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A technique is presented for triangulation of NURBS surfaces. This technique is built upon an advancing front technique combined with grid point projection. This combined approach has been successfully implemented for structured and unstructured grids.
A simple and efficient computational method is presented for unstructured surface grid generation. This method is built upon an advancing front technique combined with grid projection. The projection technique is based on a Newton-Raphson method. This combined approach has been successfully implemented for structured and unstructured grids. In this paper, the implementation for unstructured grid is discussed.
A very important, but often overlooked step in grid generation is acquiring a suitable geometry definition of the vehicle to be analyzed. In the past, geometry was usually obtained by generating a number of cross-sections of each component. A number of recent efforts have focussed on non-uniform rational B-spline surfaces (NURBS) to provide as single type of analytic surface to deal with inside the grid generator. This approach has required the development of tools to read other types of surfaces and convert them, either exactly or by approximation, into a NURBS surface. This paper describes a more generic parametric evaluator approach, which does not rely on a particular surface type internal to the grid generation system and is less restrictive in the number of surface types that can be represented exactly. This approach has been implemented in the McDonnell Douglas grid generation system, MACGS, and offers direct access to all types of surfaces from a Unigraphics part file.
The purpose of this paper is to present an algorithm for using NonUniform Rational B-Spline (NURBS) representation in an aeroelastic loop. The algorithm is based on creating a least-squares NURBS surface representing the aeroelastic defection. The resulting NURBS surfaces are used to update either the original Computer- Aided Design (CAD) model, Computational Structural Mechanics (CSM) grid or the Computational Fluid Dynamics (CFD) grid. Results are presented for a generic High-Speed Civil Transport (HSCT).
This paper presents some recently added capabilities to RAGGS, Rockwell Automated Grid Generation System. Included are the trimmed surface handling and display capability and structures and unstructured grid generation on trimmed Bezier and NURBS (non-uniform rational B-spline surfaces) quilted surfaces. Samples are given to demonstrate the new capabilities.
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
In the field of Grid Generation and the CAD/CAM, there are numerous geometry output formats which require the designer to spend a great deal of time manipulating geometrical entities in order to achieve a useful sculptured geometrical description for grid generation. Also in this process, there is a danger of losing fidelity of the geometry under consideration. This stresses the importance of a standard geometry definition for the communication link between varying CAD/CAM and grid system. The IGES (Initial Graphics Exchange Specification) file is a widely used communication between CAD/CAM and the analysis tools. The scientists at NASA Research Centers - including NASA Ames, NASA Langley, NASA Lewis, NASA Marshall - have recognized this importance and, therefore, in 1992 they formed the committee of the 'NASA-IGES' which is the subset of the standard IGES. This committee stresses the importance and encourages the CFD community to use the standard IGES file for the interface between the CAD/CAM and CFD analysis. Also, two of the IGES entities -- the NURBS Curve (Entity 126) and NURBS Surface (Entity 128) -- which have many useful geometric properties -- like the convex hull property, local control property and affine invariance, also widely utilized analytical geometries can be accurately represented using NURBS. This is important in today grid generation tools because of the emphasis of the interactive design. To satisfy the geometry transformation between the CAD/CAM system and Grid Generation field, the CAGI (Computer Aided Geometry Design) developed, which include the Geometry Transformation, Geometry Manipulation and Geometry Generation as well as the user interface. This paper will present the successful development IGES file transformer and application of NURBS definition in the grid generation.
A new metthodology for interactive design of turbomachinery blades is presented. Software implementation of the meth- ods provides a user interface that is intuitive to aero-designers while operating with standardized geometric forms. The primary contribution is that blade sections may be defined with respect to general surfaces of revolution which may be defined to represent the path of fluid flow through the turbomachine. The completed blade design is represented as a non-uniform rational B-spline (NURBS) surface and is written to a standard IGES file which is portable to most design, analysis, and manufacturing applications.
The grid generation used to model rotorcraft configurations for Computational Fluid Dynamics (CFD) analysis is highly complicated and time consuming. The highly complex geometry and irregular shapes encountered in entire rotorcraft configurations are typically modeled using overset grids. Another promising approach is to utilize unstructured grid methods. With either approach the majority of time is spent manually setting up the topology. For less complicated geometries such as isolated rotor blades, less time is obviously required. This paper discusses the capabilities of a tool called Rotor blade Optimized Topology Organizer and Renderer(ROTOR) being developed to quickly generate block structured grids and unstructured tetrahedral grids about isolated blades. The key algorithm uses individual airfoil sections to construct a Non-Uniform Rational B-Spline(NURBS) surface representation of the rotor blade. This continuous surface definition can be queried to define the block topology used in constructing a structured mesh around the rotor blade. Alternatively, the surface definition can be used to define the surface patches and grid cell spacing requirements for generating unstructured surface and volume grids. Presently, the primary output for ROTOR is block structured grids using 0-H and H-H topologies suitable for full-potential solvers. This paper will discuss the present capabilities of the tool and highlight future work.
GRIDGEN is a government domain software package for interactive generation of multiple block grids around general configurations. Though it has been freely available since 1989, it has not been widely embraced by the internal flow community due to a misconception that it was designed for external flow use only. In reality GRIDGEN has always worked for internal flow applications, and GRIDGEN ongoing enhancements are increasing the quality of and efficiency with which grids for external and internal flow problems may be constructed. The software consists of four codes used to perform the four steps of the grid generation process. GRIDBLOCK is first used to decompose the flow domain into a collection of component blocks and then to establish interblock connections and flow solver boundary conditions. GRIDGEN2D is then used to generate surface grids on the outer shell of each component block. GRIDGEN3D generates grid points on the interior of each block, and finally GRIDVUE3D is used to inspect the resulting multiple block grid. Three of these codes (GRIDBLOCK, GRIDGEN2D, and GRIDVUE3D) are highly interactive and graphical in nature, and currently run on Silicon Graphics, Inc., and IBM RS/6000 workstations. The lone batch code (GRIDGEN3D) may be run on any of several Unix based platforms. Surface grid generation in GRIDGEN2D is being improved with the addition of higher order surface definitions (NURBS and parametric surfaces input in IGES format and bicubic surfaces input in PATRAN Neutral File format) and double precision mathematics. In addition, two types of automation have been added to GRIDGEN2D that reduce the learning curve slope for new users and eliminate work for experienced users. Volume grid generation using GRIDGEN3D has been improved via the addition of an advanced hybrid control function formulation that provides both orthogonality and clustering control at the block faces and clustering control on the block interior.
Progress realized in the development of a Computer Aided Grid Interface (CAGI) software system in integrating CAD/CAM geometric system output and/or Interactive Graphics Exchange Standard (IGES) files, geometry manipulations associated with grid generation, and robust grid generation methodologies is presented. CAGI is being developed in a modular fashion and will offer fast, efficient and economical response to geometry/grid preparation, allowing the ability to upgrade basic geometry in a step-by-step fashion interactively and under permanent visual control along with minimizing the differences between the actual hardware surface descriptions and corresponding numerical analog. The computer code GENIE is used as a basis. The Non-Uniform Rational B-Splines (NURBS) representation of sculptured surfaces is utilized for surface grid redistribution. The computer aided analysis system, PATRAN, is adapted as a CAD/CAM system. The progress realized in NURBS surface grid generation, the development of IGES transformer, and geometry adaption using PATRAN will be presented along with their applicability to grid generation associated with rocket propulsion applications.
The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.
The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code "fixp3d". The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a "visually" common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect the second surface. No two intersection relationships will result in a common intersection point of three surfaces. The output files of iPatch are IGES, d3m, and mapbc files that define the CFD geometry in VGRID format. The IGES file gives the NURBS definition of the outer mold line in the geometry. The d3m file defines how the outer mold line is broken into surface patches whose boundary curves are defined by points. The mapbc file specifies what the boundary condition is on each patch and the corresponding NURBS surface definition of each non-planar patch in the IGES file.
This document specifies a subset of an existing product data exchange specification that is widely used in industry and government. The existing document is called the Initial Graphics Exchange Specification. This document, a subset of IGES, is intended for engineers analyzing product performance using tools such as computational fluid dynamics (CFD) software. This document specifies how to define mathematically and exchange the geometric model of an object. The geometry is represented utilizing nonuniform rational B-splines (NURBS) curves and surfaces. Only surface models are represented; no solid model representation is included. This specification does not include most of the other types of product information available in IGES (e.g., no material properties or surface finish properties) and does not provide all the specific file format details of IGES. The data exchange protocol specified in this document is fully conforming to the American National Standard (ANSI) IGES 5.2.
The N2B hybrid wing body aircraft was conceptually designed to meet environmental and performance goals for the N+2 generation transport set by the Subsonic Fixed Wing project of NASA Fundamental Aeronautics Program. In the present study, flow simulations are conducted around the N2B configuration by a Reynolds-averaged Navier-Stokes flow solver using unstructured meshes. Boundary conditions at engine fan face and nozzle exhaust planes are provided by the NPSS thermodynamic engine cycle model. The flow simulations reveal challenging design issues arising from boundary layer ingestion offset inlet and airframe-propulsion integration. Adjoint-based optimal designs are then conducted for the inlet shape to minimize the airframe drag force and flow distortion at fan faces. Design surfaces are parameterized by NURBS, and the cowl lip geometry is modified by a spring analogy approach. By the drag minimization design, flow separation on the cowl surfaces are almost removed, and shock wave strength got remarkably reduced. For the distortion minimization design, a circumferential distortion indicator DPCP(sub avg) is adopted as the design objective and diffuser bottom and side wall surfaces are perturbed for the design. The distortion minimization results in a 12.5 % reduction in the objective function.
This grant was initiated in April 1993 and completed in September 1996. The primary goal of the project was to exploit the emerging defacto CAD standard of Non- Uniform Rational B-spline (NURBS) based curve and surface geometry to integrate and streamline the process of turbomachinery structural analysis. We focused our efforts on critical geometric modeling challenges typically posed by the requirements of structural analysts. We developed a suite of software tools that facilitate pre- and post-processing of NURBS-based turbomachinery blade models for finite element structural analyses. We also developed tools to facilitate the modeling of blades in their manufactured (or cold) state based on nominal operating shape and conditions. All of the software developed in the course of this research is written in the C++ language using the Iris Inventor 3D graphical interface tool-kit from Silicon Graphics. In addition to enhanced modularity, improved maintainability, and efficient prototype development, this design facilitates the re-use of code developed for other NASA projects and provides a uniform and professional 'look and feel' for all applications developed by the Iowa State Team.
The algorithm for surface modeling and volume grid generation using parametric Non-Uniform Rational B-splines (NURBS) geometric representation are presented. The enhanced re-parameterization algorithm which can yield a desired physical distribution on the curve, surface, and volume is also presented. This approach bridges the gap between computer aided design surface/volume definition and surface/volume grid generation.
Two distinct parametrization procedures of generating free-form surfaces to represent aerospace vehicles are presented. The first procedure is the representation using spline functions such as nonuniform rational b-splines (NURBS) and the second is a novel (geometrical) parametrization using solutions to a suitably chosen partial differential equation. The main idea is to develop a surface which is more versatile and can be used in an optimization process. Unstructured volume grid is generated by an advancing front algorithm and solutions obtained using an Euler solver. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an automatic differentiator precompiler software tool. Aerodynamic shape optimization of a complete aircraft with twenty four design variables is performed. High speed civil transport aircraft (HSCT) configurations are targeted to demonstrate the process.