Characterization of a Bubble Curtain for PIV Measurements - Selected Topics of Computational and Experimental Fluid Mechanics - page 252

1.1 Theoretical Framework

The most common nondimensional parameter used to characterize fluid motion is
the Reynolds number, defined as,

DV
ʽ

Re = , (1)

ʽ

where D is a characteristic length, V is a characteristic velocity and is the kinematic

viscosity (Crowe et al. 2009 ).
Due to the viscosity of the fluid, when it comes in contact with any solid boundary,
the speed is diminished near the surface. This zone is known as boundary layer, and
is characterized by low velocity and high speed gradients. The latter are responsible
for generating vorticity ˉ which is defined mathematically as,

ˉ =∇× V

, (2)

where V represents the velocity field.
When the surface is curved, pressure gradients appear in the streamwise direction.
If the pressure gradient is adverse, flow reversal can occur and the boundary layer
separates creating a wake with well-defined vortical structures, as shown in Fig. 1 .
As the flow velocity increases, the vortices formed due to flow reversal, start to
shed at a frequency proportional to the velocity. The pattern thus formed is known
as the von Kármán street and is shown in Fig. 2 a. The effect of von Kármán's street
on drag has been largely studied for different geometric forms, in particular behind
cylinders (2D) and spheres (3D). There are active and passive forms of manipulation
of the wake vortices that can diminish the drag, or even create propulsion. For exam-
ple, vortices are manipulated by animals, with the motion of their wings or fins, to
form a modified pattern as shown in Fig. 2 b, (Triantafyllou et al. 2012 ). This pattern,
that increases propulsion, is known as the reversed von Kármán street.

Fig. 1 Velocity profile in the surface of a curved body immersed in a fluid. In the region where the
pressure gradient is adverse, flow reversal occurs and vortices are generated