Three-Dimensional Singular Points in Aerodynamics
Abstract
When three-dimensional separation occurs on a body immersed in a flow governed by the incompressible Navier-Stokes equations, the geometrical surfaces formed by the three vector fields (velocity, vorticity and the skin-friction) and a scalar field (pressure) become interrelated through topological maps containing their respective singular points and external points. A mathematically consistent flow description of these singular points becomes inevitable when we want to study the geometry of the flow separation. A separated stream surface requires, for example, the existence of a saddle-type singular point on the skin-friction surface. This singular point is actually, in the proper language of mathematics, a saddle of index two. The index is a measure of the dimension of the outset (set leaving the singular point). Hence, when we say a saddle of index two, the implication of a two dimensional surface being separated from the osculating plane of the saddle is already there. This note shows how we can interpret the three-dimensional singular points mathematically and discuss the most common aerodynamical singular points through this perspective.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1988
- Accession Number
- ADA197978
Entities
People
- Aynur Unal
Organizations
- National Aeronautics and Space Administration