SEARCH · Engineering Papers

Results for “Singularity”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47

All sources NASA NTRS DOE OSTI

NASA NTRS1973

Analysis of stratified and closely spaced jets exhausting into a crossflow

Procedures have been developed for determining the flow field about jets with velocity stratification exhausting into a crossflow. Jets with three different types of exit velocity stratification have been considered: (1) jets with a relatively high velocity core; (2) jets with a relatively low velocity core; and (3) jets originating from a vaned nozzle. The procedure developed for a jet originating from a high velocity core nozzle is to construct an equivalent nozzle having the same mass flow and thrust but having a uniform exit velocity profile. Calculations of the jet centerline and induced surface static pressures have been shown to be in good agreement with test data for a high velocity core nozzle. The equivalent ideal nozzle has also been shown to be a good representation for jets with a relatively low velocity core and for jets originating from a vaned nozzle in evaluating jet-induced flow fields. For the singular case of a low velocity core nozzle, namely a nozzle with a dead air core, and for the vaned nozzle, an alternative procedure has been developed. The internal mixing which takes place in the jet core has been properly accounted for in the equations of motion governing the jet development. Calculations of jet centerlines and induced surface static pressures show good agreement with test data these nozzles.

Ziegler, H.↗

NASA NTRS1973

Cracked finite elements proposed for NASTRAN

The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.

Aberson, J. A.↗

NASA NTRS1973

Analysis of the Flow About Delta Wings with Leading Edge Separation at Supersonic Speeds

A research program was conducted to develop an improved theoretical flow model for the flow about sharp edge delta wings with leading-edge separation at supersonic speeds. The flow model incorporates a representation of the secondary separation region which occurs just inboard of the leading edge on such wings and is based on a slender-wing theory whereby the full three-dimensional problem is reduced to a quasi two-dimensional problem in the cross-flow plane. The secondary separation region was modeled by a surface distribution of singularities or a linearized type of cavity representation. The primary vortex and separation were modeled by a concentrated vortex and cut in the cross-flow potential which represents its feeding sheet. The cross-flow solutions for the cavity model were obtained, but these solutions have physical significance only in a very restricted range of angle of attack. The reasons for the failure of the flow model are discussed. The analysis is presented so that other interested researchers may critically review the work.

Nenni, J. P.↗

NASA NTRS1974

Relevance of ERTS-1 to the State of Ohio

The author has identified the following significant results. During the first year of project effort the ability of ERTS-1 imagery to be used for mapping and inventorying strip-mined areas in south eastern Ohio, the potential of using ERTS-1 imagery in water quality and coastal zone management in the Lake Erie region, and the extent that ERTS-1 imagery could contribute to localized (metropolitan/urban), multicounty, and overall state land use needs were experimentally demonstrated and reported as significant project results. Significant research accomplishments were achieved in the technological development of manual and computerized methods to extract multi-feature information as well as singular feature information from ERTS-1 data as is exemplified by the forestry transparency overlay. Fabrication of an image transfer device to superimpose ERTS-1 data onto existing maps and other data sources was also a significant analytical accomplishment.

Sweet, D. C.↗

NASA NTRS1974

An Analytical Investigation of Wing-Jet Interaction

The aerodynamic interaction between the wing and an inviscid jet with Mach number nonuniformity is formulated by using a two-vortex-sheet model for the jet. One of the vortex sheets accounts for the induced jet flow and the other the induced outer flow. No additional source distribution is needed for the jet at an angle of attack. The above problem is solved by satisfying the jet and wing tangency and the jet pressure-continuity conditions and using a quasi vortex lattice method for computing the induced flow field. The latter method is derived through theoretical consideration by properly accounting for singularities present in the equations and possesses the same simplicity and generality as the conventional vortex lattice method but has a better rate of numerical convergence. The resulting system of algebraic equations is solved by Purcell's vector method. The numerical formulation is first applied to the wing-slipstream interaction problem. Results for one centered-jet configuration are compared with those predicted by some existing theories.

Lan, E. C.↗

NASA NTRS1974

An extension of the Laplace transform to Schwartz distributions

A characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the characterization as the definition of the Laplace transform. The definition uses sequences of linear transformations on the space of distributions which extends the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.

Price, D. R.↗

NASA NTRS1974

Application of ultrasonic signature analysis for fatigue detection in complex structures

Ultrasonic signature analysis shows promise of being a singularly well-suited method for detecting fatigue in structures as complex as aircraft. The method employs instrumentation centered about a Fourier analyzer system, which features analog-to-digital conversion, digital data processing, and digital display of cross-correlation functions and cross-spectra. These features are essential to the analysis of ultrasonic signatures according to the procedure described here. In order to establish the feasibility of the method, the initial experiments were confined to simple plates with simulated and fatigue-induced defects respectively. In the first test the signature proved sensitive to the size of a small hole drilled into the plate. In the second test, performed on a series of fatigue-loaded plates, the signature proved capable of indicating both the initial appearance and subsequent growth of a fatigue crack. In view of these encouraging results it is concluded that the method has reached a sufficiently advanced stage of development to warrant application to small-scale structures or even actual aircraft.

Zuckerwar, A. J.↗

NASA NTRS1974

ASRDI oxygen technology survey, Volume 7: Characteristics of metals that influence system safety

A literature survey and analysis of the material and process factors affecting the safety of metals in oxygen systems is presented. In addition, the practices of those who specify, build, or use oxygen systems relative to the previous is summarized. Alloys based on iron, copper, nickel, and aluminum were investigated representing the bulk of metals found in oxygen systems. Safety-related characteristics of other miscellaneous metals are summarized. It was found that factors affecting the safety of metals in oxygen systems exit in all phases of the evolutionary process, from smelting and mill techniques through end-production fabrication. The safety of a given metal in an oxygen system was determined to be influenced by the particular service requirement. The metal characteristics should favorably influence fulfillment of these requirements. Thus, no singular metal or alloy could be classified as safest for all types of oxygen service.

Pelouch, J. J., Jr.↗

NASA NTRS1973

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Pacella, A. H.↗

NASA NTRS1973

Transverse cracks in a strip with reinforced surfaces

The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometrics and degrees of surface reinforcement.

Krenk, S.↗

NASA NTRS1974

A users manual for a computer program which calculates time optical geocentric transfers using solar or nuclear electric and high thrust propulsion

This manual is a guide for using a computer program which calculates time optimal trajectories for high-and low-thrust geocentric transfers. Either SEP or NEP may be assumed and a one or two impulse, fixed total delta V, initial high thrust phase may be included. Also a single impulse of specified delta V may be included after the low thrust state. The low thrust phase utilizes equinoctial orbital elements to avoid the classical singularities and Kryloff-Boguliuboff averaging to help insure more rapid computation time. The program is written in FORTRAN 4 in double precision for use on an IBM 360 computer. The manual includes a description of the problem treated, input/output information, examples of runs, and source code listings.

Sackett, L. L.↗

NASA NTRS1974

Analysis of wing-body interaction flutter for a preliminary space shuttle design

Subsonic flutter analyses for a preliminary space shuttle design were performed to determine the effect of wing-body aerodynamic interaction on the vehicle flutter speed. It was found that the proximity of the large bodies of the shuttle to the wing reduces critical flutter speed by 11%. Aerodynamic reflection off the bodies is the dominant interaction effect while aerodynamic forces caused by body motion are of secondary importance in most cases. The analyses employed a doublet-lattice representation of the space shuttle, where in the wing and body surfaces were modeled by a lattice of nonplanar lifting surface elements. Axial singularities were introduced to account for body incidence, volume, and camber (slender body) effects. A series of studies on the placement and number of these elements was performed to ensure convergence of the results.

Chipman, R. R.↗

NASA NTRS1974

Vehicle control for fuel optimization

The problem of predicting the minimum fuel trajectory for a six degree of freedom vehicle which has a motion characterized by the first order differential equations of translational and rotational dynamics is considered. The thrust direction and center of gravity of the vehicle are assumed to be fixed with respect to the vehicle. Thrust magnitude and the control moment are used as control variables and appear linearly in the equation of motion. Pontryagin's Maximum Principle is used to solve the variational problem. With this formulation, the extremal controls are bang-bang with the exception of the singular case.

Dannenberg, K. D.↗

NASA NTRS1973

Optimal low thrust geocentric transfer

A computer code which will rapidly calculate time-optimal low thrust transfers is being developed as a mission analysis tool. The final program will apply to NEP or SEP missions and will include a variety of environmental effects. The current program assumes constant acceleration. The oblateness effect and shadowing may be included. Detailed state and costate equations are given for the thrust effect, oblateness effect, and shadowing. A simple but adequate model yields analytical formulas for power degradation due to the Van Allen radiation belts for SEP missions. The program avoids the classical singularities by the use of equinoctial orbital elements. Kryloff-Bogoliuboff averaging is used to facilitate rapid calculation. Results for selected cases using the current program are given.

Edelbaum, T. N.↗

NASA NTRS1973

Plastic intensity factors for cracked plates subjected to biaxial loading

An elastic-plastic analysis is performed for an infinite plate under plane stress conditions which contains a finite line crack and is subjected to biaxial loading. In the large scale yielding range, the amplitude of the dominant singularity at the crack tip, the plastic stress (or strain) intensity factor, is found to depend on the magnitude of loading parallel to the crack direction. The predicted value for the fracture initiation stress which is based on a plastic intensity factor fracture criterion, increases under lateral, tensile loading. Compressive loading parallel to the crack has the opposite effect on the fracture initiation stress.

Hilton, P. D.↗

NASA NTRS1973

Thermoelastic flutter models for elements of flexible satellites

Models of thermally induced flutter of the flexible elements of a satellite, such as beams, circular plates, and cylindrical shells have been obtained. These models form the necessary blocks for analyzing the motion of satellites. The heat input is considered to be caused by solar radiations. The partial differential equations for all the elements of the satellite are linear in the space dependent variables and nonlinear in the time-dependent variables. These equations are coupled through the motion of the center of mass of the satellite. Galerkin's method has been used to remove the space-dependence of these equations. In the succeeding paper, a further reduction of these equations is made into singular perturbation equations, which are amenable to solution for complex problems of extremely large number of degrees of freedom.

Huang, T. C.↗

NASA NTRS1974

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin Transforms the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given in the paper include the stress intensity factors, the strain energy release rates, and the probable clevage angles giving the direction of crack propagation.

Erdogan, F.↗

NASA NTRS1974

Fast direct numerical solution of the nonhomogeneous Cauchy-Riemann equations

A fast direct (noniterative) 'Cauchy-Riemann Solver' is developed for solving the finite-difference equations representing systems of first-order elliptic partial differential equations in the form of the nonhomogeneous Cauchy-Riemann equations. The method is second-order accurate and requires approximately the same computer time as a fast cyclic-reduction Poisson solver. The accuracy and efficiency of the direct solver are demonstrated in an application to solving an example problem in aerodynamics: subsonic inviscid flow over a biconvex airfoil. The analytical small-perturbation solution contains singularities, which are captured well by the computational technique. The algorithm is expected to be useful in nonlinear subsonic and transonic aerodynamics.

Lomax, H.↗