Topology of Three-Dimensional Separated Flows
Abstract
A Legendre formulation for a pattern of streamlines adjacent to a surface considered as trajectories with properties consistent with those of a constant vector field is used to develop a mathematical framework for three-dimensional separated flows. Convergence of skin-friction lines onto a particular skin-friction line originating from a particular saddle point is defined as a necessary condition for flow separation. Steady, three-dimensional flow is considered, and singular points occurring in the skin-friction lines are shown to happen where the skin friction or the surface vorticity become zero, and become nodal or saddle points. The separation initiates and continues only globally, as a mixture of an infinite set of friction lines, or locally, with one line. The topography of streamlines in two-dimensional sections of three-dimensional flows is discussed, and examples are provided of a round-nosed body of revolution at varying angles of attack.
- Publication:
-
Annual Review of Fluid Mechanics
- Pub Date:
- 1982
- DOI:
- 10.1146/annurev.fl.14.010182.000425
- Bibcode:
- 1982AnRFM..14...61T
- Keywords:
-
- Computational Fluid Dynamics;
- Flow Geometry;
- Separated Flow;
- Skin Friction;
- Three Dimensional Flow;
- Topology;
- Angle Of Attack;
- Bodies Of Revolution;
- Convergence;
- Flow Characteristics;
- Laminar Flow;
- Legendre Functions;
- Nodes (Standing Waves);
- Saddle Points;
- Steady Flow;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer