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XXIV ICTAM, 21-26 August 2016, Montreal, Canada
INSTABILITIES IN THE FLOW BEHIND ROTATING BLUFF BODIES
M. Krutnik1, M. Skarysz1, K. Gibiński1, S. Goujon-Durand² and J.E. Wesfreid²a
1
Institute of Aeronautics and Applied Mechanics, MEiL, Warsaw University of Technology,
Warsaw, Poland
²
PMMH, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris,
UMR7636 CNRS-ESPCI-P6-P7, Paris, France
Summary The wake and its instabilities behind rotating sphere and a simplified model of propeller were investigated for moderate Reynolds
numbers, in a low- velocity water channel. We observed different vortex structures with LIF method and the velocity field was measured with
PIV. The influence of rotation speed on vortex shape and size was analysed. The explored range of Reynolds number was from 0 to 400 and the
swirl or rotation parameter Ω was not higher than 4 for the sphere and 2 for the rotor. For non-rotating bodies, is very well know the existence
of various flow regimes with axisymmetric base flow, pairs of stationary counter-rotating vortices, and unsteady vortex shedding with hairpins.
We described the occurrence of new regimes in presence of rotation with lower and higher helical modes. In this talk new results about the nonlinear evolution of the instability modes are presented.
Introduction
Many experimental and numerical researches were carried out to describe the phenomenon of wakes and
instabilities behind 3D bluff bodies. The structures created by fluid instabilities past spheres, cubes, disks and models of
propeller have been investigated by our group[1-4]. This paper presents the first experimental results concerning wakes
and its instabilities behind rotating sphere and a model of propeller. For static bodies, it is well known the existence of three
main regimes, depending on Reynolds number. The initial regime is an axisymmetric base flow in the case of the sphere
with a bifurcation with two counter-rotating streamwise vortices (CRV) with a planar symmetry between each other, at Re =
212. After a second transition, at Re = 270, two CRV evolve into hairpin, unsteady periodic vortex shedding. When rotation
is introduced[5-6], in the case of two counter-rotating vortices, one of them becomes stronger and another one is weakened
and is observed the phenomenon of “frozen” spiral and subsequent unsteady behavior.
Experimental details
The experimental set up consists of a low-velocity
water channel of 86 cm length and with a cross-section of
10 cm x 10 cm. Both, the sphere and propeller were fixed by
a rigid thin hollow tube (d=0,2cm) connected to a brushless
electric motor and a dye input. The pipe axis was aligned
with free stream direction. The motor was also located
inside the channel, around one meter behind the support.
The water stream achieved the velocity up to 4 cm/sec.
To perform flow visualization, fluorescein dye was
injected through the slits in the objects, using Laser Induced
Fluorescence (LIF) techniques. For velocity measurements,
Particle Image Velocimetry (PIV) was adopted and the
video camera was capable of recording images with the
frequency of 15 Hz. Tracer particles, with the diameter
around a few µm, were seeded in the water. For the velocity
field calculation, the program used cross-correlation method
and multi-pass iteration. Laser slices, perpendicular to the
flow, were located at the distance of 2,5 diameter of the
Figure 1: Visualization of the wake behind the
object (where we found maximum amplitude of the velocity
sphere for Re = 250 (left) and Re =300 (right)as
perturbations), which is around 0,5 diameter behind the
a function of Ω
recirculation zone, in order to evaluate the streamwise
vorticity behind the bodies. The Reynolds number range was up to 1000 with the possibility of steps increment of ΔRe
equal to 2 and the swirl or rotation parameter Ω was not higher than 4 for the sphere and 2 for the rotor, with steps of ΔΩ
a
Corresponding author,E-mail:[email protected]
equal to 0.1. This fine change in the flow parameters let us to perform very detailed description of the frequencies and the
non-linear evolution of the instability fluctuations. The rotor was built from three identical propellers, which thickness was
0,06 cm. The blade width was 0,3 cm. In both cases of rotor and sphere, the diameter was 2 cm.
Results
The investigation was focused on different regimes of
wakes behind bodies, changing the swirl parameter Ω, which is the
ratio of the maximum azimuthal velocity of the object to the free
streamwise velocity, to explore the influence of rotation. In the case
of the sphere (Figure 1), different structures are observed for Re =
250 and Re = 300. In particular, for Re=250, the steady flow (Ω=0)
becomes a “frozen” flow up to Ω=0,2. With the increment of the
swirl parameter, low helical frozen wake appears. The next images
presents unsteady flow, which changes into high helical, when
Ω=1,2.
Having the possibility to perform detailed measurements of
the bifurcation branches of perturbation, we study the modification
of the content of the azimuthal modes of enstrophy, obtained by
polar Fourier decomposition. We present in our talk the first
experimental evidence of the changes of the mean mode of
homogeneous or global vorticity induced by the nonlinear
Figure 2: Dimensionless enstrophy of
mode=0 as a function of Ω and Re
interaction of the fluctuating perturbations. One example of this
behavior is observed in the figure 2, showing in the axisymmetric
mode of vorticity (azimuthal mode m = 0) this nonlinear anticyclonic contribution due to the presence of instabilities, at
different Reynolds numbers.
In addition, we present on the figure 3, a flow visualization and the measurements of the streamwise vorticity and
its spatio-temporal reconstruction, for the case of a rotating rotor with three blades at Ω = 1, with indication of the CRVs
twist, where is observed as the negative vortex is pushed to the middle of the wake and surrounded by positive ones.
Figure 3: The visualization, instantaneous streamwise vorticity and its spatio-time
reconstruction for the simple rotor, at Ω = 1
References
[1] K. Gumowski, J. Miedzik, S. Goujon-Durand, P. Jenffer, and J. E. Wesfreid, Transition to a time-dependent state of
fluid flow in the wake of a sphere Phys. Rev. E 77, 055308(R), 2008
[2] Szaltys, P., Chrust, M., Przadka, A., Goujon-Durand, S., Tuckerman, L. and Wesfreid, J. E., Nonlinear evolution of
instabilities behind spheres and disks; Journal of Fluids and Structures 28, 483-487, 2012
[3] Klotz, L.; Goujon-Durand, S.; Rokicki, J ; Wesfreid, J.E. ; Experimental investigation of flow behind a cube for
moderate Reynolds numbers ; Journal of Fluid Mechanics 750, 73-98, 2014
[4] Bobinski, T.; Goujon-Durand, S.; Wesfreid, J. E. ; Instabilities in the wake of a circular disk ; Physical Review E 89,
053021, 2014
[5] Kim D. and Choi H., Laminar flow past a sphere rotating in the streamwise direction; Journal of Fluid Mechanics 461
365386, 2002
[6] Pier B., Periodic and quasiperiodic vortex shedding in the wake of a rotating sphere; Journal of Fluids and Structures 41 4350, 2012