB solution of the microscale system is presented.

Whang, Y. C.↗

NASA NTRS1981

Computation of unsteady turbulent boundary layers with flow reversal and evaluation of two separate turbulence models

A procedure which solves the governing boundary layer equations within Keller's box method was developed for calculating unsteady laminar flows with flow reversal. This method is extended to turbulent boundary layers with flow reversal. Test cases are used to investigate the proposition that unsteady turbulent boundary layers also remain free of singularities. Turbulent flow calculations are performed. The governing equations for both models are solved. As in laminar flows, the unsteady turbulent boundary layers are free from singularities, but there is a clear indication of rapid thickening of the boundary layer with increasing flow reversal. Predictions of both turbulence models are the same for all practical purposes.

Cebeci, T.↗

NASA NTRS1981

Topology of three-dimensional separated flows

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Tobak, M.↗

NASA NTRS1980

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Atluri, S. N.↗

NASA NTRS1981

Optimal trajectories in atmospheric flight

Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.

Vinh, N. X.↗

NASA NTRS1982

Subsonic panel method for the efficient analysis of multiple geometry perturbations

An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

Bristow, D. R.↗

NASA NTRS1981

Boundary layer thermal stresses in angle-ply composite laminates, part 1

Thermal boundary-layer stresses (near free edges) and displacements were determined by a an eigenfunction expansion technique and the establishment of an appropriate particular solution. Current solutions in the region away from the singular domain (free edge) are found to be excellent agreement with existing approximate numerical results. As the edge is approached, the singular term controls the near field behavior of the boundary layer. Results are presented for cases of various angle-ply graphite/epoxy laminates with (theta/-theta/theta/theta) configurations. These results show high interlaminar (through-the-thickness) stresses. Thermal boundary-layer thicknesses of different composite systems are determined by examining the strain energy density distribution in composites. It is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers. The interlaminar thermal stresses are compressive with increasing temperature. The corresponding residual stresses are tensile and may enhance interply delaminations.

Wang, S. S.↗

NASA NTRS1982

Creep crack-growth: A new path-independent integral (T sub c), and computational studies

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Stonesifer, R. B.↗

NASA NTRS1982

Solution of second-order linear system by matched asymptotic expansions

Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed.

Ardema, M. D.↗