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flow visualization and, for example, PIV or laser Doppler
velocimetry (LDV). This design has been subsequently
exploited in at least four other Couette flow apparatuses
around the world (France, Norway, the United States, and
Japan, by
Daviaud et al.
[1992],
Malerud et al.
[1995],
Zettner and Yoda
[2001], and
Hagiwara et al.
[2002],
respectively). However, so far only the original appara-
tus at KTH has been used to study the flow with system
rotation.
A drawing of the RPCF apparatus is shown in Figure
4.9. The full length of the apparatus is 2500 mm and the
test section height is 360 mm and its length is 1500 mm.
Thetotalweightof theilledchannelisaround300kg.The
distancebetweenthebeltwallsisadjustableandistypically
10 or 20 mm but can accommodate distances up to 70 mm.
The larger the wall distance, the larger the rotation rate
that can be achieved since
Ω
x
Ω
x
Figure 4.8.
Azimuthal velocity profile in laminar (left) and
turbulent (right), axially rotating pipe flow.
b
2
: doubling the channel
width gives a fourfold increase in the maximum rotation
rate. However, the larger the distance between the walls,
the worse the aspect ratio of the test channel.
Since the upper water surface is free under rotation
it will have a parabolic shape, and this is a limiting
factor on the rotational speed to about
z
= 0.6 rad/s.
In order to avoid a sloshing motion of the water in the
channel, the rotating table supporting the channel needs
to be accurately balanced.
The research so far on the RPCF has mainly been
focused on flow visualization, using reflective flakes, of the
various flow regimes for
=
∼
In the turbulent case, rotation breaks the azimuthal
reflection symmetry. This means that, in the turbulent
case, a nonzero azimuthal/radial Reynolds stress compo-
nent is established. This makes the pressure drop (or rather
skin friction) decrease and the mean velocity profile tends
to become more parabolic, i.e., closer to the laminar pro-
file. This also influences the azimuthal mean velocity dis-
tribution such that it no longer increases linearly with the
radius, as it would if the fluid were in solid-body rotation,
but rather has a parabolic distribution as illustrated by
Figure 4.8. This has been observed in several experiments
(for further discussion of this, see Section 4.4.3) but also
in the numerical simulation by
Orlandi and Fatica
[1997].
30. However, recently some
new results including two-dimensional (2D) PIV mea-
surements in the streamwise-spanwise plane have been
reported, also for higher
[
Suryadi et al.
, 2012, 2013].
±
4.3. LABORATORY FACILITIES
4.3.1. Rotating Plane Couette Flow
4.3.2. von Kármán Boundary Layer Flow
The rotating plane Couette flow has so far only been
studied in the Fluid Physics Laboratory at KTH and
results have been presented in a few papers [
Tillmark
and Alfredsson
, 1996;
Alfredsson and Tillmark
, 2005;
Hiwatashi et al.
, 2007;
Tsukahara et al.
, 2010a, 2010b].
Even without rotation the plane Couette flow channel
is a rather complicated mechanical system and several
variations have been tried. An innovative idea for the con-
struction of an experimental plane Couette flow channel
was introduced by
Tillmark and Alfredsson
[1991, 1992]
(who also provide a review of earlier concepts). This new
concept involves an “infinite” transparent belt moving in
the horizontal direction sliding against two vertical glass
walls, thereby giving a counter movement of the two walls.
The belt mechanism is immersed in an open water tank
giving a free surface through which the belt is slightly
protruding. This latter fact proved to be crucial since
the surface tension between the belt and the glass plates
keeps the belt well attached to the walls. By using a trans-
parent belt, the channel is optically accessible both for
When designing a rotating disk experiment there are
certain limitations that need to be taken into account. If
the laminar flow, its stability, and subsequent transition to
turbulence are the objects of the study, it is important to
note that the thicknes
is of t
he laminar boundary layer is
approximately
δ
=5
√
ν/
z
whereas the nondimensional
radius (or Reynolds number) needed to capture the
transition region is at least Re = 600, giving
r/δ >
120.
Therefore, for a boundary layer thickness of 2 mm, which
may be the smallest practical thickness if boundary
layer measurements are to be made, the diameter of the
rotating disk would need to be at least 480 mm. This is
independent of the fluid used, although most studies of
the von Kármán flow have had a disk rotating in air. To
reach Re = 600 in air at
r
= 240 mm, the angular speed
needs to be
z
=94 rad/s, or about 15 rev/s (900 rpm).
This relatively high rotation rate means that balancing
the disk is crucial and that other vibrational sources need
to be minimized.
