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Geometry Modeling Tools for Unstructured Methods

Automated tool set for surface triangulation and volume mesh generation including perturbation, morphing, and surface merging for rapid analysis and design of spacecraft.

Offers rapid grid generation for high fidelity analysis of complete/complex configurations for crew safety, performance, and stability for the Crew Exploration Vehicle or other flight components.


Caption: Apollo Launch Escape Vehicle, M=1.3 a =61 deg, pressure coefficients.

Research Overview
Utilities for Surface Triangulation
Although tetrahedral mesh generation is a fully automated procedure, the user must generate a surface triangulation. Commercially available software is used to generate surface triangulations from CAD data. However, many other tools have been developed at NASA Ames to enhance this process. The program APTRIANG provides a series of comprehensive checks on the integrity of the surface triangulation. It determines whether the surface forms a closed manifold (i.e. is "water tight"), whether there are duplicated points, and whether all surface normals point outward. APTRIANG can read and write a variety of data formats. It can also read structured grids and convert to unstructured datasets.

Another utility, TRISURF, is used to create surface triangulations of the symmetry plane and far-field boundaries. These surfaces are necessary for the application of the unstructured volume mesh generation method.

Volume Grid

Caption: Top left: slice through an unstructured tetrahedral volume grid. Bottom right: slice through a structured hexahedral volume grid.

Perturbation Utilities
Three utilities (APSHAPER, MESHMV, and APMORPH) are available to speed up or automate the process of deforming an existing surface grid of a baseline geometry or mapping the surface from one configuration to another. Small perturbations of an existing shape can be made to significantly improve the performance of an aircraft. An experienced designer can apply shape functions to an aircraft's surface which perturb the surface in some desirable way. APSHAPER makes use of the existing surface grid and applies analytical shape functions over a specified portion of the surface. The tetrahedral cells with faces on the surface are deformed using MESHMV. This can eliminate completely the need to generate a new volume grid for small perturbations. The program will stop if reversed cell volumes are encountered, in which case a new volume mesh would be needed.

Surface grids can also be automatically generated for similar yet different configurations by moving the surfaces from one configuration to another using APMORPH. Surface grid generation for complex configurations can take days to accomplish, whereas APMORPH takes only minutes. This has been very useful for providing analysis checks of a configuration undergoing small geometrical changes as are often encountered at intermediate stages during a design-by-optimization process. An association or mapping function is created between the triangulated surface mesh and a structured or unstructured mesh representing the same baseline geometry. This mapping function is then used to "morph" the baseline triangulated surface onto the surface of the new geometry.

surface trianulations

Left: Merged surface triangulations before application of ICU for a wing/body intersection showing the trailing edge as viewed from above the wing. Right: Merged surface after application of ICU with a significant improvement in the quality of the triangles along the intersection.

Surface Merging Method
The surface merging method utilizes an existing intersection program and a clean-up program, ICU (Intersection Clean Up). The intersection program intersects and removes interior triangles from the joined components, although while accurate surface representation is achieved, poor quality triangles (triangles with small aspect ratios) are formed along the intersections. ICU was developed for improving the quality of unstructured triangulated surface meshes in the vicinity of component intersections. Thus, these programs combined provide a method for automated merging of individual triangulated surfaces. This is a useful procedure for the automated design environment of aircraft or spacecraft that allows for individual component surfaces to be moved or deformed relative to each another without any further grid generation by the user. An example of this is a wing moving upward, downward, or fore and aft on a stationary fuselage. This method requires that the individual aircraft components be triangulated in their entirety to start with. This is often a simpler process than generating surface grids for intersected components. Once the individual components’ surface grids are generated, the component intersections can be found, the triangles inside the configuration can be discarded, and the connections near component intersections can be re-established with reasonably high-quality triangles automatically.

Grid generation is one of the major bottlenecks for analysis and design via numerical optimization methods. This bottleneck can be eliminated when an unstructured mesh is used allowing the first analysis of a new geometry or the commencement of design to be obtained in a few days instead of weeks. The unstructured approach simplifies the handling of complete and complex geometries because only the surface of a configuration needs to be discretized, since the creation of a volume mesh of tetrahedra is automated.

Use of tetrahedral meshes offers several advantages over other grid generation methods. The tetrahedral method offers a smooth gradation of the cells in the volume grid. A very gradual and smooth transition from the smaller sized cells at the configuration surface to the larger sized cells at the far-field is important to obtain accurate computational solutions on the surface. This is an advantage relative to unstructured Cartesian methods which must transition in cell size discontinuously, typically by a factor of 2 or more between adjacent grid densities. Grid points are naturally conserved using unstructured methods compared with conventional structured methods; i.e. the number of points used to represent the surface is not carried to the far-field boundaries as it is for structured methods.