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At least 325 records · Page 18

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NASA NTRS1986

Elliptic generation of composite three-dimensional grids about realistic aircraft

An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid-generation method are presented along with results of the present application, a wing/body configuration based on the F-16 fighter aircraft.

Sorenson, Reese L.↗

NASA NTRS1988

Millimeter-wave diode-grid phase shifters

Monolithic diode grids have been fabricated on 2-cm square gallium-arsenide wafers with 1600 Schottky-barrier varactor diodes. Shorted diodes are detected with a liquid-crystal technique, and the bad diodes are removed with an ultrasonic probe. A small-aperture reflectometer that uses wavefront division interference was developed to measure the reflection coefficient of the grids. A phase shift of 70 deg with a 7-dB loss was obtained at 93 GHz when the bias on the diode grid was changed from -3 V to 1 V. A simple transmission-line grid model, together with the measured low-frequency parameters for the diodes, was shown to predict the measured performance over the entire capacitive bias range of the diodes, as well as over the complete reactive tuning range provided by a reflector behind the grid, and over a wide range of frequencies from 33 GHz to 141 GHz. This shows that the transmission-line model and the measured low-frequency diode parameters can be used to design an electronic beam-steering array and to predict its performance. An electronic beam-steering array made of a pair of grids using state-of-the-art diodes with 5-ohm series resistances would have a loss of 1.4 dB at 90 GHz.

Lam, Wayne W.↗

NASA NTRS1987

Algebraic grid generation

Algebraic grid generation is the direct expression of a physical coordinate system as a function of a uniform grid in a rectangular computational coordinate system. Algebraic grid generation is based on mathematical interpolation and is presented in general terms of multivariate transfinite interpolation. The multisurface method and the two-boundary technique are described as univariate procedures that can be applied within the context of transfinite interpolation. A technique for grid clustering is described. Problems that are commonly encountered in three-dimensional grid generation are discussed and approaches for dealing with complex physical domains using multiple computational grid blocks are presented.

Smith, Robert E.↗

NASA NTRS1988

Three-dimensional self-adaptive grid method for complex flows

A self-adaptive grid procedure for efficient computation of three-dimensional complex flow fields is described. The method is based on variational principles to minimize the energy of a spring system analogy which redistributes the grid points. Grid control parameters are determined by specifying maximum and minimum grid spacing. Multidirectional adaptation is achieved by splitting the procedure into a sequence of successive applications of a unidirectional adaptation. One-sided, two-directional constraints for orthogonality and smoothness are used to enhance the efficiency of the method. Feasibility of the scheme is demonstrated by application to a multinozzle, afterbody, plume flow field. Application of the algorithm for initial grid generation is illustrated by constructing a three-dimensional grid about a bump-like geometry.

Djomehri, M. Jahed↗

NASA NTRS1989

Generation of three-dimensional body-fitted grids by solving hyperbolic and parabolic partial differential equations

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Steger, Joseph L.↗

NASA NTRS1989

A simple algebraic grid adaptation scheme with applications to two- and three-dimensional flow problems

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented which provides high flowfield resolution when applied to two-dimensional and three-dimensional flow problems. The present scheme locally adjusts the grid density using gradients of selected flow variables from either finite difference or finite volume calculations, and it can specify user-prescribed grid stretching such that control of the grid spacing can be maintained in areas of known flowfield behavior. A robust and efficient grid smoothing technique has been incorporated into the adaptive grid routine.

Hsu, Andrew T.↗

NASA NTRS1989

Surface grid generation for flowfield applications using B-spline surfaces

The adequate discretization of the flowfield domain in structured grid techniques depends on the body surface, the zones, and the interior grid. Attention is presently given to the problem of obtaining a versatile surface-definition and grid-generation technique; a general surface grid-generation technique is presented which develops three-dimensional patches from point data. The grid is generated on a two-dimensional field on the basis of either a direct or inverse interpolation procedure. It is then mapped onto physical space to yield the surface grid.

Atwood, Christopher A.↗

NASA NTRS1989

Solar flare gamma-ray and hard x ray imaging with the GRID-on-a-balloon

A primary scientific objective for solar flare research during the rapidly approaching maximum in solar activity is the imaging of gamma-ray and hard x ray sources of solar flare emissions. These goals will be pursued by the Gamma Ray Imaging Device (GRID) instrument, one of three instruments recently selected for NASA's Max '91 Solar Balloon Program. The GRID instrument is based on the technique of Fourier transform imaging and utilizes scanning modulation grid collimator optics to provide full-Sun imaging with 1.9-arcsecond resolution over the energy range from 20 to 700 keV at time resolutions from 0.1 to 2 s. The GRID telescope will employ 32 subcollimators, each composed of a matched pair of high-Z collimator grids separated by 5.2 meters and a phoswich scintillation spectrometer detector having no spatial resolution. The subcollimators and integrally-mounted fine aspect system are contained within a telescope canister which will be pointed to 0.1 degree accuracy and cyclically scanned to produce source modulation. The 32 subcollimators provide a uniform distribution of grid slit orientations and a logarithmic distribution of slit spacings corresponding to angular dimensions of 1.9 arcseconds to several arcminutes. The instrument is several orders of magnitude more sensitive than the HXIS instrument on the Solar Maximum Mission (SMM) and nearly 10 times more sensitive than any similar instrument scheduled to fly during the next solar maximum. The payload, designed for long-duration high-altitude balloon capability, is scheduled for its first science flight (8 to 14 days duration) from the Antarctic in January of 1992.

Orwig, Larry E.↗

NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split, modular, user-friendly grid point distribution code is applied to several test problems. The code is self-adaptive in the sense that grid point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and constants relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flow-field gradients and/or geometric features, are used to determine the point distribution. Points are redistributed along grid lines in a specified direction in an elliptic manner over a user-specified subdomain, while orthogonality and smoothness are controlled in a parabolic (marching) manner in the remaining directions. Multidirectional adaption is achieved by sequential application of the method in each coordinate direction. The flow-field solution is redistributed onto the newly distributed grid points after each unidirectional adaption by a simple one-dimensional interpolation scheme. For time-accurate schemes such interpolation is not necessary and time-dependent metrics are carried in the fluid dynamic equations to account for grid movement.

Deiwert, G. S.↗

NASA NTRS1990

On computations of the integrated space shuttle flowfield using overset grids

Numerical simulations using the thin-layer Navier-Stokes equations and chimera (overset) grid approach were carried out for flows around the integrated space shuttle vehicle over a range of Mach numbers. Body-conforming grids were used for all the component grids. Testcases include a three-component overset grid - the external tank (ET), the solid rocket booster (SRB) and the orbiter (ORB), and a five-component overset grid - the ET, SRB, ORB, forward and aft attach hardware, configurations. The results were compared with the wind tunnel and flight data. In addition, a Poisson solution procedure (a special case of the vorticity-velocity formulation) using primitive variables was developed to solve three-dimensional, irrotational, inviscid flows for single as well as overset grids. The solutions were validated by comparisons with other analytical or numerical solution, and/or experimental results for various geometries. The Poisson solution was also used as an initial guess for the thin-layer Navier-Stokes solution procedure to improve the efficiency of the numerical flow simulations. It was found that this approach resulted in roughly a 30 percent CPU time savings as compared with the procedure solving the thin-layer Navier-Stokes equations from a uniform free stream flowfield.

Chiu, I-T.↗

NASA NTRS1989

Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations

Hyperbolic grid generation procedures are described which have been used in external flow simulations about complex configurations. For many practical applications a single well-ordered (i.e., structured) grid can be used to mesh an entire configuration, in other problems, composite or unstructured grid procedures are needed. Although the hyperbolic partial differential equation grid generation procedure has mainly been utilized to generate structured grids, an extension of the procedure to semiunstructured grids is briefly described. Extensions of the methodology are also described using two-dimensional equations.

Steger, Joseph L.↗

NASA NTRS1989

Grids for DSMC computation of two and three-dimensional flows

Contemporary grid schemes for use in Direct Simulation Monte Carlo (DSMC) method of computing two- and three-dimensional flows are briefly surveyed. The grids described include: (1) simple, constant area cells defined by a rectangular grid; (2) multilevel rectangular grids; (3) adaptive rectangular cells; (4) 'point reference' scheme; (5) body-fitted 'analytical' cells; (6) 'general' schemes; (7) 'general' schemes with subcells; (8) orthogonal transformation to rectangular grid; (9) structural tetrahedral grids; (10) rectangular multilevel subcells with adaptive body-fitted cells.

Bird, G. A.↗

NASA NTRS1988

Three-dimensional self-adaptive grid method for complex flows

Djomehri, M. Jahed↗

NASA NTRS1990

Adaptive grid embedding for the two-dimensional Euler equations

A numerical algorithm is presented for solving the two-dimensional flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for an NACA 0012 airfoil in a freestream with Mach numbers of 0.95 and 1.054. Excellent resolution of the shock structures is obtained with the adaptive grid embedding method with significantly fewer grid points than the comparable structured grid.

Warren, Gary P.↗

NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗

NASA NTRS1991

Unstructured grid generation using the distance function

A new class of methods for obtaining level sets to generate unstructured grids is presented. The consecutive grid levels are computed using the distance functions, which corresponds to solving the Hamilton-Jacobi equations representing the equations of motion of fronts propagating with curvature-dependent speed. The relationship between the distance function and the governing equations will be discussed as well as its application to generating grids. Multi-ply connected domains and complex geometries are handled naturally, with a straightforward generalization to several space dimensions. The grid points for the unstructured grid are obtained simultaneously with the grid levels. The search involved in checking for overlapping triangles is minimized by triangulating the entire domain one level at a time.

Bihari, Barna L.↗

NASA NTRS1991

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

NASA NTRS1991

A grid-independent approximate Riemann solver with applications to the Euler and Navier-Stokes equations

A new two-dimensional approximate Riemann solver has been developed that obtains fluxes on grid faces via wave decomposition. By utilizing information propagation in the velocity-difference directions rather than in the grid-normal directions, this flux function more appropriately interprets and hence more sharply resolves shock and shear waves when they lie oblique to the grid. The model uses five waves to describe the difference in states at a grid face. Two acoustic waves, one shear wave, and one entropy wave propagate in the direction defined by the local velocity difference vector, while the fifth wave is a shear wave that propagates at a right angle to the other four. Test cases presented include a shock reflecting off a wall, a pure shear wave, supersonic flow over an airfoil, and viscous separated airfoil flow. Results using the new model give significantly sharper shock and shear contours than a grid-aligned solver. Navier-Stokes computations over an aifoil show reduced pressure distortions in the separated region as a result of the grid-independent upwinding.

Rumsey, Christopher L.↗