C5 Transport Aircraft Geometry Repair

An example of work described in the paper "Gridgen's Synergistic Implementation of CAD and Grid Geometry Modeling", from the proceedings of the 5th International Conference on Numerical Grid Generation in Computational Field Simulations, held at Mississippi State University, 01-05 Apr 96.

The goal of this study is to demonstrate some of Gridgen's geometry modeling tools that are useful in repairing geometry models in preparation for gridding. Useful features of Gridgen shown in this study are:

1. removing extraneous components from a geometry model to make the grid generation process simpler,
2. copying and translating pieces of geometry to replace missing parts of a geometry model,
3. constructing surfaces of revolution to build axisymmetric parts, and
4. constructing polyconic surfaces to fair over gaps with a smooth angular transition.

The starting point for this study is an IGES file containing geometry information for a Lockheed C-5A Galaxy aircraft. The original IGES file includes 431 entities, consisting of 412 curves and 19 surfaces. They are shown in Figure 1. Most of the geometry needed to build a grid for external airflow analysis of this aircraft is in the file: aircraft fuselage, T-tail, nacelles, pylons, wings, and front landing gear pod. The model includes additional geometric details not needed for the analysis: front and rear landing gear, pilot seats, and wing and fuselage bulkheads at a variety of butt-lines and fuselage stations.

Delete extraneous geometry

The first step in the repair of this model is to remove the components not needed for a CFD analysis of the external airflow. All of the wing and fuselage bulkheads are deleted as are the seats, landing gear, and other unidentifiable geometry components. Due to the geometric similarity between the engines, most of the components are removed from three of the four engines. The lone engine pod saved is on the outboard right side, which can easily be copied and translated into the other three engine locations after cleanup. After this step the geometry contains approximately 60 entities, including 18 surfaces and more than 40 curves. The cleanup step is not required, but by removing some of the clutter from the model the rest of the grid generation process is simplified. Another option would be to turn off display of extraneous entities, but keep them in the database.

After cleanup, three major problem areas are identified:

• the wings do not intersect the fuselage,
• the leading edges of the nacelles and some of the internal nacelle surfaces are missing, and
• the vertical stabilizer does not intersect the T-tail.

The repair strategies used in each of these regions are discussed below.

Repair the wing-fuselage junction

As Figure 2 illustrates, the wing does not intersect the fuselage. In regions such as this one, you can construct geometry components that will complete the geometry definition and make it "analysis-ready." Whenever geometry components are missing, you run a risk of constructing surfaces that stray from the design shape. However, if the design shape is unavailable, little recourse exists. You have to rely on engineering judgement to construct pieces of the geometry that look reasonable.

The gap between the wing and fuselage is filled by constructing a small surface that begins at the inboard station of the wing and extends inward, crossing through the fuselage. Since the wing has little taper at the root, this is done by copying the inboard portion of the wing surface and translating it inward to extend the wing through the fuselage. These wing extension surfaces are displayed in Figure 3. Then, surface - surface intersections are computed between each wing and the two fuselage surfaces. The resulting six intersection curves are also displayed in the figure. This completes the geometry repair in this region, since enough definition exists to proceed with grid generation.

Add missing engine pod geometry

The engine pods present a different set of geometric problems. Here, the only geometry components are a surface describing the nacelle pylon, a surface defining the fore region of the outer nacelle, and a series of cross-sectional curves describing the internal flow diverter shape at various stations extending from downstream of the leading edge through the engine exhaust. The leading edge of the nacelle, the inner nacelle surface, the flow diverter surface, and the engine are missing (see Figure 4).

The surface of the flow diverter is constructed from the set of cross-section curves. This is done by forming ruled surfaces connecting neighboring cross section curves, six of which are displayed in Figure 5.

The cross-sectional shape of the nacelle leading edge is a circular arc. The arc is formed to maintain slope continuity with both the upper nacelle surface and the internal sections.

The shape of the internal nacelle is formed using an Akima curve with control points at the vertical crown points of the internal cross-sections. The Akima curve works best in this case because the sections are arranged at widely varying distances. Both the circular arc and Akima curve generated at the vertical stations are shown in Figure 6.

Finally, two surfaces of revolution are formed by rotating the circular arc and Akima curve described above around the nacelle centerline axis. The resulting leading edge and inner nacelle surfaces are also displayed in Figure 6. It should be noted that the faceted appearance of the surfaces of revolution in this figure is due solely to the rendering algorithm used for surface display. The surface itself is continuous throughout.

Repair the vertical stabilizer/T-tail junction

The final repair to the test geometry is at the junction of the vertical and horizontal tails. Figure 7 shows a gap between the vertical tail surface and the pod from which the horizontal tails protrude. One perfectly viable technique to fill the gap, and probably the simplest solution, would be to extend the tail into the pod and then to calculate intersections with the pod, following the technique described above for the wing - fuselage junction. Instead, to illustrate another construction technique available in Gridgen, polyconic surfaces are used to fair the gap with a fillet-type surface that blends smoothly into both the tail and pod.

The polyconic surface requires a minimum of three forming curves: two rail curves that define the boundaries of the polyconic, and a slope control (tangent intersection) curve.

A curve at the top of the tail surface is extracted from the surface to serve as the first rail curve. The second rail curve is generated in several steps. First, a Catmull-Rom curve is used to form an enlarged upper tail cross-section shape. Next, the curve is copied and translated upward into the pod, and a ruled surface is formed from the two curves. The ruled surface is intersected with the pod surface, resulting in an enlarged tail section shaped intersection curve lying on the pod. This is used as the second rail curve.

The slope control curve is formed in a similar manner: copy and translate the upper tail section upward into the pod, form a ruled surface, and then form intersection curves between the pod and ruled surface. The intersection curves are well-suited for the slope control curves because they are on the pod surface and nearly parallel to the tail surface.

The polyconic surfaces formed using these curves are illustrated in Figure 8. Note that the surfaces blend from the tail to the pod with slope continuity across surfaces.

Conclusion

This case study has shown examples of several of the geometry cleanup and construction tools available in Gridgen to simplify the task of generating complex multiple block grids. While not a full-fledged CAD system with all it s clutter, Gridgen includes the geometry creation and modification features that you need to prepare a model for analysis.