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NASA NTRS2014

Three-Dimensional Imaging and Numerical Reconstruction of Graphite/Epoxy Composite Microstructure Based on Ultra-High Resolution X-Ray Computed Tomography

A combined experimental and computational study aimed at high-resolution 3D imaging, visualization, and numerical reconstruction of fiber-reinforced polymer microstructures at the fiber length scale is presented. To this end, a sample of graphite/epoxy composite was imaged at sub-micron resolution using a 3D X-ray computed tomography microscope. Next, a novel segmentation algorithm was developed, based on concepts adopted from computer vision and multi-target tracking, to detect and estimate, with high accuracy, the position of individual fibers in a volume of the imaged composite. In the current implementation, the segmentation algorithm was based on Global Nearest Neighbor data-association architecture, a Kalman filter estimator, and several novel algorithms for virtualfiber stitching, smoothing, and overlap removal. The segmentation algorithm was used on a sub-volume of the imaged composite, detecting 508 individual fibers. The segmentation data were qualitatively compared to the tomographic data, demonstrating high accuracy of the numerical reconstruction. Moreover, the data were used to quantify a) the relative distribution of individual-fiber cross sections within the imaged sub-volume, and b) the local fiber misorientation relative to the global fiber axis. Finally, the segmentation data were converted using commercially available finite element (FE) software to generate a detailed FE mesh of the composite volume. The methodology described herein demonstrates the feasibility of realizing an FE-based, virtual-testing framework for graphite/fiber composites at the constituent level.

Czabaj, M. W.↗

NASA NTRS2008

Rotor Airloads Prediction Using Unstructured Meshes and Loose CFD/CSD Coupling

The FUN3D unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been modified to allow prediction of trimmed rotorcraft airloads. The trim of the rotorcraft and the aeroelastic deformation of the rotor blades are accounted for via loose coupling with the CAMRAD II rotorcraft computational structural dynamics code. The set of codes is used to analyze the HART-II Baseline, Minimum Noise and Minimum Vibration test conditions. The loose coupling approach is found to be stable and convergent for the cases considered. Comparison of the resulting airloads and structural deformations with experimentally measured data is presented. The effect of grid resolution and temporal accuracy is examined. Rotorcraft airloads prediction presents a very substantial challenge for Computational Fluid Dynamics (CFD). Not only must the unsteady nature of the flow be accurately modeled, but since most rotorcraft blades are not structurally stiff, an accurate simulation must account for the blade structural dynamics. In addition, trim of the rotorcraft to desired thrust and moment targets depends on both aerodynamic loads and structural deformation, and vice versa. Further, interaction of the fuselage with the rotor flow field can be important, so that relative motion between the blades and the fuselage must be accommodated. Thus a complete simulation requires coupled aerodynamics, structures and trim, with the ability to model geometrically complex configurations. NASA has recently initiated a Subsonic Rotary Wing (SRW) Project under the overall Fundamental Aeronautics Program. Within the context of SRW are efforts aimed at furthering the state of the art of high-fidelity rotorcraft flow simulations, using both structured and unstructured meshes. Structured-mesh solvers have an advantage in computation speed, but even though remarkably complex configurations may be accommodated using the overset grid approach, generation of complex structured-mesh systems can require months to set up. As a result, many rotorcraft simulations using structured-grid CFD neglect the fuselage. On the other hand, unstructured-mesh solvers are easily able to handle complex geometries, but suffer from slower execution speed. However, advances in both computer hardware and CFD algorithms have made previously state-of-the-art computations routine for unstructured-mesh solvers, so that rotorcraft simulations using unstructured grids are now viable. The aim of the present work is to develop a first principles rotorcraft simulation tool based on an unstructured CFD solver.

Biedron, Robert T.↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS1981

Summary of results of January climate simulations with the GISS coarse-mesh model

The large scale climates generated by extended runs of the model are relatively independent of the initial atmospheric conditions, if the first few months of each simulation are discarded. The perpetual January simulations with a specified SST field produced excessive snow accumulation over the continents of the Northern Hemisphere. Mass exchanges between the cold (warm) continents and the warm (cold) adjacent oceans produced significant surface pressure changes over the oceans as well as over the land. The effect of terrain and terrain elevation on the amount of precipitation was examined. The evaporation of continental moisture was calculated to cause large increases in precipitation over the continents.

Spar, J.↗

NASA NTRSDate not supplied

Simulating High Energy Dynamic Impact of IM7/PEKK Continuous Fiber Laminated Thermoplastic Composite using Open Hole Coupon Experiments

The use of advanced thermoplastic composites (TPC) for structural applications in the aerospace and automotive industries has grown increasingly popular due to their high performance, high manufactured part output, and sustainability. Enhancing verification simulations of the progressive failure in TPCs at the coupon scale is needed to better validate advanced composite material models at larger length scales, such as element level panels. MAT_213, a tabulated composite material model, has been applied to simulate high velocity dynamic impact (HEDI) and is integrated in the LS-DYNA explicit finite element (FE) software. Previous efforts using MAT_213 have calibrated HEDI simulated failures with experimental data. Traditionally simulations have relied on a structured mesh to represent quasi-isotropic panels. For this study, a continuous fiber unidirectional tape, IM7/PEKK, was analyzed through a series of verification studies of notched laminate coupons, then validation analyses of quasi-isotropic panels under HEDI were compared with experimental data. Experiments using unidirectional TPC were performed to obtain tabulated stress vs strain curves using Digital Image Correlation (DIC) for input into MAT_213. Next, notched coupon experiments were used as an intermediate step to calibrate the damage and failure behavior in MAT_213. Lastly, investigations into differences between HEDI simulations using a fiber aligned mesh were compared with experimental failure patterns and damage sizes. The use of experimentally generated material behavior along with selective mesh layout improved HEDI predictions with minimal material parameter calibration.

Polymer matrix composites↗

NASA NTRS2010

Evaluation of Solid Modeling Software for Finite Element Analysis of Woven Ceramic Matrix Composites

Three computer programs, used for the purpose of generating 3-D finite element models of the Repeating Unit Cell (RUC) of a textile, were examined for suitability to model woven Ceramic Matrix Composites (CMCs). The programs evaluated were the open-source available TexGen, the commercially available WiseTex, and the proprietary Composite Material Evaluator (COMATE). A five-harness-satin (5HS) weave for a melt-infiltrated (MI) silicon carbide matrix and silicon carbide fiber was selected as an example problem and the programs were tested for their ability to generate a finite element model of the RUC. The programs were also evaluated for ease-of-use and capability, particularly for the capability to introduce various defect types such as porosity, ply shifting, and nesting of a laminate. Overall, it was found that TexGen and WiseTex were useful for generating solid models of the tow geometry; however, there was a lack of consistency in generating well-conditioned finite element meshes of the tows and matrix. TexGen and WiseTex were both capable of allowing collective and individual shifting of tows within a ply and WiseTex also had a ply nesting capability. TexGen and WiseTex were sufficiently userfriendly and both included a Graphical User Interface (GUI). COMATE was satisfactory in generating a 5HS finite element mesh of an idealized weave geometry but COMATE lacked a GUI and was limited to only 5HS and 8HS weaves compared to the larger amount of weave selections available with TexGen and WiseTex.

Nemeth, Noel N.↗

NASA NTRSDate not supplied

Rapid Hypersonic Simulations using US3D and Pointwise

For hypersonic simulations, unstructured flow solvers typically have problems predicting surface heat fluxes when strong shocks are present. To address these issues, this paper outlines a workflow that applies best practices developed for structured grids to unstructured meshes. In addition, unstructured grid generation can significantly reduce the time required to create quality grids for complex geometries. Several examples are computed using DPLR, a structured grid flow solver, and US3D flow, an unstructured mesh solver. Results from the two codes are compared, and they show excellent agreement. Overall, the unstructured grid workflow offers a viable and attractive alternative for hypersonic simulations.

C. Tang↗

NASA NTRSDate not supplied

Rapid Hypersonic Simulations using US3D and Pointwise

Chun Tang↗

NASA NTRS2000

An Application of the Quadrature-Free Discontinuous Galerkin Method

The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.

Lockard, David P.↗

NASA NTRS1983

Adaptive mesh schemes based on grid speeds

Successful methods for generating solution adaptive grids using grid speeds are reviewed in this paper. The computational mesh is constructed by integrating the grid speeds as opposed to solving a steady grid equation. Advantages and disadvantages for each grid speed scheme are discussed and a number of examples of grids produced with the various schemes are presented. Suggestions are made for the development of new schemes based upon a form of Euler's expansion formula for the grid and the equi-distribution of some parameter over the mesh. Consideration is also given to grid skewness for the multidimensional schemes.

Anderson, D. A.↗

NASA NTRS1996

Adaptive grid methods for RLV environment assessment and nozzle analysis

Rapid access to highly accurate data about complex configurations is needed for multi-disciplinary optimization and design. In order to efficiently meet these requirements a closer coupling between the analysis algorithms and the discretization process is needed. In some cases, such as free surface, temporally varying geometries, and fluid structure interaction, the need is unavoidable. In other cases the need is to rapidly generate and modify high quality grids. Techniques such as unstructured and/or solution-adaptive methods can be used to speed the grid generation process and to automatically cluster mesh points in regions of interest. Global features of the flow can be significantly affected by isolated regions of inadequately resolved flow. These regions may not exhibit high gradients and can be difficult to detect. Thus excessive resolution in certain regions does not necessarily increase the accuracy of the overall solution. Several approaches have been employed for both structured and unstructured grid adaption. The most widely used involve grid point redistribution, local grid point enrichment/derefinement or local modification of the actual flow solver. However, the success of any one of these methods ultimately depends on the feature detection algorithm used to determine solution domain regions which require a fine mesh for their accurate representation. Typically, weight functions are constructed to mimic the local truncation error and may require substantial user input. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. These weight functions can then be used to construct blending functions for algebraic redistribution, interpolation functions for unstructured grid generation, forcing functions to attract/repel points in an elliptic system, or to trigger local refinement, based upon application of an equidistribution principle. The popularity of solution-adaptive techniques is growing in tandem with unstructured methods. The difficultly of precisely controlling mesh densities and orientations with current unstructured grid generation systems has driven the use of solution-adaptive meshing. Use of derivatives of density or pressure are widely used for construction of such weight functions, and have been proven very successful for inviscid flows with shocks. However, less success has been realized for flowfields with viscous layers, vortices or shocks of disparate strength. It is difficult to maintain the appropriate mesh point spacing in the various regions which require a fine spacing for adequate resolution. Mesh points often migrate from important regions due to refinement of dominant features. An example of this is the well know tendency of adaptive methods to increase the resolution of shocks in the flowfield around airfoils, but in the incorrect location due to inadequate resolution of the stagnation region. This problem has been the motivation for this research.

Thornburg, Hugh J.↗

NASA NTRS1988

Generation of a crowned pinion tooth surface by a plane

The topology of a crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is described. The geometry of the modified pinion tooth surface and of the regular involute gear tooth surface is discussed. The tooth contact analysis between the meshing surfaces is also described. Generating a modified pinion tooth surface by a plane whose motion is controlled by a 5-degree-of-freedom system is investigated. The numerical results included indicate that the transmission error remains low as the gears are misaligned.

Litvin, F. L.↗

NASA NTRS2010

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗

NASA NTRS2017

JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere

An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

geophysical fluid dynamics↗

NASA NTRS2011

Image Segmentation, Registration, Compression, and Matching

A novel computational framework was developed of a 2D affine invariant matching exploiting a parameter space. Named as affine invariant parameter space (AIPS), the technique can be applied to many image-processing and computer-vision problems, including image registration, template matching, and object tracking from image sequence. The AIPS is formed by the parameters in an affine combination of a set of feature points in the image plane. In cases where the entire image can be assumed to have undergone a single affine transformation, the new AIPS match metric and matching framework becomes very effective (compared with the state-of-the-art methods at the time of this reporting). No knowledge about scaling or any other transformation parameters need to be known a priori to apply the AIPS framework. An automated suite of software tools has been created to provide accurate image segmentation (for data cleaning) and high-quality 2D image and 3D surface registration (for fusing multi-resolution terrain, image, and map data). These tools are capable of supporting existing GIS toolkits already in the marketplace, and will also be usable in a stand-alone fashion. The toolkit applies novel algorithmic approaches for image segmentation, feature extraction, and registration of 2D imagery and 3D surface data, which supports first-pass, batched, fully automatic feature extraction (for segmentation), and registration. A hierarchical and adaptive approach is taken for achieving automatic feature extraction, segmentation, and registration. Surface registration is the process of aligning two (or more) data sets to a common coordinate system, during which the transformation between their different coordinate systems is determined. Also developed here are a novel, volumetric surface modeling and compression technique that provide both quality-guaranteed mesh surface approximations and compaction of the model sizes by efficiently coding the geometry and connectivity/topology components of the generated models. The highly efficient triangular mesh compression compacts the connectivity information at the rate of 1.5-4 bits per vertex (on average for triangle meshes), while reducing the 3D geometry by 40-50 percent. Finally, taking into consideration the characteristics of 3D terrain data, and using the innovative, regularized binary decomposition mesh modeling, a multistage, pattern-drive modeling, and compression technique has been developed to provide an effective framework for compressing digital elevation model (DEM) surfaces, high-resolution aerial imagery, and other types of NASA data.

Yadegar, Jacob↗

NASA NTRS1983

A Computer Program for the Calculation of Three-Dimensional Transonic Nacelle/Inlet Flowfields

A highly efficient computer analysis was developed for predicting transonic nacelle/inlet flowfields. This algorithm can compute the three dimensional transonic flowfield about axisymmetric (or asymmetric) nacelle/inlet configurations at zero or nonzero incidence. The flowfield is determined by solving the full-potential equation in conservative form on a body-fitted curvilinear computational mesh. The difference equations are solved using the AF2 approximate factorization scheme. This report presents a discussion of the computational methods used to both generate the body-fitted curvilinear mesh and to obtain the inviscid flow solution. Computed results and correlations with existing methods and experiment are presented. Also presented are discussions on the organization of the grid generation (NGRIDA) computer program and the flow solution (NACELLE) computer program, descriptions of the respective subroutines, definitions of the required input parameters for both algorithms, a brief discussion on interpretation of the output, and sample cases to illustrate application of the analysis.

Vadyak, J.↗

NASA NTRS1981

Do initial conditions matter? A comparison of model climatologies generated from different initial states

A coarse mesh (8 by 10) 7 layer global climate model was used to compute 15 months of meteorological history in two perpetual January experiments on a water planet (without continents) with a zonally symmetric climatological January sea surface temperature field. In the first of the two water planet experiments the initial atmospheric state was a set of zonal mean values of specific humidity, temperature, and wind at each latitude. In the second experiment the model was initialized with globally uniform mean values of specific humidity and temperature on each sigma level surface, constant surface pressure (1010 mb), and zero wind everywhere. A comparison was made of the mean January climatic states generated by the two water planet experiments. The first two months of each 15 January run were discarded, and 13 month averages were computed from months 3 through 15.

Spar, J.↗