Why FlightStream?

Industry Need

Current industry trends point toward an increasing use of optimization-based design principles in conceptual design. For complex systems, optimizer routines require hundreds or thousands of design evaluations. Since each of these designs must be tested for aerodynamic or fluid-dynamic performance, a balance between minimizing the computation time versus maintaining the fidelity of the solution and the validity of the physics must be made. This balancing represents a major limitation in the comprehensive use of multidisciplinary-optimization (MDO) design pipelines.

Navier-Stokes (e.g. RANS, LES) solvers are rapidly making inroads into the MDO environment, however this approach is restricted to simpler optimization cases. On the other hand, pressure-based potential flow solvers are highly susceptible to imperfections in surface mesh quaility and refinement. Finally, most vorticity based solvers are currently limited to structured thin surface geometries.

Why Unstructured Meshes?

A structured surface mesh is typically defined as one where a given surface is mapped along two numerical axes (“i-j” or “u-v”) and each face is bound by four vertices extracted from the rectangular structure of the underlying map (known as the U-V map). As such, any structured surface mesh is essentially quadrilateral in nature. Consequently, facets have to be “forced” to assume triangular shapes to meet geometrical demands. This is accomplished by vertex merging in physical space. In numerical space, such triangles still retain the underlying quadrilateral U-V map. The advantages and disadvantages of such approaches to mesh generation are obvious. The forced quadrilateral U-V mappings of the underlying facets ensure that the memory requirement for a given forced structured triangle is always more than an equivalent unstructured triangle. In addition, forced U-V mappings ensure that regions of high curvature or concave warping are always populated with more facets than actually required. Furthermore, the quality of such facets is typically very poor. Finally, the typical quadrilateral facet has to be sanitized to establish its “effective” surface normal direction. With triangular faces, this is not required, given the deterministic nature of the triangle geometry in three-dimensional space. A general rule of thumb obtained from the current effort shows that the computation time for the solution convergence is directly proportional to the square of the mesh face count. Despite the aforementioned shortcomings of the structured surface meshes, with potential flow solvers (and especially vorticity solvers), they offer certain unique advantages. Arguably, vorticity solvers in their prior form have been made possible mainly because of the inherent advantages of the structured mesh. Vorticity solvers require a face-edge pool to be split into bound and trailing vortices during the application of the Kutta–Joukowski formulation. This means that faces of arbitrary orientation (as obtained from unstructured meshes) cannot be applied. Traditionally, the U-V mapping of the structured meshes has been used in all legacy vorticity solvers to establish bound and trailing vortices. The bound vortices are simply marked as those facet edges aligned along a certain numerical axis, and the other edges are marked as trailing. Note that a such marking usually only corresponds to the correct flowfield if the physical space warping and curvature are not significantly different from the alignment of the numerical axes. Furthermore, the classical induced load formulation requires knowledge of the vorticity in the downstream bound vortex. This reduces the computational burden on the solver and allows the evaluation of loads in a simple and straightforward manner.

Sources

[1] Ahuja, V., & Hartfield, R. J. (2016). Aerodynamic Loads over Arbitrary Bodies by Method of Integrated Circulation. Journal of Aircraft, 53(6), 1719–1730. https://doi.org/10.2514/1.c033619