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

- 1 -

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


- 2 -

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


- 3 -

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.).


- 4 -

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


- 5 -

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


- 6 -

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.


- 7 -

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


- 8 -

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.


- 9 -

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


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


- 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


- 10 -

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


- 11 -

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


(x/D=2.74) of Cp’ for

H/D=0.75


(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


- 12 -

(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

unsteady near wake of a flat disk normal to a wall -...

Documents