Civil Engineering Reference
In-Depth Information
the 1970s [WAL 78] to the 2000s [ATI 04]. Our analysis here
will be based primarily on the latter publication. Readers
can also consult [DOL 94] for an older review of the subject.
The physics of unsteady separation is a rich domain. The
steady flow separation is characterized by a local zero wall
shear stress. This characteristic is not, in itself, sufficient to
define unsteady separation, which manifests itself by a
violent ejection of vorticity from the wall toward the outer
layer, and the appearance of a singularity in the solution of
the boundary layer problem it induces [RIL 75, SEA 75],
similar to Goldstein's singularity [GOL 48]. A vortex gives
rise to a zone of recirculation detached from the wall, which
interacts greatly with the outer flow after a spectacular
spatial growth [ERS 85]. The considerable thickening of the
boundary layer causes high values of the wall-normal
velocity component. Numerical solving of the Eulerian
boundary layer equations therefore requires a refinement to
be made to the mesh, in terms of both time and space, as the
singularity appears, which is very costly in terms of
computation time. The problem can be circumvented by
using the Lagrangian coordinates, in which the momentum
balance equation in the streamwise direction
x
contains
u
but not
y
or
v
[VAN 80, VAN 90, VAN 91]. We will briefly
discuss these points below.
Atik
et al.
[ATI 04] consider the boundary layer
engendered by a 3D structure such as the HPV shown in
Figure 5.12. The structure is at a distance
ya
from the
=
wall, and its circulation intensity is
. The evolution of such
a structure is complex: the vortex is convected by the velocity
field induced by the Biot-Savart law and the image
structure. Thus, the structure can continually change form
in time and space without ever reaching a spatiotemporal
invariance. The authors of [ATI 04] opt for a simplified
model, supposing that the potential flow generated by the
ΞΆ
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