3-D Flow Separation

Summary

Definition of flow separation in three-dimensional flows is somewhat elaborate, since is must describe several topological features at solid walls that are not present in two-dimensional flows. The features of interest are skin friction lines, e.g. velocity components and streamlines. Some other features can be identified in the field.

In 2-D flows separation is identified by a region of backflow, and at the wall by a zero skin friction. In 3-D a streamline can turn backward, while maintaining the flow attached.

Streamline Topology at the Wall

The nature of 3-D separation can be studies from the analysis of skin friction lines. At a solid wall skin friction lines can:

1. Converge to a point
2. Diverge from a point
3. Spiral around a point
4. Deviate from a point
5. Converge to a line
6. Diverge from a line

When the skin friction lines converge to, or diverge from a point the point is called node (nodal point of separation or attachment, respectively). Nodal points can have one line to which all skin friction lines are tangent to, or none. In the latter case the node is called focus (of separation or attachment).

Nodal points of separation and attachement can be viewed as sinks and sources of skin friction, respectively. Nodal points of attachement are typically stagnation points on a forward facing surface (ex. a blunt nose).

There are cases where the skin friction lines deviate from a point as from a stagnation point. There are only two lines (normal to each other) through the point, which is called saddle. Both types of points can be featured in the 3-D flow, but the number of nodes must be equal to the number of saddles plus 2 (Lighthill, 1963).

Field Streamlines

Skin friction lines converging to, or diverging from, a line define a attachment or separation lines, respectively. These line are also called limiting streamlines. Limiting streamlines from a separation line must leave the surface, as shown by Lighthill (1963), while streamlines converging to an attachement line land on the surface.

Nodal points of separation and attachment are other interesting features: they become edges of vortex cores. In some cases there is also a distinction between primary and secondary lines of separation.

Devices most commonly used for the study of 3-D separation include prolate spheroids, blunt and pointed cones at incidence, where non-axisymmetric vortex formation appear (all axisymmetric bodies at incidence are very prone to flow separation with consequent instability).

Also of interest are the delta wing at all speeds and angle of attack ranges, slender bodies (missiles and rockets), aircraft afterbodies, high angle of attack aerodynamics.

Examples of the features described above are shown in Fig. 1 that represents the result of a 3-D Navier-Stokes solution of a particular aeronautical problem.

Figure 1: 3-D skin friction lines.

A large number of flow separation features is reviewed by Peake-Tobak, 1980.

Selected References

• Lighthill J. Attachment and Separation in Three-Dimensional Flow, in Laminar Boundary Layers, Oxford Univ. Press, Sect. II, pages 72-82, 1963.

• Chang PK. Separation of Flow, Pergamon Press, 1966.

• Peake DJ, Tobak M. Three-Dimensional Interactions and Vortical Flows with Emphasis on High Speeds, AGARDograph AG-252, July 1980. (ISBN 92-835-1366-5)
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