Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Approximate boundary”

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.

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

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Direct numerical solution of the transonic perturbation integral equation for lifting and nonlifting airfoils

The linear transonic perturbation integral equation previously derived for nonlifting airfoils is formulated for lifting cases. In order to treat shock wave motions, a strained coordinate system is used in which the shock location is invariant. The tangency boundary conditions are either formulated using the thin airfoil approximation or by using the analytic continuation concept. A direct numerical solution to this equation is derived in contrast to the iterative scheme initially used, and results of both lifting and nonlifting examples indicate that the method is satisfactory.

Nixon, D.↗
NASA NTRS1979

Decay of the zincate concentration gradient at an alkaline zinc cathode after charging

The transport of the zincate ion to the alkaline zinc cathode was studied by observing the decay of the zincate concentration gradient at a horizontal zinc cathode after charging. This decay was found to approximate first order kinetics as expected from a proposed boundary layer model. The concentrations were calculated from polarization voltages. The decay half life was shown to be a linear function of the thickness of porous zinc deposit on the cathode indicating a very rapid transport of zincate through porous zinc metal. The rapid transport is attributed to an electrochemical mechanism. From the linear dependence of the half life on the thickness the boundary layer thickness was found to be about 0.010 cm when the cathode was at the bottom of the cell. No significant dependence of the boundary layer thickness on the viscosity of electrolyte was observed. The data also indicated a relatively sharp transition between the diffusion and convection transport regions. When the cathode was at the top of the cell, the boundary layer thickness was found to be roughly 0.080 cm. The diffusion of zincate ion through asbestos submerged in alkaline electrolyte was shown to be comparable with that predicted from the bulk diffusion coefficient of the zincate ion in alkali.

Kautz, H. E.↗
NASA NTRS1979

The shape and location of the sector boundary surface in the inner solar system

Simultaneous observations by Helios-1 and Helios-2 over four solar rotations were used to determine the latitudinal dependence of the polarity of the interplanetary magnetic field within plus or minus 7.23 deg of the solar equator and within 1 AU. The longitudinal and latitudinal positions of the sector boundary crossing are consistent with a warped sector boundary which extended from the sun to 1 AU and was inclined approximately 10 deg with respect to the heliographic equator. This is consistent with simultaneous Pioneer 11 observations, which showed unipolar fields at latitude approximately 16 deg at heliocentric distances greater than 3.5 AU. Two sectors were observed at southern latitudes; however, four sectors were observed at northern latitudes on two rotations, indicating a distortion from planarity of the sectory boundary surface.

Villante, U.↗
NASA NTRS1979

Decay of the zincate concentration gradient at an alkaline zinc cathode after charging

The study was carried out by observing the decay of the zincate concentration gradient at a horizontal zinc cathode after charging. This decay was found to approximate first order kinetics as expected from a proposed boundary layer model. The decay half life was shown to be a linear function of the thickness of porous zinc deposit on the cathode indicating a very rapid transport of zincate through porous zinc metal. The rapid transport is attributed to an electrochemical mechanism. The data also indicated a relatively sharp transition between the diffusion and convection transport regions. The diffusion of zincate ion through asbestos submerged in alkaline electrolyte was shown to be comparable with that predicted from the bulk diffusion coefficient of the zincate ion in alkali.

Kautz, H. E.↗
NASA NTRS1981

Measurements of laminar and turbulent flow in a curved duct with thin inlet boundary layers

Laser Doppler velocimetry was used to measure the laminar and turbulent flow in a 90 deg square bend of strong curvature. The boundary layers at the inlet to the bend were approximately 25 percent and 15 percent of the hydraulic diameter for the laminar and turbulent flows, respectively. The development of the pressure driven secondary motion is more rapid for laminar flow: the maximum cross stream component measured was 60 percent of the bulk velocity in contrast to 40 percent for turbulent flow. The streamwise isotachs show that, for laminar flow, large velocities are found progressively nearer to the outer radius of the bend and along the sidewalls. For turbulent flow, the isotachs move towards the inner radius until about 60 deg around the bend where strong secondary motion results in a similar redistribution. Turbulence level and shear stress measurements are also presented.

Taylor, A. M. K. P.↗
NASA NTRS1983

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Baker, A. J.↗
NASA NTRS1983

Numerical solution of three-dimensional unsteady transonic flow over wings including inviscid/viscous interactions

A numerical procedure is presented for computing the unsteady transonic flow field about three dimensional swept wings undergoing general time dependent motion. The outer inviscid portion of the flow is assumed to be governed by the modified unsteady transonic small disturbance potential equation which is integrated in the time domain by means of an efficient alternating direction implicit approximate factorization algorithm. Gross dominant effects of the shock boundary layer interaction are accounted for by a simple empirically defined model. Viscous flow regions adjacent to the wing surface and in the trailing wake are described by a set of integral equations appropriate for compressible turbulent shear layers. The two dimensional boundary layer equations are applied quasi-statically stripwise across the span. Coupling with the outer inviscid flow is implemented through use of the displacement thickness concept within the limitations of small disturbance theory. Validity of the assumptions underlying the method is established by comparison with experimental data for the flow about a high aspect ratio transport wing having an advanced airfoil section.

Rizzetta, D. P.↗
NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.↗
NASA NTRS1984

Feedback in separated flows over symmetric airfoils

For a flow over an airfoil with laminar separation, a feedback cycle may exist whereby a Kelvin-Helmholtz instability wave emanating from the separation point on the airfoil surface grows along the shear layer and is diffracted as it interacts with the sharp trailing edge of the airfoil, causing acoustic radiation which, in turn, propagates upstream and regenerates the initial instability wave. The analysis is restricted to the high frequency limit. Solutions to the boundary-value problem are obtained using the slowly varying approximation and the method of matched asymptotic expansions. Resonant solutions exist for certain discrete values of the Reynolds and Strouhal numbers. The results are discussed and compared with available data.

Atassi, H. M.↗
NASA NTRS1984

Feedback in separated flows over symmetric airfoils

For a flow over an airfoil with laminar separation, a feedback cycle may exist whereby a Kelvin-Helmholtz instability wave emanating from the separation point on the airfoil surface grows along the shear layer and is diffracted as it interacts with the sharp trailing edge of the airfoil, causing acoustic radiation which , in turn, propagates upstream and regenerates the initial instability wave. The analysis is restricted to the high frequency limit. Solutions to the boundary-value problem are obtained using the slowly varying approximation and the method of matched asymptotic expansions. Resonant solutions exist for certain discrete values of the Reynolds and Strouhal numbers. The results are discussed and compared with available data.

Atassi, H. M.↗
NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Raju, I. S.↗
NASA NTRS1987

The time-varying geomagnetic field

Information (obtained from Magsat and other sources) published by the U.S. authors between 1983 and 1986 on the large-scale geomagnetic field of deep internal origin and its secular variation (SV) is reviewed. Results on the main field modeling, including reference fields, and on the separaton of core and crustal fields are discussed together with the advances made in geomagnetic field theory and applications of novel methods. Consideration is also given to global SV, short-term global SV, and regional CV analyses; nonsecular impulses, featuring the sudden geomagnetic jerk of 1969; and the frozen-flux core approximation, including downward continuation to the core-mantle boundary constraints, westward drift, and estimates of the fluid velocity at the top of the core.

Voorhies, Coerte V.↗
NASA NTRS1990

A laser Doppler velocimeter approach for near-wall three-dimensional turbulence measurements

A near-wall laser Doppler velocimeter approach is described that relies on a beam-turning probe which makes possible the direct measurement of the crossflow velocity at a grazing incident and the placement of optical components close to the flow region of interest regardless of test facility size. Other important elements of the approach are the use of digital frequency processing, an optically smooth measurement surface, and observation of the sensing volume at 90 degrees. The combination was found to dramatically reduce noise-in-signal effects caused by surface light scattering. Turbulent boundary-layer data to within 20 microns (y(sup+) approximately equal to 1) of the surface are presented which illustrate the potential of the approach.

Johnson, D. A.↗
NASA NTRS1990

Keyhole and weld shapes for plasma arc welding under normal and zero gravity

A first order study of the interfacial (keyhole) shape between a penetrating argon plasma arc jet and a stationary liquid metal weld pool is presented. The interface is determined using the Young-Laplace equation by assuming that the plasma jet behaves as a one-dimensional ideal gas flow and by neglecting flow within the weld pool. The solution for the keyhole shape allows an approximate determination of the liquid-solid metal phase boundary location based on the assumption that the liquid melt is a stagnant thermal boundary layer. Parametric studies examine the effect of plasma mass flow rate, initial plasma enthalpy, liquid metal surface tension, and jet shear on weldment shape under both normal and zero gravity. Among the more important findings of this study is that keyhole and weld geometries are minimally affected by gravity, suggesting that data gathered under gravity can be used in planning in-space welding.

Keanini, R. G.↗
NASA NTRS1990

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Schwenke, David W.↗
NASA NTRS1991

A geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading

An analytical study of interlaminar stresses in unsymmetrically laminated plates is presented. The study examines the linear elastic, large deflection response of square laminated composite plates subjected to uniform thermal loading. Both cross-ply and angle-ply, symmetric and unsymmetric, laminates are examined to evaluate the effects of mismatch between adjacent layers in elastic constants and coefficients of thermal expansion. A geometrically nonlinear kinematic description is used to predict the large out-of-plane (transverse) deflections. The nonlinear, three-dimensional boundary value problems are formulated from elasticity theory and approximate solutions are determined using the finite element method. A global/local analysis procedure is used to obtain improved free edge stress predictions. For the laminates and loading conditions considered, the results indicate that the out-of-plane deflections of the unsymmetric laminates reduce interlaminar shear stresses. These deflections also reduce interlaminar normal stresses in some laminates and increase these stresses for others. The results indicate that as the out-of-plane deflections become large, the differences in interlaminar stress predictions between linear and nonlinear theory can become quite large.

Norwood, D. S.↗
NASA NTRS1993

Opaque-rich lithology in the Divnoe achondrite: Petrology and origin

An opaque-rich lithology (ORL) makes up to approximately 9 vol. percent of the Divnoe achondrite. It is characterized by enrichment of troilite and pyroxene, compared to the bulk Divnoe, and by the presence of tiny remnants of olivine in low-CA pyroxene and low minor element concentrations in pyroxene. The ORL was formed by local reaction between gaseous sulfur and olivine in the Divnoe. The Divnoe meteorite is an olivine-rich achondrite with subchondritic chemistry and mineralogy. It has a granoblastic coarse-grained olivine groundmass (CGL: coarse-grained lithology) with relatively large (2-10 mm) poikilitic patches (PP) of pyroxene and, rarely, plagioclase. The groundmass also contains an opaque-rich fine-grained lithology (ORL) which comprises approximately 9 vol. percent of the meteorite, displays reaction boundaries with the groundmass, and differs in mineral chemistry from it. Numerous micron- to mm-thick veins of troilite and, rarely, metal cross all the lithologies found in the meteorite. The Divnoe itself appears to represent a sample of an igneous source region.

Petaev, M. I.↗
NASA NTRS1994

The cosmic-ray oxygen and helium spectra measured at Pioneer 10 over the time of the 1987 modulation minimum, and implications for the He/O source ratio

At the time of the recent sunspot minimum in 1987 when the cosmic-ray intensity within the heliosphere was a maximum, Pioneer 10(P10) was at a radial distance of approximately 42 AU. The solar modulation parameter Phi is estimated to have reached a minimum value of approximately 150 MV at P10 at that time, as compared with a minimum value of approximately 500 MV at the Earth. Thus P10 is in a sense effectively approximately 0.7 of the way to the heliospheric modulation boundary whatever its physical distance in astronomical units. Accordingly, the spectra of the various cosmic-ray species are much nearer to the interstellar spectra than any spectra ever before measured. We have therefore examined the penetrating high energy telescope (HET) data from P10 for a 2.5 yr period around 1987 to obtain a statistically accurate spectrum of oxygen nuclei over the energy range from 90 to 450 MeV/nucleon for comparison with a 'reference' interstellar spectrum. A similar spectrum is derived for helium nuclei. These two spectra and their ratios constitute important 'reference' spectra for all of the heavier cosmic-ray nuclei. The cosmic-ray source ratio required to explain the observed He/O ratio, when a full Galactic propagation calculation is carried out including secondary He-4 and He-3 production, is 15.9. The implications of this very low ratio and a comparison with the He/O ratio measured at high energies are discussed.

Webber, W. R.↗