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.
The nature of 3-D separation can be studies from the analysis of skin friction
lines.
At a solid wall skin friction lines can:
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).
Skin friction lines diverging from nodal points cannot cross, due to the
presence of a saddle point between them. One of the lines through the saddle
is a separation line.
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.
Streamline Topology at the Wall
Field Streamlines
A large number of flow separation features is reviewed by Peake-Tobak, 1980.
Selected References