INTRODUCTION
In recent years NURBS (Non-Uniform Rational B-Splines) have been used in the parametric modeling of airfoil structures. This methodology has been shown to have some distinct advantages over conventional “point-data” surface modeling techniques. Among these advantages are the ability to discretize the geometry to any level of fidelity, the inherent smoothing of the surface definition – if desired, and the ability to map analytical data onto the geometric definition. As CAD/CAM packages have added NURBS-based surface modeling capabilities the ability to take advantage of some capabilities of NURBS has become available to designers. Any given analytical discipline can discritize an airfoil as deemed appropriate, perform an analysis, and then map the resulting analytical data back onto the geometry, which then becomes available to other disciples. Each NURBS-based definition of a design iteration can “carry” with it all analytical data associated with that given design. Though the initial NURBS-based definition of a given airfoil may be provided by a CAD/CAM package, the additional desired functionality of discretizing the geometric definition for a given discipline’s analysis and mapping analytical data back onto the surface is not generally provided by these packages and must be obtained by the developing additional software.
BACKGROUND
SABER (Structural Airfoil and Blade Engineering Routines), a software tool has being developed at the NASA Glenn Research Center and at the University of Akron, is a NURBS-based special purpose finite element structural model generator for turbomachinery blading and airfoils. When provided with a NURB definition of an airfoil’s geometry, SABER can generate various types of finite element meshes for several popular commercial finite element solvers. If NURB field data, such as pressures and temperatures are provided, SABER will interpolate the temperature or pressure data to the finite element model nodes. SABER also enables users to specify load conditions, displacement boundary conditions, and analysis control parameters.
WHAT’S A NURB? A NURB (Non-Uniform Rational B-Splines) is a mapping of fitted data to a parametric space. The NURB is defined as a series of overlapping functions, termed “basis functions”. These individual functions combine to define a parametrically continuous definition (with any number of independent variables and any number of dependent variables). Each overlapping function is only active over a discrete parametric range but they combine to behave as a single continuous function while maintaining derivative continuity.
HOW SABER WORKS. SABER utilizes NURBS for the modeling of geometry as well as allowing for the fitting of analysis data, “attaching” the analysis data to the geometric definition of the structure. The associating of analysis data to the geometry definition allows for a more seamless sharing of data between analysis disciplines and quicker design/analysis cycles. The ability to map ancillary data to a NURB is done by defining another (i.e. child) NURB whose dependent variables consist of the parameter values of the original (i.e. parent) NURB as well as any additional data to be associated to the point prescribed by those parameter values. When the child NURB is fit, a continuous function is defined which describes the mapping of the supplementary data to locations in the parent NURB’s independent-variable space. Sampling of the child NURB yields the data associated with the parent NURB as well as parameter values that describe the point of association in the parent NURB.
No limit on the number of dependent or independent variables exists nor is there any limit to the number of child NURBS associated with a given parent NURB. Multiple hierarchical levels of child NURBS can also be defined, where the child of one NURB is the parent of another. This means of mapping auxiliary data to a NURB is referred to as subranging.
Inside SABER, analysis data (e.g. pressure and temperature) is associated with a given airfoil’s geometry via the methods described above. Since the geometry and the analysis data are defined as continuous functions, discretization for analysis can be done to best suit a given discipline’s requirements. When an analysis is completed, that discipline’s results can be mapped backed to the geometry for the next analyst or for the next design iteration. Multiple subranges can be included to relate various design/analysis conditions back to the corresponding geometry. A data storage repository that is available to each discipline and some attention to version control is all that is required for the sharing of the data once the NURB-enabled software tools are in place. SABER is capable of generating finite element input decks for several common commercial analysis codes using a variety of finite element types with various boundary conditions. Point-data files can also be generated by SABER using several prevalent file formats.
SABER is written in C++ and exists in a batch version on the SGI, SUN, DEC, and Windows 2000 platforms. A graphical user interface version currently exist on the Silicon Graphics workstation platform utilizing the Open Inventor 3D-rendering graphics package for the display of airfoil and flowpath geometries. SABER‘s graphical user interface on the SGI is written using X/Motif. A Windows 2000 graphical user interface version is currently under development using Open-GL 3D-rendering graphics and Microsoft Foundation Classes for the graphical user interface.
SABER has it’s own scripting language, the SABER Command Language (SCL), and during interactive execution SABER generates a script that refects the actions of the user. The generated script and can be executed by SABER at a later time in either interactive or batch modes. SABER also generates a logfile in HTML format to document the current execution session. The HTML logfile may be viewed at any time from the graphical interface (PC-only).
(SGI) Hot to Cold Shape Correction
SABER utilizes the DTNURBS library in many of it’s NURBS related routines. The DTNURBS library is a set of N-dimensional NURB math routines written in FORTRAN and developed by Boeing Computer Services through the support of the David Taylor Naval Surface Warfare Center. Currently, Boeing Computer Services is rewritting the library in C++ under the name “GEML” but it is still in beta testing.
A few words about DTNURBS from Bob Ames of the US NAVY:
“The use of N-Dimensional NURB surfaces provides a powerful technique for inclusion of analytical and physical properties in three dimensional objects of arbitrary shape and dimension. The DTNURBS math library allows for modeling and interpolation of any number of geometric and analysis variables; and by any number of independant parameters such as time, frequency, or iteration. The Navy has applied this technology to virtual prototyping for ship design. and this technology has also been applied to the design of products as diverse as microwave power tubes, non-destructive testing, medical modeling, and jet engine modeling and simulation at NASA. … N-Dimensional NURBS, … representation of engineering information can be applied to tasks such as the representation of tolerence variations in CAD geometry, the representation of electromagnetic fields, the mapping between different types of grid representations and analysis of engineering data, the the modeling of prestressed solids, or the storing of machining knowledge in part geometry.”