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Results for “gradient methods”

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NASA NTRS1983

A comparison of methods for computing the sigma-coordinate pressure gradient force for flow over sloped terrain in a hybrid theta-sigma model

In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.

Johnson, D. R.↗

NASA NTRS1979

Utilization of nuclear methods for materials analysis and the determination of concentration gradients

The various types of nuclear chemical analysis methods are discussed. The possibilities of analysis through activation and direct observation of nuclear reactions are described. Such methods make it possible to analyze trace elements and impurities with selectivity, accuracy, and a high degree of sensitivity. Such methods are used in measuring major elements present in materials which are available for analysis only in small quantities. These methods are well suited to superficial analyses and to determination of concentration gradients; provided the nature and energy of the incident particles are chosen judiciously. Typical examples of steels, pure iron and refractory metals are illustrated.

Darras, R.↗

NASA NTRS1988

Measurement of Seebeck coefficient using a large thermal gradient

The integral method of measuring the Seebeck voltage, V(T), has been applied to short rod-shaped samples. In the present method, one end of the sample is held at a fixed temperature and the other end is automatically varied through a temperature T range of interest, up to a maximum temperature of 1000 C. The Seebeck coefficient is then obtained from the slope of the V(T) vs T curve. The method offers simplicity of sample handling and minimal operator involvement.

Wood, C.↗

NASA NTRSDate not supplied

Extending an Economical Third-Order Inviscid Nodal-Gradient Cell-Centered Finite-Volume Method to Mixed-Element Grids

In this paper, we extend an economical third-order nodal-gradient cell-centered finite-volume method, originally developed for tetrahedral grids, to mixed-element grids. It is shown that the efficient quadratic interpolation formula essential to eliminating second derivatives from a third-order accurate discretization can be easily extended to an arbitrary cell type. For the surface flux integration, we consider a split-face approach, where a quadrilateral face is split into two triangles, and the third-order method for tetrahedra is directly applied. Also, we derive a second-derivative-free, high-order, volume quadrature formula for an arbitrary cell. Numerical results are presented for accuracy verification and applications with three-dimensional nontetrahedral grids.

Computational Fluid Dynamics↗

NASA NTRSDate not supplied

Comparison of Two Approaches to Constructing Second- and Third-Order Nodal-Gradient Cell-Centered Finite-Volume Methods for Mixed-Element Grids

In this paper, we introduce a third-order nodal-gradient cell-centered ﬁnite volume scheme applicable to mixed-element grids based on a single numerical ﬂux per face. Previously, we considered a split-quadrilateral-face approach, where we split each quadrilateral face of a non-tetrahedral cell into two triangles and then apply second- and third-order schemes designed for tetrahedral grids. This approach is relatively simple to implement but expensive because it requires two numerical ﬂux evaluations per quadrilateral face. In this study, we consider another approach, where the surface ﬂux quadrature is performed with a single numerical ﬂux per face with ﬂux corrections. It requires a 3×3 correction matrix to be stored at each face but is more economical than the split-quadrilateral-face approach. The two approaches are compared for three-dimensional ﬂows on irregular hexahedral grids, and their relative merits are discussed.

Third-order scheme↗

NASA NTRS1998

Scaling up the Single Transducer Thickness-Independent Ultrasonic Imaging Method for Accurate Characterization of Microstructural Gradients in Monolithic and Composite Tubular Structures

Ultrasonic velocity/time-of-flight imaging that uses back surface reflections to gauge volumetric material quality is highly suited for quantitative characterization of microstructural gradients including those due to pore fraction, density, fiber fraction, and chemical composition variations. However, a weakness of conventional pulse-echo ultrasonic velocity/time-of-flight imaging is that the image shows the effects of thickness as well as microstructural variations unless the part is uniformly thick. This limits this imaging method's usefulness in practical applications. Prior studies have described a pulse-echo time-of-flight-based ultrasonic imaging method that requires using a single transducer in combination with a reflector plate placed behind samples that eliminates the effect of thickness variation in the image. In those studies, this method was successful at isolating ultrasonic variations due to material microstructure in plate-like samples of silicon nitride, metal matrix composite, and polymer matrix composite. In this study, the method is engineered for inspection of more complex-shaped structures-those having (hollow) tubular/curved geometry. The experimental inspection technique and results are described as applied to (1) monolithic mullite ceramic and polymer matrix composite 'proof-of-concept' tubular structures that contain machined patches of various depths and (2) as-manufactured monolithic silicon nitride ceramic and silicon carbide/silicon carbide composite tubular structures that might be used in 'real world' applications.

Roth, Don J.↗

NASA NTRS1987

Solving Finite-Element Problems on a Concurrent Processor

By use of "conjugate gradients" technique, concurrent efficiency greater than 90 percent. Algorithm applies method of conjugate gradients to iterative solution of finite-element problems on concurrent processor. With algorithm, iteration rates nearly proportional to number of processors. For sufficiently large problems, fraction of proportional speedup achieved, called concurrent efficiency, exceeds 90 percent. Results indicate future application of this and related algorithms to large finite-element problems depend primarily upon applicability of iteratiave techniques, not upon issues of concurrency or efficiency.

Lyzenga, G. A.↗

NASA NTRS1976

A turbulence model for nonequilibrium adverse pressure gradient flows

This paper presents a method for calculating compressible adverse pressure gradient boundary layers by using an algebraic eddy viscosity turbulence model that has been modified for variable pressure gradient and turbulence memory effects. The pressure gradient corrections are based on previous incompressible data correlations. Several methods for including the effects of turbulence memory are evaluated. A new lag model, which gives good agreement with available experimental data, is developed. Finally, a correlation is developed for the lag length parameter employed in the model as a function of the known experimental flow variables.

Horstman, C. C.↗

NASA NTRS1984

Separation of cells from the rat anterior pituitary gland

Data concerned with analyzing the cellular organization of the rat anterior pituitary gland are examined. The preparation of the cell suspensions and the methods used to separate pituitary cell types are described. Particular emphasis is given to velocity sedimentation at unit gravity, density gradient centrifugation, affinity methods, fluorescence activated cell sorting, and density gradient and continuous-flow electrophoresis. The difficulties encountered when attempting to compare data from different pituitary cell separation studies are discussed, and results from various experiments are presented. The functional capabilities of the separated cell populations can be tested in various culture systems.

Hymer, W. C.↗

NASA NTRS1990

Statistical analysis of static shape control in space structures

The article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures. Two approaches for improving efficiency are considered. One is an adjoint technique for calculating distortion shapes: the second is a modal expansion of distortion shapes in terms of pseudo-vibration modes. The two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna. The adjoint analysis technique is used with a discrete-variable optimization method. The modal approximation technique is coupled with a standard conjugate-gradient continuous optimization method. The agreement between the two sets of results is good, validating both the approximate analysis and optimality of the results.

Burdisso, Ricardo A.↗

NASA NTRS1997

Methods for Sensitivity Analysis in Gradient-Based Shape Optimization: A Review

CFD is now being widely used in the design of mechanical and aerospace systems and their components. Improving the accuracy and efficiency of this process can reduce its cost and increase its effectiveness. Other motivating factors that push and pull CFD into design optimization are; (1) the need for design methodologies (single- and multi-disciplinary) to reduce cost and time in developing new fluid and aero systems for fast response to market changes; (2) new design requirements outside existing database; (3) new CFD algorithms and growth in computing power; (4) need for increased product quality and reliability; (5) lack of test facilities; (6) limitations and cost of testing techniques; (7) limitations of existing design practices; and (8) prohibitive cost of and conflicting designs derived from isolated component analyses and design, which are repetitive in nature and omit mutual interference.

Baysal, Oktay↗

NASA NTRS2020

Face- and Cell-Averaged Nodal-Gradient Approach to Cell-Centered Finite-Volume Method on Mixed Grids

In this paper, the averaged nodal-gradient approach previously developed for triangular grids is extended to mixed triangular-quadrilateral grids. It is shown that the face- averaged approach leads to deteriorated iterative convergence on quadrilateral grids. To develop a convergent solver, we consider cell-averaging instead of face-averaging for quadri- lateral cells. We show that the cell-averaged approach leads to a convergent solver and can be efficiently combined with the face-averaged approach on mixed grids. The method is demonstrated for various inviscid and viscous problems from low to high Mach numbers on two-dimensional mixed grids.

Nishikawa, Hiroaki↗

NASA NTRS2005

Analysis of plasmaspheric plumes: CLUSTER and IMAGE observations and numerical simulations

Plasmaspheric plumes have been routinely observed by CLUSTER and IMAGE. The CLUSTER mission provides high time resolution four-point measurements of the plasmasphere near perigee. Total electron density profiles can be derived from the plasma frequency and/or from the spacecraft potential (note that the electron spectrometer is usually not operating inside the plasmasphere); ion velocity is also measured onboard these satellites (but ion density is not reliable because of instrumental limitations). The EUV imager onboard the IMAGE spacecraft provides global images of the plasmasphere with a spatial resolution of 0.1 RE every 10 minutes; such images acquired near apogee from high above the pole show the geometry of plasmaspheric plumes, their evolution and motion. We present coordinated observations for 3 plume events and compare CLUSTER in-situ data (panel A) with global images of the plasmasphere obtained from IMAGE (panel B), and with numerical simulations for the formation of plumes based on a model that includes the interchange instability mechanism (panel C). In particular, we study the geometry and the orientation of plasmaspheric plumes by using a four-point analysis method, the spatial gradient. We also compare several aspects of their motion as determined by different methods: (i) inner and outer plume boundary velocity calculated from time delays of this boundary observed by the wave experiment WHISPER on the four spacecraft, (ii) ion velocity derived from the ion spectrometer CIS onboard CLUSTER, (iii) drift velocity measured by the electron drift instrument ED1 onboard CLUSTER and (iv) global velocity determined from successive EUV images. These different techniques consistently indicate that plasmaspheric plumes rotate around the Earth, with their foot fully co-rotating, but with their tip rotating slower and moving farther out.

Darouzet, Fabien↗

NASA NTRS1974

Method for compression molding of thermosetting plastics utilizing a temperature gradient across the plastic to cure the article

A method is described for compression molding of thermosetting plastics composition. Heat is applied to the compressed load in a mold cavity and adjusted to hold molding temperature at the interface of the cavity surface and the compressed compound to produce a thermal front. This thermal front advances into the evacuated compound at mean right angles to the compression load and toward a thermal fence formed at the opposite surface of the compressed compound.

Heier, W. C.↗

NASA NTRS2009

Advances in Non-contact Measurement of Creep Properties

Our team has developed a novel approach to measuring creep at extremely high temperatures using electrostatic levitation (ESL). This method has been demonstrated on niobium up to 2300 C, while ESL has melted tungsten (3400 C). High-precision machined spheres of the sample are levitated in the NASA MSFC ESL, a national user facility, and heated with a laser. The laser is aligned off-center so that the absorbed photons transfer their momentum to the sample, causing it to rotate at up to 250,000+ RPM. The rapid rotation loads the sample through centripetal acceleration, causing it to deform. The deformation of the sample is captured on high-speed video, which is analyzed by machine-vision software from the University of Massachusetts. The deformations are compared to finite element models to determine the constitutive constants in the creep relation. Furthermore, the noncontact method exploits stress gradients within the sample to determine the stress exponent in a single test. This method was validated in collaboration with the University of Tennessee for niobium at 1985 C, with agreement within the uncertainty of the conventional measurements. A similar method is being employed on Ultra-High-Temperature ZrB2- SiC composites, which may see application in rocket nozzles and sharp leading edges for hypersonic vehicles.

Hyers, Robert W.↗

NASA NTRS1980

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗

NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗

NASA NTRSDate not supplied

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗