BBAA VI International Colloquium on:Bluff Bodies Aerodynamics & Applications

Milano, Italy, July, 20–24 2008

THE INTERACTING WAKES OF TWO FLAT PLATES

Franco Auteri, Marco Belan, Carlo Cassinelli and Giuseppe Gibertini

Politecnico di Milano, Dipartimento di Ingegneria Aerospaziale,Via La Masa 34, 20156 Milano, Italy

e-mail: giuseppe.gibertini@polimi.it

Keywords: Flat plate, Wake interference, Laser Doppler

1 INTRODUCTION

The study of the aerodynamic interference between two normal flat plates in tandem is aninteresting topic both as an idealized model of some wind engineering applications. In a pre-vious paper [1] an investigation carried out by means of hot wire measurements and oil smokevisualizations has been presented. In the present work we extend the range of tested Reynoldsnumber up to nearly 105 by new hot wire anemometry measurements, moreover new LDA mea-surements are presented which help gaining further insight in the flow mechanism.

2 Experimental setup

All measurements have been carried out in an open loop wind tunnel with a rectangulartest section 500 mm wide, 700 mm high and 2000 mm long. With respect to previous ex-periments [1], the settling chamber has been refined, leading to a substantial reduction of theturbulence level which is now less than 0.2%.

Two identical, 500 mm long, flat plates were employed spanning the full test section. Theplate chord was c = 70 mm, corresponding to an aspect ratio of about 7 and to a 10% solidblockage. The plates were 3.5 mm thick and chamfered on the top and bottom edges with anangle of 28◦, see Fig. 1. The fore plate was fixed to the tunnel walls while the aft plate wasmounted on sliding guides to adjust its position within the range [0.05c; 8c].

7m

m

10m

m

14mm

10m

m

14mm

V

D

c =

70m

m

3.5mm

Figure 1: The fore and the aft hot wire positions

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Franco Auteri, Marco Belan, Carlo Cassinelli and Giuseppe Gibertini

Several measurements have been taken by a two channel constant temperature hot wireanemometer (HWA). Two single tungsten wire probes of diameter 5µm and 1.25 mm longwere employed, each one positioned close to one of the plates, as sketched in Fig. 1. A low passfilter with cut frequency of 1 kHz and 48 dB/oct attenuation has been employed to retain onlythe portion of the signal pertaining to large, coherent structures.

The test set-up included also a two component Laser Doppler Anemometer (LDA) mountedon an x − y positioning system. The LDA measurements were taken in the middle plane, tominimize the wall interference.

3 Spectrums of Hot Wire signals

In order to verify the effects of the solid blockage of the fluid vein on the Strouhal number,defined as St = fc

V∞, preliminary tests have been carried out with the upstream plate only.

A Strouhal number St = 0.158 was found, independent of the Reynolds number within theexamined range 2.7 · 104 < Re < 105, where Re = V∞c

ν. This value is in good agreement

with the formula proposed by Ota, Okamoto and Yoshikawa [3] to take into account blockageeffects. In the following, to make the results more general, i.e. less dependent on blockage,the Strouhal numbers will be presented in terms of ratio respect to this single plate Strouhalnumber, that will be indicated by Stref .

The power spectrums of the anemometer signals, measured near the fore and aft plates re-spectively, indicate that two distinct flow regimes occur for short and long distances betweenthe plates. For intermediate distances, similarly to what happens with rectangular cylinders [2],both regimes are alternatively observed. In the present case, however, the bistability region isvery narrow.

The spectrums of the fore and aft anemometer signals at Re = 4.68 · 104 give some in-dications about the flow, as discussed in the following. For a distance between the plates ofD/c = 0.9 the vortex street behind the second plate seems to present strongly organized struc-tures, as can be deduced by the sharp peak in the spectrum of the signal measured by theaft anemometer. The corresponding Strouhal number is quite close to the value of the singleplate being St/Stref = 1.03. The spectrum measured by the fore anemometer displays a peakcorresponding to the fundamental with the same Strouhal and a second peak which is its firstharmonic. This is a ”one body mode” as defined in [2]: in this case, the shear layer starting fromthe upstream plate edge rolls up past the downstream plate to form the vortex street as can alsobe observed with the oil smoke visualizations presented in [1] and from the LDA maps reportedlater on.

When the distance is set to a value above a certain threshold both spectrums display a clearlyrecognizable narrow peak at the same Strouhal number, for instance St/Stref = 1.18 for D/c =1.1. In this case, as evident again from smoke visualizations [1] and LDA measurements, thevortex formation starts just behind the first plate. The vortices are shed behind the fore plateand interact with the second one. By virtue of this interaction the vortex shedding past both thefore and the aft plate occur at the same frequency.

When intermediate distances are considered, an interesting phenomenon can be observed.Comparing the spectrum of the fore and aft anemometer signals, for instance for a plate distanceD/c = 1.03, it can be clearly seen that one peak, whose Strouhal number is St/Stref = 1.21,is present with its harmonics in both spectrums while the aft anemometer signal also shows adifferent peak, at a frequency not commensurable with the previous one, with Strouhal numberSt/Stref = 1.03, which is not present in the spectrum of the fore anemometer signal. Thisapparent anomaly can be explained by considering the spectrogram of the aft anemometer signal

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Franco Auteri, Marco Belan, Carlo Cassinelli and Giuseppe Gibertini

t [s]

St/

St r

ef

10 20 30 40 50 60 70 80 90

0.5

1

1.5

2

2.5

3

3.5

1.21

t [s]

St/

St r

ef

10 20 30 40 50 60 70 80 90

0.5

1

1.5

2

2.5

3

3.5

1.21

1.03

Figure 2: Velocity power spectrum as a function of time (spectrogram) from the fore (left) and aft (right) anemome-ters, D/c = 1.03.

plotted in Fig. 2. From the figure, it can be clearly seen that the two aforementioned peaks arenot present at the same time but alternatively. Then it can be deduced that the flow can assumeat least two different configurations with different Strouhal numbers. Both configurations seemto be stable, in fact each configuration usually lasts for a sufficient number of periods to beclearly observed. Nevertheless, perturbations in the main stream can switch the flow from oneconfiguration to the other. In the present experiment, since an open circuit wind tunnel wasemployed, no control of small free stream perturbations was practical, therefore apparentlycasual shifts from one flow configuration to the other were observed.

In Fig. 3 the Strouhal number of the aft anemometer signal versus plate distance is shown. Itcan be seen the double Strouhal number in a very narrow region around D/c = 1. The positionand amplitude of this region seem to slightly depend on the Reynolds number. For instance, thedouble Strouhal number is observed in the interval 1 ≤ D/c ≤ 1.06, for Re = 4.68 · 104.

1 2 3 4 5 6 70.85

0.9

0.95

1

1.05

1.1

1.15

1.2

D/c

St/

St r

ef

Re = 2.24*104

Re = 3.15*104

Re = 4.68*104

Re = 6.22*104

Re = 7.85*104

Figure 3: Aft plate Strouhal number, as a fraction of the single plate Strouhal, versus distance between the plates.Solid symbols indicate the Strouhal of the second peak where a double peak is found.

4 LDA flow survey

The mean flow for the same Reynolds number Re = 4.68 · 104 has been mapped on a ratherfine grid by a two component LDA. The grid was composed by two nonuniform patches, onebetween the two plates and one behind the aft plate, plus a few points located near the aftplate edges. Two different plate distances have been tested, for D/C = 0.9 and D/c = 1.1,displaying the one body and the two body flow configuration respectively.

The mean flow for a plate distance D/C = 0.9, shown in Fig. 4 on the left, clearly presents

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Franco Auteri, Marco Belan, Carlo Cassinelli and Giuseppe Gibertini

a) D/c = 0.9. b) D/c = 1.1 .

Figure 4: Flow fields from LDA measurements

two large recirculating regions after the second plate. Two recirculating regions are also presentbetween the two plates. Quite surprisingly, however, these regions rotate the opposite waywith respect to those located in the wake of the aft plate. The mean flow for a plate distanceD/c = 1.1, the dual body flow configuration, is shown in the same figure, on the right. In thiscase also, two recirculating regions form behind each plate, but for this flow configuration theyrotate the same way.

It is of interest to note the difference between the aft plate wakes for two flow configurations.The one body mode features a wider wake, with larger recirculating regions, while the two bodymode displays a narrower wake with quite small recirculating regions. This different behaviourcould shed some light on the difference between the Strouhal numbers observed for the twoflow configurations. When plates are quite near, a longer shear layer has to develop before itrolls up behind the aft plate, so that the vortex shedding is relatively low. When the aft plate ismoved downstream, the shear layer rolls up behind the first plate, so that a shorter shear layerhas to develop thus increasing shedding frequency.

5 Conclusions

Experiments on the unsteady flow about two, in tandem, flat plates normal to the undisturbedflow have been reported. The measurement and visualizations reported show that the flowassumes two different configurations as the distance between the plates is increased. For lowdistances the flow behaves as that past “single” body, since the shear layer rolls up behind theaft plate to form the vortex street. For higher distances, vortices are formed behind the foreplate and interact with the second. This interaction tunes the shedding from the two plates tothe same frequencies. In a narrow intermediate range of distances, both the flow configurationsare intermittently observed.

REFERENCES

[1] F. Auteri, M. Belan , G. Gibertini and D. Grassi. Normal flat plates in tandem: an experi-mental investigation. J. Wind Eng. Ind. Aerodyn., to appear.

[2] C.H. Liu and J.M. Chen. Observations of hysteresis in flow around two square cylindersin a tandem arrangement. J. Wind Eng. Ind. Aerodyn., 90, 1019–1050, 2002.

[3] T. Ota, Y. Okamoto and H. Yoshikawa H. A correction formula for wall effects on unsteadyforces of two-dimensional bluff bodies. J. Fluids Eng., 116, 414–418, 1994.

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