Unsteady near wake of a flat disk normal to a wall -...
Transcript of Unsteady near wake of a flat disk normal to a wall -...
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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Unsteady near wake of a flat disk normal to a wall
Tony Ruiz, Christophe Sicot, Laurent E. Brizzi, Janick Laumonier,
Jacques Borée, Yves Gervais
Laboratoire d’Etudes Aérodynamiques (LEA), Université de Poitiers, ENSMA, CNRS, [email protected]
Abstract The unsteady wake of a flat disk (diameter D) located at a distance H of a flat plate has been experimentally investigated at a Reynolds number ReD = 1.3 10
5. Tests have been performed for a range of gap ratio (H/D),
spanning from 0 to 1.75. Moreover, the leading edge of the flat plate is either streamlined (elliptical) or blunt (square). The wake of the disk then interacts with a turbulent boundary layer either triggered downstream the streamlined leading edge or originating from the upstream separated region. These configurations have been studied with PIV and multi-arrayed off-set fluctuating pressure measurements. The results show a progressive increase of the complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D (H>D), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak associated with the wake meandering (St=0.131) – St=fD/U0 is the Strouhal number. For lower values of H/D, the magnitude of the wall fluctuating pressure increases significantly due to the intensification of the meandering peak (St=0.145) and to a large band contribution associated to the wake turbulence impinging and sweeping the wall. For the lowest values of H/D, the interaction is much more complex. The near wall mean flow is modified with two stagnation points associated with a tridimensional separated region inducing a great modification of the fluctuating pressure at the wall. A critical value of H/D (about 0.3-0.4) has been determined. Bellow this critical value, the vertical wake meandering is suppressed while the meandering parallel to the plate still exists and is amplified.
1. Introduction
Near wake of bluff bodies is a wide field of investigation - see e.g. Williamson, (1996). In
particular, vortex shedding, which is a naturally occurring phenomenon, has been the subject of
many researches due to its engineering application. The non-stationary flow produces oscillating
forces on the body and results in a complex wake structure. If the bluff body is located near a solid
wall, the unsteady wake flow is expected to induce particular spatio-temporal properties of the
fluctuating pressure field on the surface. Thus, many studies have been carried out to investigate the
unsteady wake of bluff bodies in the vicinity of a solid wall.
A large part of these studies concerns 2D mean flows, for example a cylinder parallel to a wall.
Many experimental or numerical works showed that the vortex shedding downstream a cylinder
near a plane boundary is suppressed at gap ratio less than 0.3, depending on the thickness of the
boundary layer (Bearman and Zdravkovich (1978), Lei et al. (1999), Straatman et Martinuzzi
(2003)). The mechanisms that cause the suppression of this periodic motion are complex and not
yet fully understood.
The 3D situation is much more complicated. Several works have investigated the flow around a
wall-mounted finite length cylinder. It has also been established that when the aspect ratio, the ratio
of cylinder length (H) to characteristic width (d) falls below a critical value, about 3-4,
antisymmetric vortex shedding is suppressed and the near wake is dominated by tip vortices (Wang
et al 2006, Sumner et al. 2004 and Sakamoto et Arie 1983).
The subject of this paper is to study the influence of the proximity of a wall on the development
of the 3D unsteady near wake of a disk. It has strong links with the aerodynamic and aeroacoustic
of passenger vehicles. In this domain, to make significant progress, it is indeed necessary to take
into account (i) the presence of unsteady separated regions of different nature; (ii) the impact of
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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their interaction as the spatio-temporal properties of the fluctuating wall pressure field is concerned.
This interaction, i.e. between the disk wake and the wall, is nowadays not well known whereas the
flow past a disk placed in a uniform flow has been extensively studied. The works of Fuchs et al.
(1979), Cannon et al. (1993) and Berger et al. (1990) showed that the wake disk is dominated by
three instability mechanisms: axisymmetric pulsation of the recirculation bubble at very low
frequency f1 (St1=f1D/Uo=0.05); antisymmetric fluctuations induced by a helical vortex structure at
a frequency f2 (St2=0.135) and a high frequency instability of the separated shear layer f3
(St3=1.62). The main objective of this study is the understanding of the modification of this well
known situation by the proximity of a wall. In particular, the impact of non linear interactions
between different flows structures on the wall pressure fluctuation.
Two generic configurations have been tested. The wake flow is generated by a bevelled disk
supported by a thin supporting strut perpendicular to a flat plate. The flow along the flat plate in the
absence of disk is either attached (Fig. 1 - the turbulent boundary layer being tripped and much
thinner than the distance plate/disk) or separated (Fig. 2 - Kiya and Sasaki 1983, Cherry et al.
1984). The disk and plate geometry is fixed and the varying parameter is the distance H of the disk
to the wall. Two kinds of measurements have been gathered: PIV measurements and fluctuating
pressure measurements using off-set microphones. This present paper analyses in large part results
obtained in the configuration having a streamlined leading edge (Fig. 1.) and a brief comparison
will be made between the two cases.
2. Experimental set-up and measurements techniques
Fig. 1. Configuration with an elliptical
leading edge. Attached incoming flow.
Fig. 2. Configuration with a blunt leading edge.
Detached incoming flow – see section 5.
The experiments are performed in a 1/2 open throat anechoic low-speed Eiffel type’s wind
tunnel. The square nozzle section has dimensions of 460 mm × 460 mm. The blunt flat plate is 30
mm thick, 1300 mm long and 460 mm wide giving a solid blockage of 6.5 % and an aspect ratio of
15.3. The plate is parallel to the nominally smooth stream. Its leading edge is either square (Fig. 1.)
or elliptical (Fig. 2.) and equipped with a tripping device (aspect ratio of the ellipse: 4). The leading
edge is located 300 mm downstream the jet outlet. The trailing edge is streamlined to minimize any
wake-induced unsteadiness. The disk is located in the symmetry plane, has a diameter D of 50 mm
and is supported by a circular strut having a diameter of 4 mm. The experiments are performed at a
free-stream velocity of 40 m.s-1
(ReD = 1.3 105). Tests have been performed for a range of height,
H, between the bottom of the disk and the flat plate, spanning from H/D=0.1 to 1.75. A mirror disk
is placed on the lower surface of the flat plate in order to assure the symmetry of the experimental
set-up relative to the incoming stream.
A PIV (Particle Image Velocimetry) system is used to record flow velocity field
information (2D-2C or 2D-3C). Illumination is provided by a double pulsed Nd:YAG laser emitting
two pulses of 120 mJ each (laser sheet thickness < 1 mm). An oil generator and a specially designed
“seeding grid” located upstream the convergent nozzle of the wind tunnel provide seeding with a
mean particles diameter of about 1 µm. The physical size of the measured image is about 196 mm x
148 mm. For evaluation, both frames are then divided into interrogation areas corresponding to
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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16x16 pixels with 50 % overlap.
The flow will be described henceforth using a cartesian co-ordinate system (x,y,z) to indicate the
axial, transverse and vertical directions. The origin is set on the symmetry plane and vertical to the
disk front. The components of the instantaneous velocity field are denoted respectively by (U,V,W).
The symbol < > indicates averaging operator. The components of the instantaneous fluctuating
velocity field are denoted respectively by (u,v,w). 2D-2C data were acquired in symmetry (y/D=0)
and near wall planes (z/D=0.04 that is to say z=2mm above the flat plate). 2D-3C data were
acquired in transverse planes (x/D=2.4 and x/D=3.7). For each configuration, 1000 images pairs
were acquired at a frequency of 4.5 Hz for 2D-2C and 2Hz for 2D-3C.
The measurements of the surface fluctuating pressure are obtained with off-set sensors
because the distance between pressure holes can be much smaller than the one achieved with flush
mounted sensors. Off-set sensors also have the advantage to increase the pressure range of sensors
because the fluctuating pressure decreases along the flexible tube between the pressure tab and the
sensor. Those sensors are differential with a bandwidth of [0Hz-1.6kHz] and a pressure range of
250Pa or 1250Pa. The use of those differential sensors has been developed on the basis of
“electret” microphone measurement (Hoarau et al 2006). The pressure probes are connected to
pressure tabs (inner diameter 0.9mm) via a pneumatic circuit (a flexible tube of length 0.2m). Note
that a long tube of 3m length (impedance tube) is connected downstream to each measuring input to
avoid acoustic resonances. In order to optimize the sensors pressure, the impedance tube is
connected via a buffer volume to the reference input. For each probe, the frequency response is
measured (magnitude and phase) with specially designed coupler and a reference microphone B&K.
Pressure fluctuations having a satisfactory energy content in the low frequency band are generated
in the coupler by a pulse generator. The frequency response of each pressure probe is used to
correct the magnitude and phase of the spectral functions - Power Spectral Density (PSD), cross-
spectrum. The signal recorder is able to simultaneously acquire 30 pressure probe signals with an
effective sampling frequency of 5.12 kHz and a cut-off frequency of the anti-aliasing filters set at 2
kHz. The time series data is split into segments of 4096 points with a 50% overlap and a Hamming
window is used to compute the modified periodogram of each segment. The number of segments is
400. Acquisitions along the axial line and different transverse lines will be described in the present
paper.
3. Attached incoming flow: Analysis of the mean and rms velocity data.
An integral calculation of the turbulent boundary layer development shows that the boundary
layer thickness (δ) is about 2 mm (δ/D<0.04) at the disk longitudinal position. This value is
significantly lower than the lowest gap ratio studied here (H/D=0.3).
The PIV results displayed in what follows show that the near wake and near wall flows strongly
depends on the value of H/D. First of all, the disk and its supporting strut is a 3D body immersed in
the main flow along the plate. The three components of the mean velocity in a transverse plane
located at 2.4 D downstream the disk are presented in Fig. 3 for H/D=0.75. A downwash flow is
observed (Sumner et al. 2004). For all H/D, the mean flow is therefore three dimensional and the
wake flow pattern is transported toward the wall as one moves downstream. Three kinds of
interactions can be inferred from the velocity data (Fig. 4.).
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Fig. 3. Three components of the mean velocity in a
transverse plane located at 2.4D downstream the disk
Fig. 4. Sketch of the streamlines in the three kinds of interactions (Dotted line: approximate location
of <U>=0): (a) H/D=1.75 ; (b) H/D=0.75 ; (c) H/D=0.3
- Large H/D values (H/D ≤≤≤≤1.25)
A weak interaction (see sketch of Fig. 4a.) takes place for large H/D values (typically H/D>1).
The mean velocity field of Fig. 5a shows that the development of the near wake is only slightly
modified by the presence of the wall. A moderate velocity increase is measured under the disk and
the mean recirculation bubble of the wake is only slightly non symmetrical. Fig. 6a shows that the
rms velocity in a near wall plane (z/D=0.04) are very weak. The turbulence of the wake of the disk
is transported by the main stream and does not interact with the flat plate in the measurement
domain.
- Intermediate H/D values (0.4≤≤≤≤H/D≤≤≤≤0.75)
A strong interaction is illustrated by PIV results at H=3D/4 (Fig. 5b and 6b.) and corresponds to
a downwash of the fluctuating wake down to the wall in the near wake region (sketch of Fig. 4b.).
The mean velocity field in the symmetry plane of Fig. 5b shows a strong acceleration of the flow
constrained between the wake and the wall. In Fig. 6b, we also notice a very strong increase of rms
velocity fluctuations when the near wake flow interacts with the wall. Downstream xI/D≈2 and in a
wall region expanding downstream, a wide range of turbulent scales, generated in the near wake
shear flow, is transported along the wall by the mean flow. Their signature will be observed on the
fluctuating wall pressure presented in what follows.
- Low H/D values (H/D≤≤≤≤0.3)
A further decrease of H/D results in a decrease of the momentum flux induced below the disk
and in a massive interaction described in Fig. 5c and 6c for H/D=0.3. Two mean stagnation points
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are detected along the near wall data of the symmetry plane. The first one (S1) is a saddle point and
corresponds to the mean separation of the flow constrained between the wake and the wall. The
Fig. 5. Mean velocity in the symmetry
plane (y/D=0): (a) H/D=1.75 ; (b)
H/D=0.75 ; (c) H/D=0.3. Level: 22 ><+>< WU
Fig. 6. Total rms and mean streamlines in
the near wall plane (z=2mm): (a)
H/D=1.75 ; (b) H/D=0.75 ; (c) H/D=0.3.
Level: ><+>< 22vu
separation results from the adverse pressure gradient and the turbulent fluxes in the shear flow
separating the underflow and the wake. The second mean stagnation point S2 is a node and
corresponds to the mean reattachment of the separation bubble of the disk. The topology of the near
wall mean velocity field (Fig. 6c) reveals two separatrices, more precisely convergent regions,
connected to the saddle point S1 (Delery 2004). Observing Fig. 6c, one notices a very important
variation of the rms of the velocity across S1. Indeed, the turbulent flow has a very different history
on both sides of this critical point. Upstream S1, turbulence is generated by the high velocity and
strongly sheared flow under the disk. Fig. 5c and instantaneous snapshots not shown here for
brevity show that this highly fluctuating flow separates and bursts in the mean separation bubble.
Downstream S1, the motion of the fluid particles is associated with the mean reattachment of the
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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wake of the disk. The weaker mean and fluctuating flows are typical of such reattachment for an
obstacle (quasi)flush mounted to the wall with mean streamlines (Fig. 5c) originating from the
upper shear layer.
It is however clear that the separation observed here is 3D and unsteady and this is expected for
a single 3D obstacle. The unsteadiness is particularly clear on instantaneous snapshots and high
speed PIV data are presently acquired to study this aspect. The two separatrices of Fig. 6c are
associated with a 3D separation (Delery 2004) of the near wall flow. Two “conical” structures are
thus induced on both sides of S1. They can be educed if one considers PIV measurement planes
parallel to the symmetry plane of Fig. 5 but shifted in the lateral direction (for example y/D=0.25).
These data are available but not shown here for brevity. Fig. 6c shows that these structures engulf
both incoming fluid from the upstream flat plate boundary layer and reattached fluid of the
recirculating near wake of the disk (streamlines originating from S2). Therefore, these branches
correspond to highly fluctuating regions.
The transition between these three interaction types is of course complex and progressive as
H/D decreases. For example, we can prove that the near wall separation occurs intermittently for
intermediate values of H/D. Multi point pressure and pressure/velocity data are currently analysed
to illustrate the very important changes of the spatio-temporal properties of the wall pressure field
in these different regimes.
4. Attached incoming flow: Mean and fluctuating wall pressure field.
Our objective in this part is first to discuss the global structure of the mean and fluctuating wall
pressure field associated with these three typical flow structures. We will first discuss the evolution
of ( ) ( )22∞∞−= UppC p ρ and ( )222
' ∞= UpC p ρ data. For a stationary mean flow, it is
then interesting to compute power spectral densities (PSD) in order to educe the frequency content
of the pressure signals. PSD are defined by ( ) ( ) ( )fpfpfPSD *ˆˆ= where ( )fp̂ is the Fourier
transform of the pressure signal at the sensor and ( )fp*ˆ its complex conjugate. In the present
experiment, the variance of the fluctuating pressure 2p is obtained by integrating the PSD in the
[ ]kHzHz 6.1,0 frequency band.
4.1 Longitudinal and transversal evolution of Cp and Cp’
The longitudinal evolution of pC and 'pC for the three typical flow structures (H/D=1.75;
H/D=0.75; H/D=0.3) are respectively shown in Fig. 7 and 8. The lateral evolution of 'pC along
the transverse line x/D=2.74 is displayed in Fig. 9. Note that the location of this line is shown in
Fig. 6a, b and c.
Whatever the disk location, Fig. 7 shows that the mean pressure field is modified. The
acceleration of the flow under the disk is typically associated with a low pressure level. This effect
is all the more pronounced as the disk-wall distance is decreased. For H/D=0.3, the nearest disk
location studied here, the slope of the mean pressure recovery changes notably at S1 and S2. For all
situations, 0≈pC beyond x/D=4.
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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Fig. 7. Mean pressure on the longitudinal line
(y/D=0) for the three kind of interaction
Fig. 8. Fluctuating pressure on the longitudinal
line (y/D=0) for the three kind of interaction
The 'pC data of both Fig. 8 and 9 show a very profound influence of the disk location. 'pC data
nearly coincide at the first longitudinal station x/D=0.5 displayed in Fig. 8. We believe that the
influence of the supporting strut is still dominant here as x/D=0.5 corresponds approximately to 6
strut diameters. The influence of the disk is nevertheless clearly overwhelming further downstream
for H/D=0.75 and H/D=0.3.
A single maximum of 'pC is observed for intermediate disk position H/D=0.75 on the
longitudinal evolution. The location of this maximum corresponds to the sharp increase of rms
velocity detected on near wall PIV measurements (Fig. 6c.). Our interpretation is that the near wake
turbulence impinges the wall about that location and is “swept” by the mean flow along the wall
further downstream. The maximum of 'pC is then associated with the mean location of this
interaction and with the associated turbulent structures. The transverse data of Fig. 9 shows that
'pC decreases steadily when one moves away from the axis. This is expected for the round
obstacle studied here.
Two maxima of 'pC are detected on the longitudinal plot of Fig. 8 for H/D=0.3. The first one
is very high and steep. It is located upstream the first saddle point S1, in the region of maximal rms
velocity (Fig. 6c.). The second one is found in the region of wake reattachment, slightly
downstream the mean node S2. The decrease of the rms pressure is quasi symmetrical on both sides
of this second maximum. Therefore, a local minimum is observed at x/D≈2.5 between S1 and S2.
The transverse evolution shown in Fig. 9 for this situation is remarkable in that two clear maxima
are very precisely associated with the transverse location of the mean 3D separation lines (y/D≈+/-
0.6 at x/D=2.74, see Fig. 6c.). The massive and non linear interaction observed for the disk located
close to the wall is thus responsible for a complex footprint of the fluctuating pressure on the wall.
Moreover, we see that the study of the near wall mean flow topology (Depardon et al. 2006) is
interesting to educe salient features of the flow – here an unsteady 3D separation – responsible for
such a footprint.
4.2 Frequency content of the fluctuating pressure signal
It is now necessary to study the frequency content of the fluctuating pressure signal in order to
understand which flow structure are associated with the high level of Cp’. We will concentrate our
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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discussion on H/D=0.75 and H/D=0.3 cases. With the semi Log representation adopted here, we
have, in a frequency domain [ ]21 f,f : ( ) ( ) ( )∫∫ =2
1
2
1
. f
f
f
ffdLnfPSDfdffPSD . This
representation is therefore useful because the energy content is readily visualised. This
representation is of course not adapted to detect precisely spectral peaks. These peaks were
determined using a standard dB representation not shown here.
Fig. 9. Fluctuating pressure on
transverse line (x/D=2.74) for the three
kind of interaction
- Intermediate H/D values (0.4≤≤≤≤H/D≤≤≤≤0.75)
The surface plots of Fig. 10 and 11 show respectively the longitudinal – line y/D=0 – and
transversal – line x/D=2.74 – evolution of the PSD for H/D=0.75. A wide band contribution is
observable and due to the turbulence of the flow. We saw in Fig. 5b and 6b that the near wake
turbulence is “swept” by the mean flow along the wall downstream 2/ ≈DxI . In the same way,
the longitudinal evolution of the PSD reveals that the energy in the frequency band
HzfHz 500150 << is noticeable dowstream 2/ ≈DxI . However, the emerging feature is a very
clear peak, precisely located at f=116 Hz corresponding to 145.0. == ∞UDfStD . We can expect
that the proximity of the flat plate in this situation induces an increase of shedding frequency of the
wake. Indeed, for a higher position of the disk (H/D=1.75), the meandering peak is precisely located
at f=105Hz ie 131.0. == ∞UDfStD closer to the wake meandering of a disk in a uniform
incoming flow )135.0( =DSt - Berger et al. (1990). The characteristic frequency of this meandering
is thus a strong constraint for the wall fluctuating pressure. In the Fig. 10, we see that the
longitudinal position of the maximum of the meandering peak ( 2/ ≈Dx ) corresponds to the
maximum of Cp’ (Fig. 8.). Dowstream this region, the meandering intensity decreases but is still
dominant. The transverse evolution )74.2/( ≈Dx of the PSD in the region “swept” by near wake
turbulence shows a decrease of all components of fluctuating pressure signal with the increase of
Dy / .
In the present situation, both global aerodynamics and turbulence carried by the aerodynamics
contribute to the near wall pressure data. The role of meandering is therefore two-fold. First, it
modifies the global aerodynamical field. For example, any flapping of the near wake will induce a
modification of the accelerated flow (of potential nature) under the disk. The corresponding peak is
therefore expected to emerge (and is also detected when the disk is far from the wall). Second, it
modulates the generation and transport of the large scale rotational turbulent structures generated by
the near wake shear.
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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Fig. 10. Longitudinal evolution (y/D=0) of the
f×PSD levels for H/D=0.75
Fig. 11. Transversal evolution (x/D=2.74) of the
f×PSD levels for H/D=0.75
Fig. 12. Longitudinal evolution (y/D=0) of
the f×PSD levels for H/D=0.3 Fig. 13. Transversal evolution (x/D=2.74) of the
f×PSD levels for H/D=0.3
- Low H/D values (H/D≤≤≤≤0.3)
The Fig. 12 and 13 show the longitudinal and transversal surface plots of the PSD for the near
wall disk position, namely H/D=0.3. As expected, the picture is more complex but still reveals
salient features of this particular configuration. A first remark is that a wide frequency range
contributes significantly to 'pC at each measurement location except at the farthest lateral location
)3.1/( =Dy displayed in Fig. 13, located outside the 3D separation branches and where a narrow
peak at f=126Hz )158.0( =DSt is detected. Therefore, the region of 3D separation and disk wake
reattachment is highly unsteady. A second remark is that a very clear peak at f≈30 Hz (Fig. 12.)
emerges upstream the mean stagnation point S1 and contributes to the maximum value of 'pC at
that location. Fig. 12 shows that this peak disappears downstream S1 while Fig. 13 shows that it has
a weak signature near the 3D separation branches )6.0/( ≈Dy . Our interpretation is thus that we
observe here the signature of a low frequency unsteadiness of the separation in the region of the
saddle point S1. It should have a strong impact on 'pC values because it characterises the rms
effect of the accelerated flow under the disk. Further experiments are on their way to educe the
pressure/velocity correlations in these situations and to use them to recover the dynamical links
between both fields. A third remark is the observed large band contribution in the wake
reattachment region and the total absence of the wake meandering peak on the longitudinal data.
This means that the vertical flapping of the near wake is suppressed when approaching the disk
toward the wall. Such observations have also been made in experiments devoted to 2D cylinders
located parallel to a wall and close to it (Lei et al. 1999). In these works, the vertical flapping of the
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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wake, associated with a modified Karman vortex street, is suppressed when the distance between
the cylinder and the wall is lower than 0.2 to 0.3 cylinder diameter. This conclusion seems here also
valid for a 3D obstacle if one looks in the symmetry plane. However, away from the symmetry
plane, we notice in Fig. 13 that the meandering peak of the disk rapidly reappears. This means that
the lateral flapping of the unsteady structure is still driven by the 3D flow around the disk. In Fig.
13, we see that a very wide range of frequencies contribute to the maximum of 'pC at y/D=0.6
(Fig. 9.) because the 3D separation branch not only fluctuates at the lateral meandering frequency
but also engulfs turbulent structures originating both from the upstream boundary layer and from
the downstream wake reattachment. On the contrary, the meandering peak is much more
pronounced and sharp for 6.0>Dy because the lateral flapping of the wake is the major
contributor to the unsteady aerodynamic around this 3D body. By comparing the magnitude of the
PSD peaks at y/D=1 between Fig. 11 and 13, one finally notices that the lateral strength of the wake
meandering is much higher for a disk close to the wall. The disk/wall distance therefore influences
the lateral extend of the footprint of the disk as near wall fluctuating pressures are concerned.
5. Main findings for a detached incoming flow
A complete set of data has been measured for the same disk locations but for a blunt flat plate (see
Fig. 2.). The goal is here to study the modification of the disk/wall interaction when the incoming
flow has experienced a previous separation and is therefore significantly unsteady and three-
dimensional. Let’s recall that without the disk, the mean reattachment of the massively separated
flow occurs at a distance ξR/e ≈5 – e being the thickness of the plate and ξ the distance from the
blunt leading edge (Kiya and Sasaki 1983; Cherry et al. 1984). The supporting strut of the disk is
located at ξS/e ≈2.5. Whatever the disk height, the separated flow is therefore constrained by the
presence of the disk. On PIV fields and oil flow visualizations not shown here for brevity, we
indeed observe that the presence of the disk and of the accelerated flow under it always forces an
early mean reattachment of the flat plate shear layer in the mid-plane at the strut location or
upstream this location (H/D=1.75 : ξR/e ≈2.6 ; H/D=0.75 : ξR/e ≈2 ; H/D=0.3 : ξR/e ≈1.8 ). The
location of the mean reattachment of the massively separated flow recovers the expected distance
ξR/e ≈5 away from the mid-plane for 5.1/ >Dy . We also noticed on the velocity data that the
global mean flow structure of the near wake is not much influenced by the presence of a detached
incoming flow and that the interaction between the disk wake and the wall may be separated into
the same three kinds described previously for an attached incoming flow. Nevertheless, it should be
stressed that the major difference in each case is a noticeable increase of the rms velocities due to
the interaction of the wake with the highly fluctuating flow induced downstream the reattachment of
separated region.
The influence of the separated region at the leading edge is clearly visible on the fluctuating
pressure fields at the wall (Fig. 14-16.). The results show a progressive decrease of the relative
influence of the incoming detached flow when the gap ratio decreases. For a gap ratio of 1.75, the
Fig. 14 shows a significant increase of the wall fluctuating pressure for a detached incoming flow.
The separated region is strongly distorted upstream the disk and the out of equilibrium boundary
layer under the wake of the disk is submitted to strong favorable mean pressure gradients. These
two factors are believed to be the major contributors to the minimum of Cp’ on the axis. Away from
the axial line, (largest Dy / values), the signature of vortex shedding of the separated region is
observed in figure 17. For 3.1/ =Dy , Fig. 17 shows a noticeable peak at f=300Hz
(St=f.ξR/U0=1.125) different of a Strouhal number based on the unperturbed reattachment length
St=f.ξR/U0=0.6 (Kiya and Sasaki 1983, Cherry et al. 1984). The frequency of this vortex shedding
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decreases with the distance from the axial line (Fig. 17). This seems coherent with the PIV results
which show a modification of the mean reattachment length, i.e. a modification of shedding
coherent structures dynamic with the distance from the axial line. The relative influence of the
detached incoming flow is still very noticeable for the intermediate values of H/D (Fig. 15.) and is
due to an increase of the energy content over all the relevant frequency range, with a particularly
important increase of the large band contribution of the turbulence. The disk becomes an
overwhelming perturbation for the lowest H/D value studied here and the relative influence of the
upstream turbulence is moderate (Fig. 16.). One may just remark in this situation a modification of
the typical frequency of the 3D unsteady separation (30Hz) probably due to the modification of the
dynamic of the flow below the disk (Fig. 18.).
Fig. 14. Transversal evolution
(x/D=2.74) of Cp’ for
H/D=1.75
Fig. 15. Transversal evolution
(x/D=2.74) of Cp’ for
H/D=0.75
Fig. 16. Transversal evolution
(x/D=2.74) of Cp’ for H/D=0.3
Fig. 17. Transversal evolution (x/D=2.74) of
f×PSD for H/D=1.75 with detached incoming
flow
Fig. 18. f×PSD evolution at
(x/D;y/D)=(1.74;0) for H/D=0.3
6. Conclusion The modification of the near wake structure of a disk in proximity to a wall and its
consequences on the spatio-temporal properties of the fluctuating wall pressure field have been
investigated using 2D-2C PIV, 2D-3C PIV and multi point pressure measurements. Tests have been
performed for a range of gap ratio (H/D), spanning from 0 to 1.75. Moreover, the leading edge of
the flat plate is either streamlined (elliptical) or blunt (square). The wake of the disk then interacts
with a turbulent boundary layer either triggered downstream the streamlined leading edge or
originating from the upstream separated region. The results show a progressive increase of the
complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D
(H>D), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak
associated with the wake meandering (St=0.131). For lower values of H/D, the magnitude of the
wall fluctuating pressure increases significantly due to the intensification of the meandering peak
14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008
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(St=0.145) and to a large band contribution associated to the wake turbulence impinging and
sweeping the wall. For the lowest values of H/D, the interaction is much more complex. The near
wall mean flow is modified and a tridimensional separated region is observed that induces a great
modification of the fluctuating pressure at the wall. A critical value of H/D (about 0.3-0.4) has been
determined. Bellow this critical value, the vertical wake meandering is suppressed while the
meandering parallel to the plate still exists and is amplified.
Further experiments are on their way to educe the pressure/velocity correlations in these situations
and to use them to recover the dynamical links between both fields. Simultaneous PIV/pressure and
high speed PIV/pressure data have been obtained. Multi-point analysing techniques like proper
orthogonal decomposition will then be used because we feel that they are very adapted to this non-
homogeneous situation dominated by energetic events having a clear effect on the wall fluctuating
pressure.
Acknowledgements The PhD grant of T. Ruiz is financed by PSA Peugeot-Citroen and Renault in the context of a
CNRT “Aérodynamique et Aéroacoustique des véhicules terrestres”. The authors thank the
scientific committee of the CNRT for scientific discussions. The technical support of M. Rossard,
F. Paillé, P. Braud and L. Philippon is warmly acknowledged.
References Bearman, P.W., Zdravkovich, M.M. (1978). "Flow around a circular cylinder near a plane boundary. " J. Fluid Mech.
89 (Part 1): 33-47.
Berger, E., Scholz, D. and Schumm, M. (1990). "Coherent vortex structures in the wake of a sphere and a circular disk
at rest and under forced vibrations" Journal of fluids and structures 4: 231-257.
Cannon, S., Champagne, F. and Glezer, A. (1993). "Observations of large scale structures in wakes behind
axisymmetric bodies " Exp. in Fluids 14: 447-450.
Cherry, N. J., Hillier, R. and Latour, M. (1984). "Unsteady measurements in a separated and reattaching flow." J. Fluid
Mech. 144: 13-46.
Delery, J. (2004). "Robert Legendre and Henri Werlé: Toward the elucidation of three dimensional separation." Ann.
Rev. Fluid Mech. 33: 129-154.
Depardon, S., Lasserre, J. J., Brizzi, L. E. and Borée, J. (2006). "Instantaneous skin-friction pattern analysis using
automated critical point detection on near-wall PIV data." Meas. Sci. Technol. 17: 1659-1669.
Fiedler, H. E. (1998). Control of free turbulent shear flows. Flow Control - Fundamental and Practices eds. M. Gad-el-
Hak, A. Pollard, J.P. Bonnet, Springer.
Fuchs, H.V., Mercker, E., Michel, U. (1979). "Large scale coherent structure in the wake of axisymmetric bodies." J.
Fluid Mech. 93 (Part 1): 185-207.
Hoarau, C., Borée, J., Laumonier, J. and Gervais, Y. (2006). "Analysis of the wall pressure trace downstream of a
separated region using extended proper orthogonal decomposition." Physics of fluids 18, (5).
Kiya, M. and Sasaki, K. (1983). "Structure of a turbulent separation bubble." J. Fluid Mech. 137: 83-113.
Laumonier, J., Goudeau, C. and Gervais, Y. (2001). "Mesures aérodynamiques sur profil NACA 0012 avec décollement.
2001. Colloque " Bruit des ventilateurs à basse vitesse , Ecole Centrale de Lyon, Novembre.
Lei, C., Cheng, L. and Kavanagh, K. (1999). "Re-examination of the effect of a plane boundary on force and vortex
shedding of a circular cylinder." Journal of Wind Engineering and Industrial Aerodynamics 80: 263-286
Miau, J. J., Leu, T. S. and Chou, J. H. (1997). "On vortex shedding behind a circular disk." Exp. in Fluids 23: 225-233.
Sakamoto, H. and Arie, M. (1983) "Vortex shedding from a circular cylinder of finite length placed on a ground plane."
J. Fluid Mech. 126 147.
Sumner, D., Heseltine, J. L. and Dansereau, O. J. P. (2004). "Wake structure of a finite circular cylinder of small aspect
ratio." Exp. in Fluids 37: 720-730.
Straatman, A.G. and Martinuzzi, R.J. (2003). "An examination of the effect of boundary layer thickness on vortex
shedding from a square cylinder near a wall." Journal of Wind Engineering and Industrial Aerodynamics 91: 1023-1037
Wang, H.F., Zhou, Y., Chan, C.K. and Lam, K.S. (2006). "Effect of initial conditions on interaction between a
boundary layer and a wall-mounted finite-length-cylinder wake" Physics of fluids 18 065106
Williamson, CHK (1996) "Vortex dynamics in the cylinder wake" Ann. Rev. of Fluid Mech. 28: 477-539