Simulation of flow over cubes is relevant to a large number of industrial applications such as: convective cooling of microprocessor chips or buildings, drag and noise reduction in cars and trucks, or control of wind-induced vibrations in highrises. The cube geometry is very simple, yet the flow around it manifests interesting 3-D structures that are prominent in more complex configurations.
The following are some
, but the actual
computational elements which are generated at the boundary of the cube
(to satisfy the no-slip boundary condition), and which evolve in the
fluid in the Lagrangian frame of reference.passive
elements
The computational elements are vorticity
weighted and hence are called vortex elements. Note that these vortex
elements are concentrated within the boundary layer of the cube faces
and the wake behind the cube, where vorticity is significant. Outside
this region, where the flow is essentially potential, no elements can
be seen. More importantly, the element assigned not by
the user, but determined a priori the dynamically by itself.flow
The wake behind the cube, while symmetric
during the early stages of its formation, is highly unsteady and
asymmetric due to the introduction of random, noise-level disturbances
to the flow field. If the flow is in the stable regime; e.g., laminar
duct flow, the perturbations do not grow. However, if the flow is
inherently unstable the random perturbations give rise to unsteady
dynamics. The fundamental non-dimensional frequency (Strouhal number)
of oscillation of the near-field wake is found to be S = 0.148-0.153) at the same Reynolds number. Note that although the instantaneous flow over the cube is non-symmetric, its time-averaged topology is symmetric.
of the cube and extend out into the wake -
prominently forming what appears as four pairs of horseshoe-like
vortices around the cube. The process leading to the development of
these streamwise vortices can be explained by a simple ring model. The
vorticity lines around the cube (closer to the upstream face) form
square-shaped rings. The high curvatures at the four corners push them
forward at a faster rate than the remainder of the ring, causing the
initiation and subsequent growth of streamwise vortices. on each face |

The above figure depicts the stationary state velocity field, normalized by the maximum speed, at selected planes cutting through the cube. z = -0.5 and z
= 0.5 are the upstream and downstream faces, respectively. Note the
development of weak vortical structures beyond z =
0.0, consistent with the earlier observation. Also note that the flow
does not separate at the upstream edge of the cube. This seems to
corroborate with simulations of flow over a square rod at the same
Reynolds number. It is interesting to note that as the Reynolds number
increases, the structure of the flow on the streamwise cube faces
becomes highly complex: separation at the upstream edge, multiple
streamwise and cross-flow vortical structures, etc. |