my Æ Daniel Buisine
Experimental and numerical study of a spiral structure at the periphery
of an aspirated rotor–stator cavity
Received: 22 September 2005 / Revised: 14 March 2006 / Accepted: 26 April 2006 / Published online: 20 June 2006
Ó Springer-Verlag 2006
Abstract The purpose of this paper is to study the range
of existence, the process of transition and the phase
velocity of the spiral structure in an aspirated rotor–
stator cavity. Experience shows that for a given ﬂow rate
and rotation, a whole range of azimuthal wave numbers
are possible. Some are highly stable while others on the
fringes of this range are subject to multiple transitions
that depend on the ﬂuctuations of the ﬂow. Numerical
simulation oﬀers the advantage of enabling control over
the wave number and the disturbance of the ﬂow. Both
approaches enable us to better understand the dynamics
of this instability.
Flow in rotating cavities has been the subject of many
studies because of its application to the turbine engi-
neering ﬁeld: axial thrust bearings, turbine disk cooling,
process engineering and computer storage. These ﬂows
develop multiple instability conﬁgurations, especially in
the peripheral zones.
Experimental studies by Schouveiler (1998) and
Schouveiler et al. (1998a, b, 2001), by Gauthier et al.
(2002) in thin cavities, Re
my et al.
(2004a, b, 2005) with aspiration, and also the computer
studies by Lopez (1996), Jacques (1997), Serre et al.
(2001a, b, 2004), Moisy et al. (2004) and Buisine et al.
(2000) have improved our knowledge of these phenom-
ena. The interest in these structures is not purely aca-
demic; apart from the fact that they anticipate the
transition to turbulence, they lead to spatial ﬂuctuations
in velocity of very high amplitude, in a ratio of zero to
three with respect to the mean velocity (see Buisine et al.
In a suﬃciently high aspirated rotor–stator cavity
(Fig. 4), with an axial jet entering into the periphery of
the rotating disk, the overall structure of the ﬂow is
‘Batchelor’ type. This ﬂow consists of a quasi-solid core
inserted between the Ekman layer on the rotating disk,
dewadt layer on the ﬁxed disk and the layer
developed on the ﬁxed cylinder from the conﬂuence of
the Ekman layer and the jet due to the aspiration. This
conﬁguration generates areas that are particularly
favorable to the triggering of instabilities with complex
shearing zones, zones of radial convergence and also
zones of intense rotation for the vortex vector.
Experimental studies carried out on such cavities
demonstrated the existence of several structures includ-
ing the ‘cross-ﬂow’ type that is speciﬁc to aspiration and
to shearing in the jet and which is studied in Re
my et al.
(2005). Another instability in the form of spiral arms
located in the ﬁxed corner of the cavity is studied here.
This structure was observed for the ﬁrst time in a closed
low cavity by Schouveiler et al. (1998a) and Gauthier
(2002). More recently, the structure was observed in an
aspirated cavity by tomography and by PIV (Re
my et al.
2004a, b). Figure 1 depicts a visualization of this struc-
ture in our case (Fig. 1a), for a very low aspiration ﬂow,
compared with that observed by Schouveiler (Fig. 1b)
and Gauthier (Fig. 1c) for no ﬂow. In our case, the
contrast is not very pronounced, yielding greater diﬃ-
culty in correctly distinguishing the structure on the still
picture rather than on the video image. Thus, we high-
light the structures in Fig. 1a using black lines. In
addition, the azimuthal periodicity is estimated in our
case to be 18 plus or minus 1. There is insuﬃcient
information to determine the frequency precisely. To
summarize, at low ﬂow, only the Reynolds number
)/m is comparable between these three exper-
The spatial ﬁeld of this structure has now been well
described. It is limited to a meridian window, the extent
of which depends only on the thickness of the layer on
the cylinder. Each structure engenders a folding of the
smoke ﬁlm coming from the edge of the rotating disk,
my (&) Æ D. Buisine
Laboratoire de Me
canique de Lille UMR CNRS 8107,
des Sciences et Technologies de Lille,
Baˆ timent M3, 59655 Villeneuve d’Ascq, France
Experiments in Fluids (2006) 41: 393–399