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NASA NTRS1991

A Lagrange multiplier based divide and conquer finite element algorithm

A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.

Farhat, C.↗

NASA NTRS1974

Research study on high energy radiation effect and environment solar cell degradation methods

The most detailed and comprehensively verified analytical model was used to evaluate the effects of simplifying assumptions on the accuracy of predictions made by the external damage coefficient method. It was found that the most serious discrepancies were present in heavily damaged cells, particularly proton damaged cells, in which a gradient in damage across the cell existed. In general, it was found that the current damage coefficient method tends to underestimate damage at high fluences. An exception to this rule was thick cover-slipped cells experiencing heavy degradation due to omnidirectional electrons. In such cases, the damage coefficient method overestimates the damage. Comparisons of degradation predictions made by the two methods and measured flight data confirmed the above findings.

Horne, W. E.↗

NASA NTRS1976

Cosmic-ray gradients from Pioneer-10 and Pioneer-11

The paper reports Pioneer 10 and 11 observations of the variation with heliocentric distance of the intensity of cosmic-ray protons, alpha particles, and high-Z nuclei with kinetic energies of at least 480 MeV/nucleon as well as cosmic-ray electrons with energies exceeding 6 MeV. The observations were with three-channel Cerenkov counters at distances between 1.02 and 4.66 AU while the spacecraft traveled from earth to Jupiter. During the 4.5-month observation period, all the counting rates rose steadily, except when they were modified by solar events, Forbush decreases, and Jovian electron events. Two methods are employed to determine the cosmic-ray integral intensity gradient for the observation period from simultaneous data obtained by the two spacecraft; effects of solar particles, Forbush decreases, and Jovian electrons are eliminated in various ways. A radial gradient of 0.15 + or - 2.3% per AU is determined, which is considered to be consistent with zero. Theoretical gradients are computed, and the observed values are found to be an order of magnitude below the expected values. Several reasons for the discrepancy are suggested.

Axford, W. I.↗

NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗

NASA NTRS1991

An adaptive grid method for computing time accurate solutions on structured grids

The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.

Bockelie, Michael J.↗

NASA NTRS1960

The Blunt Plate In Hypersonic Flow

The sonic-wedge characteristics method has been used to obtain the shock shapes and surface pressure distributions on several blunt two-dimensional shapes in a hypersonic stream for several values of the ratio of specific heats. These shapes include the blunt slab at angle of attack and power profiles of the form yb = a)P, where 0 les than m less than 1, Yb and x are coordinates of the body surface, and a is a constant. These numerical results have been compared with the results of blast-wave theory, and methods of predicting the pressure distributions and shock shapes are proposed in each case. The effects of a free-stream conical-flow gradient on the pressure distribution on a blunt slab in hypersonic flow were investigated by the sonic-wedge characteristics method and were found to be sizable in many cases. Procedures which are satisfactory for reducing pressure data obtained in conical flows with small gradients are presented.

Baradell, Donald L.↗

NASA NTRS2014

Electron Beam Freeform Fabrication of Titanium Alloy Gradient Structures

Historically, the structural optimization of aerospace components has been done through geometric methods. A monolithic material is chosen based on the best compromise between the competing design limiting criteria. Then the structure is geometrically optimized to give the best overall performance using the single material chosen. Functionally graded materials offer the potential to further improve structural efficiency by allowing the material composition and/or microstructural features to spatially vary within a single structure. Thus, local properties could be tailored to the local design limiting criteria. Additive manufacturing techniques enable the fabrication of such graded materials and structures. This paper presents the results of a graded material study using two titanium alloys processed using electron beam freeform fabrication, an additive manufacturing process. The results show that the two alloys uniformly mix at various ratios and the resultant static tensile properties of the mixed alloys behave according to rule-of-mixtures. Additionally, the crack growth behavior across an abrupt change from one alloy to the other shows no discontinuity and the crack smoothly transitions from one crack growth regime into another.

Brice, Craig A.↗

NASA NTRS2018

Generalised Primal-Dual Grids for Unstructured Co-Volume Schemes

The generation of high-quality staggered unstructured grids is considered, leading to the development of a new optimisation-based strategy designed to construct weighted 'Regular-Power' tessellations appropriate for co-volume type numerical discretisation techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble generalised orthogonal tessellations with enhanced geometric quality. The construction of these grids is motivated by the desire to improve the performance and accuracy of numerical methods based on unstructured co-volume type schemes, including various staggered grid techniques for the simulation of fluid dynamics and hyperbolic transport. In this study, a new hybrid optimisation strategy is proposed; seeking to optimise the geometry, topology and weights associated with general, two-dimensional Regular-Power tessellations using a combination of gradient-ascent and energy-based techniques. The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.

power diagrams↗

NASA NTRS1987

A finite-difference outer layer and integral inner layer method for the solution of the turbulent boundary layer equations

A new turbulent boundary-layer method is developed which models the inner region with the law of the wall while the outer region uses Clauser's eddy viscosity in Matsuno's finite-difference method. The match point between the inner and outer regions as well as the wall shear stress are determined at each marching step during the computation. Results obtained for incompressible, two-dimensional flow over flat plates and ellipses are compared with solutions from a baseline method which uses a finite-difference method for the entire boundary layer. Since the present method used the finite-difference method in the outer region only, the number of grid points required was about half that needed for the baseline method. Accurate displacement and momentum thicknesses were predicted for all cases. Skin friction was predicted well for the flat plate, but the accuracy decreased significantly for the ellipses. Adding a wake functions to the law of the wall allows some of the pressure gradient effect to be taken into account thereby increasing the accuracy of the method.

Barnwell, R. W.↗

NASA NTRS1972

Random response of rectangular panels to the pressure field beneath a turbulent boundary layer in subsonic flows

The response of a rectangular panel under the excitation of a turbulent boundary layer with a zero longitudinal mean pressure gradient in a subsonic flow was studied in detail. The method of normal mode was used together with the technique of spectral analysis. Both simply supported and clamped edge conditions of a panel were considered, and the displacement power spectral density of the panel response was computed. The results for the clamped edge panel compare favorably with existing data. Charts of structural acceptance, which provide a framework for estimating the response of other rectangular panels, are presented, and the physical significances of structural acceptances discussed.

Chyu, W. J.↗

NASA NTRS1983

Moire deflectometry with deferred analysis

A simplified version of moire deflectometry for flow visualization is presented. The modification comprises replacement of the second grating, the ground glass screen, and the camera with a plate film holder to obtain a shadow picture. Postanalysis proceeds by placing a grid transparency of the same periodicity of the remaining glass grating on the negative for projection viewing. The rotational angle between the grating and the plate alters the moire fringe periodicity. Use of the method in studying flows is predicted to reveal weak density gradient areas and shocks.

Rhodes, D. B.↗

NASA NTRS1985

A space-marching method for incompressible Navier-Stokes equations

This paper deals with the development of a space-marching method for incompressible flows. The method solves the continuity and momentum equations as a coupled system at each streamwise station. The character of the system of equations has been changed from elliptic to hyperbolic/parabolic in order to enable the equations to be marched in space. The present method has many advantages compared to the existing parabolic or space-marching methods for incompressible flow: (1) it avoids the solution of Poisson equations, (2) it conserves the mass flow with no additional computation, (3) it does not require the specification of an assumed pressure field when used in the prediction of duct flows. The present method can capture strong secondary velocities and strong transverse pressure gradients. Predictions of the flow through straight and curved ducts are in good agreement with analytical and experimental results.

Pouagare, M.↗

NASA NTRS1985

An improved viscid/inviscid interaction procedure for transonic flow over airfoils

A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag.

Melnik, R. E.↗

NASA NTRS1985

An atlas of objectively analyzed atmospheric cross sections, 1973-1980

Atmospheric variability over time scales greater than one month is conceptually simplified and readily recognized from vertical cross-sections of zonal-monthly mean data. The reduction to two dimensions, latitude and height, explicitly eliminates all zonal waves but implicity retains their effects on the thermal-pressure fields and the dynamically related zonal wind fields. This atlas contains 96 examples, spanning all latitudes in both the northern and southern hemispheres and two decades in pressure, from 1000 to 10 mb. Four analyses, representing each month from January 1973 through December 1980, depicts the potential virtual temperature, the observed zonal wind velocity, the virtual temperature and the geostrophic zonal wind velocity. Each variable is contoured at a close interval to facilitate visual estimates of stability and vorticity via their gradients. The analyses are generated and contoured by objective computer methods from just one data source: in situ measurements from the conventional rawin-radiosonde system. Although the analyses are independently made at constant pressure levels (the mandatory levels) the cross-sections are drawn with geopotential height as the ordinate. With this ordinate one can observe the seasonal expansion and contraction of the earth's atmosphere, especially that of the polar stratosphere. Also, the quasi-biannual cycle can be identified and studied directly from successive cross-sections.

Goodman, J.↗

NASA NTRS1988

An update on remote measurement of soil moisture over vegetation using infrared temperature measurements: A FIFE perspective

Using model development, image analysis and micrometeorological measurements, the object is to push beyond the present limitations of using the infrared temperature method for remotely determining surface energy fluxes and soil moisture over vegetation. Model development consists of three aspects: (1) a more complex vegetation formulation which is more flexible and realistic; (2) a method for modeling the fluxes over patchy vegetation cover; and (3) a method for inferring a two-layer soil vertical moisture gradient from analyses of horizontal variations in surface temperatures. HAPEX and FIFE satellite data will be used along with aircraft thermal infrared and solar images as input for the models. To test the models, moisture availability and bulk canopy resistances will be calculated from data collected locally at the Rock Springs experimental field site and, eventually, from the FIFE project.

Carlson, Toby N.↗

NASA NTRS1989

SAGE: A 2-D self-adaptive grid evolution code and its application in computational fluid dynamics

SAGE is a user-friendly, highly efficient, two-dimensional self-adaptive grid code based on Nakahashi and Deiwert's variational principles method. Grid points are redistributed into regions of high flowfield gradients while maintaining smoothness and orthogonality of the grid. Efficiency is obtained by splitting the adaption into 2 directions and applying one-sided torsion control, thus producing a 1-D elliptic system that can be solved as a set of tridiagonal equations.

Davies, Carol B.↗

NASA NTRS1991

An experimental investigation of boundary layer transition in an adverse pressure gradient

The evolution of a small perturbation introduced periodically into a boundary layer with a moderately strong adverse pressure gradient (APG) was investigated experimentally using the hot-wire method. The magnitude of the disturbance is found to decay with the streamwise distance in the APG before undergoing rapid growth and triggering transition in a very repetitive manner. The evidence suggests that the laminar layer separates and that the transition mechanism is an inviscid shear-layer type of instability. Contours of spanwise vorticity in the plane of the disturbance show the formation of roll-ups in the initial stages. Subsequent interaction with the wall leads to the formation of large-scale vortex loops which merge into a single vortex loop further downstream.

Watmuff, Jonathan H.↗

NASA NTRS1995

Validation of clear-sky fluxes for tropical oceans from the Earth Radiation Budget Experiment

The existence and magnitude of a systematic bias in the clear-sky longwave fluxes from the Earth Radiation Budget Experiment (ERBE) is investigated. The bias is apparently introduced because the ERBE method for scene identification does not account for large zonal gradients in longwave absorption by water vapor. The ERBE fluxes are compared to fluxes calculated with a radiative transfer model from ship radiosonde measurements. The comparison is based upon an analysis of 5 yr of coincident satellite and radiosonde observations for equatorial ocean regions. The differences between the ERBE and model fluxes are examined as functions of sea surface temperature (SST) and relative humidity. The authors use height-mean relative humidity bar-RH as an index of atmospheric moisture. The average offset between and model ERBE fluxes ranges between +2 and +6 W/sq m for SSTs above 295 K, and the gradients with respect to SST are nearly identical. However, the difference between the model and ERBE depends significantly on the tropospheric relative humidity. ERBE fluxes exceed model fluxes for bar-RH above 70%, and the maximum offset of +9 to +12 W/sq m is consistent with previous estimates. There are also indications that the clear-sky fluxes for bar-RH below 25% may be underestimated by about 10-15 W/sq m. Since extreme values of height-mean humidity are relatively infrequent, the net bias introduced in the ERBE monthly mean clear-sky fluxes is generally less than the systematic error in estimates introduced in the ERBE monthly mean clear-sky fluxes is generally less than the systematic error in estimates of the instantaneous fluxes. These findings support earlier work on the coupling between SST and the atmospheric greenhouse effect, in particular the existence of a super greenhouse effect for oceans warmer than 300 K. Recent reports of much larger systematic differences are not supported by this analysis. The results indicate that comparison of general circulation model (GCM) and ERBE clear-sky longwave fluxes will depend explicitly on atmospheric humidity.

Collins, W. D.↗