Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “gradient methods”

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 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Semidiscrete Galerkin modelling of compressible viscous flow past a circular cone at incidence

A numerical study of the laminar and compressible boundary layer, about a circular cone in a supersonic free stream, is presented. It is thought that if accurate and efficient numerical schemes can be produced to solve the boundary layer equations, they can be joined to numerical codes that solve the inviscid outer flow. The combination of these numerical codes is competitive with the accurate, but computationally expensive, Navier-Stokes schemes. The primary goal is to develop a finite element method for the calculation of 3-D compressible laminar boundary layer about a yawed cone. The proposed method can, in principle, be extended to apply to the 3-D boundary layer of pointed bodies of arbitrary cross section. The 3-D boundary layer equations governing supersonic free stream flow about a cone are examined. The 3-D partial differential equations are reduced to 2-D integral equations by applying the Howarth, Mangler, Crocco transformations, a linear relation between viscosity, and a Blasius-type of similarity variable. This is equivalent to a Dorodnitsyn-type formulation. The reduced equations are independent of density and curvature effects, and resemble the weak form of the 2-D incompressible boundary layer equations in Cartesian coordinates. In addition the coordinate normal to the wall has been stretched, which reduces the gradients across the layer and provides high resolution near the surface. Utilizing the parabolic nature of the boundary layer equations, a finite element method is applied to the Dorodnitsyn formulation. The formulation is presented in a Petrov-Galerkin finite element form and discretized across the layer using linear interpolation functions. The finite element discretization yields a system of ordinary differential equations in the circumferential direction. The circumferential derivatives are solved by an implicit and noniterative finite difference marching scheme. Solutions are presented for a 15 deg half angle cone at angles of attack of 5 and 10 deg. The numerical solutions assume a laminar boundary layer with free stream Mach number of 7. Results include circumferential distribution of skin friction and surface heat transfer, and cross flow velocity distributions across the layer.

Meade, Andrew James, Jr.↗
NASA NTRS1992

Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

Soh, Woo Y.↗
NASA NTRS1986

Numerical analysis of some supersonic viscous flows related to inlet and nozzle systems

A numerical method originally developed for three-dimensional supersonic inlet flow calculations is extended and applied to the study of two-dimensional and three-dimensional flows associated with arbitrary propulsion systems. The method is based on the forward spatial marching solution of a reduced form of the three-dimensional steady Navier-Stokes equations in which streamwise pressure gradients are retained in both the subsonic and supersonic regions. The present paper briefly describes the analysis and then shows three applications. In the first application, a wall transpiration study has been performed for the two-dimensional shock wave/turbulent boundary layer interaction flow field with application to an inlet configuration. The second application treats a rectangular high speed inlet with a swept sideplate including the effects of sideplate spillage. Finally, the method is utilized to analyze the interaction of an under-expanded supersonic jet with an ambient flow. Computed results are examined and compared with available experimental measurements. It is demonstrated that the present numerical method is capable of numerically simulating complex two- and three-dimensional flows relevant to hypersonic propulsion systems in a manner which both shows good agreement with data when such data is available, and which shows the complex flow features in the absence of data.

Kim, Y.-N.↗
NASA NTRS2018

Laser Ablation Surface Treatment of Structural Aerospace Composites and Metal Alloys for Adhesive Bonding

NASA Langley Research Center (LaRC) has been involved over the past decade in the development of laser ablation as a method to surface treat aerospace structural fiber reinforced composites (CFRPs) and metal alloys. [1- 18] Laser surface treatment has been shown to be a rapid, high precision, and reproducible method for surface treatment of these materials, and is amenable to automation. The laser ablation process removes surface contamination such as silicones, creates surface roughness, and chemically activates a surface for bonding. The degree of ablation is controllable by adjusting laser parameters. In the case of CFRPs, ablation can be performed without damage to any underlying carbon fibers. In the case of metal alloys, ablation is possible without surface embrittlement, heat damage or creation of undesirable grain structures or morphologies. The optimum laser treatment conditions are substrate dependent and generally are influenced by laser wavelength and pulse duration (typically fixed for a laser system), and laser power. In the case of metal alloys such as Ti-6Al-4V, the laser ablation process eliminates the need for several steps of the conventional processes, including hydrofluoric (HF) acid and caustic treatment. These steps are often conducted in dip tanks and require costly facilities and environmentally unfriendly liquids. In addition, the laser can create nano-porosity on the Ti-6Al-4V alloy surface allowing for sol-gel penetration and thereby creating a gradient interface with improved temperature and mechanical performance. NASA LaRC has also been involved with the development of in-line characterization methods compatible with the laser treatment process to rapidly determine the presence of key contaminates such as silicones that, even at very low concentrations, are a threat to adhesive bonding. A spectroscopic technique called micro-laser induced breakdown spectroscopy (u-LIBS) has been developed to rapidly detect silicones at concentrations below those known to cause bonding problems. This technique requires no sample preparation, vacuum or inert atmosphere, has no practical size limitations, and provides nearly instantaneous feedback to the operator. This presentation will give an overview and update of these developments with specific examples highlighted.

Connell, John W.↗
NASA NTRS1975

An experimental investigation of heat transfer to reusable surface insulation tile array gaps in a turbulent boundary layer with pressure gradient

An experimental investigation was performed to determine the effect of pressure gradient on the heat transfer to space shuttle reusable surface insulation (RSI) tile array gaps under thick, turbulent boundary layer conditions. Heat transfer and pressure measurements were obtained on a curved array of full-scale simulated RSI tiles in a tunnel wall boundary layer at a nominal freestream Mach number of 10.3 and freestream unit Reynolds numbers of 1.6, 3.3, and and 6.1 million per meter. Transverse pressure gradients were induced over the model surface by rotating the curved array with respect to the flow. Definition of the tunnel wall boundary layer flow was obtained by measurement of boundary layer pitot pressure profiles, and flat plate wall pressure and heat transfer. Flat plate wall heat transfer data were correlated and a method was derived for prediction of smooth, curved array heat transfer in the highly three-dimensional tunnel wall boundary layer flow and simulation of full-scale space shuttle vehicle pressure gradient levels was assessed.

Throckmorton, D. A.↗
NASA NTRS1975

Primer vector theory and applications

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.

Jezewski, D. J.↗
NASA NTRS1985

Application Number 3: Using Tethers for Attitude Control

Past application of the gravity gradient concept to satellite attitude control produced attitude stabilities of from 1 to 10 degrees. The satellite members were rigigly interconnected and any motion in one part of the satellite would cause motion in all members. This experience has restricted gravity gradient stabilization to applications that need attitude stability no better than 1 degree. A gravity gradient technique that combines the flexible tether with an active control that will allow control stability much better than 1 degree is proposed. This could give gravity gradient stabilization much broader application. In fact, for a large structure like a space station, it may become the preferred method. Two possible ways of demonstrating the techniques using the Tethered Satellite System (TSS) tether to control the attitude of the shuttle are proposed. Then a possible space station tether configuration is shown that could be used to control the initial station. It is then shown how the technique can be extended to the control of space stations of virtually any size.

Muller, R. M.↗
NASA NTRS1988

Goertler vortices in supersonic boundary layers

The problem of Goertler vortices in compressible boundary layers over concave walls is studied by solving parabolic partial differential equations. The numerical scheme used is based upon a fourth-order accurate compact difference scheme. The results show that both the velocity and temperature fluctuations may lead to a Goertler vortex. The vortex growth rates determined from the present method are found to differ somewhat from those given by normal mode solution. The effects of cooling, heating and pressure gradient are also studied. At a Mach number of 3.5, cooling has a small destabilizing effect. The effect of adverse pressure gradient is also found to be destabilizing on a Mach 8 boundary layer.

Spall, R. E.↗
NASA NTRS1989

Determination of the mean solid-liquid interface energy of pivalic acid

A high-confidence solid-liquid interfacial energy is determined for an anisotropic material. A coaxial composite having a cylindrical specimen chamber geometry provides a thermal gradient with an axial heating wire. The surface energy is derived from measurements of grain boundary groove shapes. Applying this method to pivalic acid, a surface energy of 2.84 erg/sq cm was determined with a total systematic and random error less than 10 percent. The value of interfacial energy corresponds to 24 percent of the latent heat of fusion per molecule.

Singh, N. B.↗
NASA NTRS1989

Elevated temperature crack growth

Alloy 718 crack growth experiments were conducted to assess the ability of the selected path-independent (P-I) integrals to describe the elevated temperature crack growth behavior. These tests were performed on single edge notch (SEN) specimens under displacement control with multiple extensometers to monitor the specimen and crack mouth opening displacement (CMOD). The displacements in these tests were sufficiently high to induce bulk cyclic inelastic deformation of the specimen. Under these conditions, the linear elastic fracture mechanics (LEFM) parameter K does not correlate the crack growth data. The experimentally measured displacement gradients at the end of specimen gage length were used as the boundary conditions in elastic-plastic finite element method (FEM) analyses. These analyses were performed with a node release approach using CYANIDE, a GEAE FEM code, which included a gap element which is capable of efficiently simulating crack closure. Excellent correlation was obtained between the experimentally measured and predicted variation of stress and CMOD with crack length and the stress-CMOD loops for Alloy 718 tests conducted at 538 C. This confirmed the accuracy of the FEM crack growth simulation approach. The experimentally measured crack growth rate data correlated well the selected P-I integrals. These investigations have produced significant progress in developing P-I integrals as non-linear fracture mechanics parameters. The results suggest that this methodology has the potential of accurately describing elevated temperature crack growth behavior under the combined influence of thermal cycling and bulk elastic-inelastic deformation states.

Kim, K. S.↗
NASA NTRS1990

Viscosity and mass transport in nonuniform Keplerian disks

A quantitative formalism for Keplerian particulate disk dynamics having its basis in a heuristic description of viscous transport is presently applied to the case of a ring with optical thickness radial gradient. A steady-state velocity distribution solution directly yields both the radial mass transport and the viscosity. The analytical method employed involves the solution of a novel form of the Krook equation through the separation of the phase-space collisional-products distribution into a symmetrical component and a delta function-approachable remainder. While this model is simplified for the case treated, its general approach may be extended to less artificially restricted cases.

Ojakangas, G. W.↗
NASA NTRS1993

The effects of orbital and climatic variations on Martian surface heat flow

Large changes in the orbital elements of Mars on timescales of 10(exp 4) to 10(exp 6) years will cause widely varying climate, specifically surface temperatures, as a result of varying insolation. These surface temperature oscillations will produce subsurface thermal gradients which contribute to the total surface heat flux. We investigate the thermal behavior of the Martian regolith on orbital timescales and show that this climatological surface heat flux is spatially variable and contributes significantly to the total surface heat flux at many locations. We model the thermal behavior of the Martian regolith by calculating the mean annual surface temperatures for each epoch (spaced 1000 years apart to resolve orbital variations) for the past 200,000 years at a chosen location on the surface. These temperatures are used as a boundary condition for the deeper regolith and subsurface temperature oscillation are then computed. The surface climatological heat flux due to past climate changes can then be found from the temperature gradient between the surface and about 150 m depth (a fraction of the thermal skin depth on these timescales). This method provides a fairly accurate determination of the climatological heat flow component at a point; however, this method is computationally time consuming and cannot be applied to all points on the globe. To map the spatial variations in the surface heat flow we recognize that the subsurface temperature structure will be largely dominated by the most recent surface temperature oscillations. In fact, the climate component of the surface heat flow will be approximately proportional to the magnitude of the most recent surface temperature change. By calculating surface temperatures at all points globally for the present epoch and an appropriate past epoch, and combining these results with a series of more precise calculations described above, we estimate the global distribution of climatological surface heat flow.

Mellon, Michael T.↗
NASA NTRS1995

Apparatus Tests Thermocouples For Seebeck Inhomogeneity

Automated apparatus reveals sources of error not revealed in calibration. Computer-controlled apparatus detects and measures Seebeck inhomogeneities in sheathed thermocouples. Measures thermocouple output voltage as function of position of probe along sharp gradient of temperature. Abnormal variations in voltage-versus-position data indicative of Seebeck inhomogeneities. Prototype for development of standard method and equipment for routine acceptance/rejection testing of sheathed thermocouples in industrial and research laboratories.

Burkett, Cecil G., Jr.↗
NASA NTRS1995

Analysis of the two-point velocity correlations in turbulent boundary layer flows

The general objective of the present work is to explore the use of Rapid Distortion Theory (RDT) in analysis of the two-point statistics of the log-layer. RDT is applicable only to unsteady flows where the non-linear turbulence-turbulence interaction can be neglected in comparison to linear turbulence-mean interactions. Here we propose to use RDT to examine the structure of the large energy-containing scales and their interaction with the mean flow in the log-region. The contents of the work are twofold: First, two-point analysis methods will be used to derive the law-of-the-wall for the special case of zero mean pressure gradient. The basic assumptions needed are one-dimensionality in the mean flow and homogeneity of the fluctuations. It will be shown that a formal solution of the two-point correlation equation can be obtained as a power series in the von Karman constant, known to be on the order of 0.4. In the second part, a detailed analysis of the two-point correlation function in the log-layer will be given. The fundamental set of equations and a functional relation for the two-point correlation function will be derived. An asymptotic expansion procedure will be used in the log-layer to match Kolmogorov's universal range and the one-point correlations to the inviscid outer region valid for large correlation distances.

Oberlack, M.↗
NASA NTRS1998

Modeling the Plasmasphere

The plasmasphere has often been considered one of the more boring regions in the magnetosphere. Its low energy plasma doesn't begin to compete against the free sources of energy available in the ring current, auroral zone, or plasma sheet. Its best known feature is its relatively highly density, archived as a result of prolonged accumulation of ionospheric outflow onto corotating flux tubes. On second look, however, the plasmasphere can be found to exhibit a remarkable influence on its more energetic cousins and display convection behavior indicative of physical processes acting throughout the magnetosphere for which we have no explanation. Plasmaspheric plasma densities and composition of heavy ions are particularly sensitive to heating by processes active in the ionosphere and all along field lines. Wave propagation and instabilities, collisional losses in the ring current, and heat transport from superthermal electrons are all equally sensitive to dense, heavy plasmaspheric densities and density gradients. It is in this context that we seek to characterize plasmaspheric populations using event based, empirical, and physical modeling methods. The modeling approaches, the challenges, and some of the results of these efforts will be presented.

Gallagher, Dennis L↗
NASA NTRS2004

Analysis and Design of Rectangular-Cross-Section Nozzles for Scramjet Engine Testing

The flow in the square-cross-section Mach-6 nozzle used in the NASA Langley Research Center Arc-Heated Scramjet Test Facility has been analyzed using three-dimensional viscous CFD methods. The primary cause of the non-uniform flow exiting the nozzle is identified as cross-flow pressure gradients imposed on wall boundary layers. The cross-flow pressure gradients cause the boundary layer to roll up into counter-rotating vortex pairs on each of the four sides of the nozzle. These four vortex pairs produce significant non-uniformity in the nozzle-exit flow. In order to improve the quality of the test flow in the facility, two alternative nozzle designs (one axisymmetric and one rectangular with a 2-D contour) have been investigated. While the axisymmetric design produced the most uniform flow, the 2-D design also produced very good flow. The 2-D design was selected for further refinement, resulting in a new nozzle design which has been constructed and awaits calibration.

Gaffney, Richard L., Jr.↗
NASA NTRS1997

High resolution magnetic resonance imaging of the calcaneus: age-related changes in trabecular structure and comparison with dual X-ray absorptiometry measurements

A high-resolution magnetic resonance imaging (MRI) protocol, together with specialized image processing techniques, was applied to the quantitative measurement of age-related changes in calcaneal trabecular structure. The reproducibility of the technique was assessed and the annual rates of change for several trabecular structure parameters were measured. The MR-derived trabecular parameters were compared with calcaneal bone mineral density (BMD), measured by dual X-ray absorptiometry (DXA) in the same subjects. Sagittal MR images were acquired at 1.5 T in 23 healthy women (mean age: 49.3 +/- 16.6 [SD]), using a three-dimensional gradient echo sequence. Image analysis procedures included internal gray-scale calibration, bone and marrow segmentation, and run-length methods. Three trabecular structure parameters, apparent bone volume (ABV/TV), intercept thickness (I.Th), and intercept separation (I.Sp) were calculated from the MR images. The short- and long-term precision errors (mean %CV) of these measured parameters were in the ranges 1-2% and 3-6%, respectively. Linear regression of the trabecular structure parameters vs. age showed significant correlation: ABV/TV (r2 = 33.7%, P < 0.0037), I.Th (r2 = 26.6%, P < 0.0118), I.Sp (r2 = 28.9%, P < 0.0081). These trends with age were also expressed as annual rates of change: ABV/TV (-0.52%/year), I.Th (-0.33%/year), and I.Sp (0.59%/year). Linear regression analysis also showed significant correlation between the MR-derived trabecular structure parameters and calcaneal BMD values. Although a larger group of subjects is needed to better define the age-related changes in trabecular structure parameters and their relation to BMD, these preliminary results demonstrate that high-resolution MRI may potentially be useful for the quantitative assessment of trabecular structure.

NASA Discipline Number 26-10↗