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NASA NTRS1998

Current Grid Generation Strategies and Future Requirements in Hypersonic Vehicle Design, Analysis and Testing

Recent advances in computational power enable computational fluid dynamic modeling of increasingly complex configurations. A review of grid generation methodologies implemented in support of the computational work performed for the X-38 and X-33 are presented. In strategizing topological constructs and blocking structures factors considered are the geometric configuration, optimal grid size, numerical algorithms, accuracy requirements, physics of the problem at hand, computational expense, and the available computer hardware. Also addressed are grid refinement strategies, the effects of wall spacing, and convergence. The significance of grid is demonstrated through a comparison of computational and experimental results of the aeroheating environment experienced by the X-38 vehicle. Special topics on grid generation strategies are also addressed to model control surface deflections, and material mapping.

Papadopoulos, Periklis↗

NASA NTRS1993

Optimal resolution in maximum entropy image reconstruction from projections with multigrid acceleration

We consider the problem of image reconstruction from a finite number of projections over the space L(sup 1)(Omega), where Omega is a compact subset of the set of Real numbers (exp 2). We prove that, given a discretization of the projection space, the function that generates the correct projection data and maximizes the Boltzmann-Shannon entropy is piecewise constant on a certain discretization of Omega, which we call the 'optimal grid'. It is on this grid that one obtains the maximum resolution given the problem setup. The size of this grid grows very quickly as the number of projections and number of cells per projection grow, indicating fast computational methods are essential to make its use feasible. We use a Fenchel duality formulation of the problem to keep the number of variables small while still using the optimal discretization, and propose a multilevel scheme to improve convergence of a simple cyclic maximization scheme applied to the dual problem.

Limber, Mark A.↗

NASA NTRS2010

Deconvolution methods and systems for the mapping of acoustic sources from phased microphone arrays

A method and system for mapping acoustic sources determined from a phased microphone array. A plurality of microphones are arranged in an optimized grid pattern including a plurality of grid locations thereof. A linear configuration of N equations and N unknowns can be formed by accounting for a reciprocal influence of one or more beamforming characteristics thereof at varying grid locations among the plurality of grid locations. A full-rank equation derived from the linear configuration of N equations and N unknowns can then be iteratively determined. A full-rank can be attained by the solution requirement of the positivity constraint equivalent to the physical assumption of statically independent noise sources at each N location. An optimized noise source distribution is then generated over an identified aeroacoustic source region associated with the phased microphone array in order to compile an output presentation thereof, thereby removing the beamforming characteristics from the resulting output presentation.

Brooks, Thomas F.↗

NASA NTRS1979

Theoretical performance of multi-layer grid patterns for solar cells

Multilayer grid patterns consist of fine closely spaced grid lines overlaid by coarser patterns of wider and thicker grid lines to collect the current from the finer grids with low series voltage drop and low active-layer sheet losses. An analytical approach leads to closed form solutions with simple relationships between the power losses in the active layer, in the grid and shadowing losses for optimum design proportions. The results show that multilayer grids, with line thickness equal to line width, greatly reduce losses in cell efficiency under concentration conditions of high current collection. (AlGa)As-pn GaAs cells of areas 1-25 sq cm and sheet resistance 40 ohms/square are considered. Also the performance of a n/p GaAs cell of dimensions 10 x 10 cm is studied. With optimized grid patterns high efficiencies are predicted for large area cells.

Flat, A.↗

NASA NTRS2012

Deconvolution Methods and Systems for the Mapping of Acoustic Sources from Phased Microphone Arrays

Mapping coherent/incoherent acoustic sources as determined from a phased microphone array. A linear configuration of equations and unknowns are formed by accounting for a reciprocal influence of one or more cross-beamforming characteristics thereof at varying grid locations among the plurality of grid locations. An equation derived from the linear configuration of equations and unknowns can then be iteratively determined. The equation can be attained by the solution requirement of a constraint equivalent to the physical assumption that the coherent sources have only in phase coherence. The size of the problem may then be reduced using zoning methods. An optimized noise source distribution is then generated over an identified aeroacoustic source region associated with a phased microphone array (microphones arranged in an optimized grid pattern including a plurality of grid locations) in order to compile an output presentation thereof, thereby removing beamforming characteristics from the resulting output presentation.

Brooks, Thomas F.↗

NASA NTRS1985

Computational methods for hypersonic viscous flow over finite ellipsoid-cones at incidence

A numerical method, which is simpler than others currently in use, is proposed for determining the full viscous flow over a finite body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt foebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined to the body wall, outflow surface and the bow shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained on a 30 by 36 by 6 grid with 400 time-marching iterations. Results for body shapes belonging to the ellipsoid-cone family are compared with the experimental data for the Apollo command module and the Viking aeroshell. Validation of the method based on self-consistency is also discussed.

Li, C. P.↗

NASA NTRS1985

Numerical procedure for three-dimensional hypersonic viscous flow over aerobrake configuration

A numerical method, which is simpler and more efficient than others currently in use, is proposed for the computation of the full viscous flow over an aerobrake body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt forebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined by the body wall, outflow surface and the shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained with a 28 x 36 x 7 grid and 400 time-marching iterations. Excellent agreement of shock location is found between the present result and the schlieren photograph. Details of the base flow and shear layer impingement on the cylindrical aft body are presented for an adiabatic wall case.

Li, C. P.↗

NASA NTRS1988

28 percent efficient GaAs concentrator solar cells

AlGaAs/GaAs heteroface solar concentrator cells which exhibit efficiencies in excess of 27 percent at high solar concentrations (over 400 suns, AM1.5D, 100 mW/sq cm) have been fabricated with both n/p and p/n configurations. The best n/p cell achieved an efficiency of 28.1 percent around 400 suns, and the best p/n cell achieved an efficiency of 27.5 percent around 1000 suns. The high performance of these GaAs concentrator cells compared to earlier high-efficiency cells was due to improved control of the metal-organic chemical vapor deposition growth conditions and improved cell fabrication procedures (gridline definition and edge passivation). The design parameters of the solar cell structures and optimized grid pattern were determined with a realistic computer modeling program. An evaluation of the device characteristics and a discussion of future GaAs concentrator cell development are presented.

Macmillan, H. F.↗

NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testing on a Blunt Mars Entry Vehicle Concept

Supersonic Retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle was simulated using the OVERFLOW Computational Fluid Dynamics (CFD) solver. Two nozzle configurations were tested (1E and 1F) as a subset of the seven total configurations in the Descent Systems Study (DSS) testing campaign. A generalized, Adaptive Mesh Refinement (AMR) shock capturing and plume refinement technique was developed and calibrated for producing automatic and optimized grid systems unique to any given testing condition. Simulations were subjected to successive levels of grid refinement in order to determine solution independence from grid resolution. OVERFLOW Reynolds Averaged Navier-Stokes (RANS) solutions produced realistic SRP flow phenomena, including Mach disk normal shocks contained in high-thrust plumes and bow shock triple-points. Solutions for the 1E nozzle configuration were steady. Conversely, a subset of the 1F test conditions were unsteady and exhibited periodic, non-sinsoidal expansions and contractions of the streamwise-oriented plume, resulting in unsteady aerodynamic loads on the vehicle.

Supersonic Retropropulsion↗

NASA NTRS1984

Shape optimization including finite element grid adaptation

The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.

Kikuchi, N.↗

NASA NTRS1998

Geometry Modeling and Grid Generation for Design and Optimization

Geometry modeling and grid generation (GMGG) have played and will continue to play an important role in computational aerosciences. During the past two decades, tremendous progress has occurred in GMGG; however, GMGG is still the biggest bottleneck to routine applications for complicated Computational Fluid Dynamics (CFD) and Computational Structures Mechanics (CSM) models for analysis, design, and optimization. We are still far from incorporating GMGG tools in a design and optimization environment for complicated configurations. It is still a challenging task to parameterize an existing model in today's Computer-Aided Design (CAD) systems, and the models created are not always good enough for automatic grid generation tools. Designers may believe their models are complete and accurate, but unseen imperfections (e.g., gaps, unwanted wiggles, free edges, slivers, and transition cracks) often cause problems in gridding for CSM and CFD. Despite many advances in grid generation, the process is still the most labor-intensive and time-consuming part of the computational aerosciences for analysis, design, and optimization. In an ideal design environment, a design engineer would use a parametric model to evaluate alternative designs effortlessly and optimize an existing design for a new set of design objectives and constraints. For this ideal environment to be realized, the GMGG tools must have the following characteristics: (1) be automated, (2) provide consistent geometry across all disciplines, (3) be parametric, and (4) provide sensitivity derivatives. This paper will review the status of GMGG for analysis, design, and optimization processes, and it will focus on some emerging ideas that will advance the GMGG toward the ideal design environment.

Samareh, Jamshid A.↗

NASA NTRS2006

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

Nielsen, Eric J.↗

NASA NTRS1993

Three-dimensional unstructured grid refinement and optimization using edge-swapping

This paper presents a three-dimensional (3-D) 'edge-swapping method based on local transformations. This method extends Lawson's edge-swapping algorithm into 3-D. The 3-D edge-swapping algorithm is employed for the purpose of refining and optimizing unstructured meshes according to arbitrary mesh-quality measures. Several criteria including Delaunay triangulations are examined. Extensions from two to three dimensions of several known properties of Delaunay triangulations are also discussed.

Gandhi, Amar↗

NASA NTRS1999

Structure Damage Simulations Accounting for Inertial Effects and Impact and Optimization of Grid-Stiffened Non-Circular Shells

The goal of this research project is to develop modelling and analysis strategy for the penetration of aluminium plates impacted by titanium impactors. Finite element analysis is used to study the penetration of aluminium plates impacted by titanium impactors in order to study the effect of such uncontained engine debris impacts on aircraft-like skin panels. LS-DYNA3D) is used in the simulations to model the impactor, test fixture frame and target barrier plate. The effects of mesh refinement, contact modeling, and impactor initial velocity and orientation were studied. The research project also includes development of a design tool for optimum design of grid-stiffened non-circular shells or panels subjected to buckling.

Mei, Chuh↗

NASA NTRS1997

Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation

A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.

Anderson, W. Kyle↗

NASA NTRS2004

Efficient Fluid Dynamic Design Optimization Using Cartesian Grids

This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.

Dadone, A.↗

NASA NTRS2001

Optimal Design of Grid-Stiffened Panels and Shells With Variable Curvature

A design strategy for optimal design of composite grid-stiffened structures with variable curvature subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. Stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions. in-plane design loads, material properties. and boundary conditions of the grid-stiffened panel or shell.

Ambur, Damodar R.↗

NASA NTRS1996

Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis

A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.

Ambur, Damodar R.↗