4.1 Overview of the 3-D design process

The 3-D design process has as its origin in the inversely design two-dimensional geometry extracted from a 2-D hypersonic flow-field. This is then coupled with the Nonweiler's waverider approach [10] of inversely carving stream surfaces from inviscid flow-fields. A caret waverider, Figure 5, is chosen as an example because it represents a 3-D geometry that was obtained from a 2-D flow-field. This caret waverider geometry is constructed from a single planer shock wave, AB3B4, as seen in Figure 5. A unique feature of this construction process is that at any cross-section of the waverider geometry there is a wedge that is supported by an oblique shock wave, with these wedges being parallel to the flow.

In reality, the caret waverider is carved from an inverse design approach that relies on the inviscid streamline principle. This principle states that any inviscid streamline can be replaced by a solid wall. The principle also states that replacing the inviscid streamline with a solid wall has no effect on the external flow. Planar inviscid stream surfaces are formed from these inviscid streamlines. These inviscid stream surfaces are then brought together to construct 3-D inviscid waverider geometries and stream tubes. An examination of Figure 5 demonstrates how the streamlines form planar stream surfaces, such as, upper inviscid surfaces, ABB3 and ABB4, or lower stream surfaces, such as, AB1B3 and AB1B4.

This approach is further explained the next sub-section and is demonstrated by the construction of a supersonic 3-D wedge followed by a 3-D supersonic caretshaped geometry. This caret-shaped geometry will then be used to generate supersonic star-shaped geometries of interest.
