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14th Int Symp on Applications of Laser Techniques to Fluid MechanicsLisbon, Portugal, 07-10 July, 2008

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Investigations of the flow field around different wall-mounted square cylinder

stump geometries

Thomas Uffinger, Stefan Becker, Antonio Delgado

Institute of Fluid Mechanics, University of

Erlangen-Nuremberg, Cauerstrasse 4, 91058 Erlangen, Germany, [email protected]

Abstract The flow around a wall-mounted square cylinder stump in a cross flow is investigatedexperimentally. In addition to the basic stump geometry, two additional cases are considered. First a wedgeis mounted in front of the square cylinder and second an elliptical afterbody is inserted into the recirculationarea behind the cylinder. The geometries are a selection of those analyzed in acoustic measurements whichhave been made previously at the Institute [1]. The flow fields of the different geometries are evaluated using

a 2D laser Doppler probe, sampling each measurement point from two directions to obtain 3D-data. Toachieve detailed information, a high-resolution 3D-grid is used. For reliable results, it has to be guaranteedthat the measurement time per point is sufficiently long. The main focus is placed on the measurement of themean values of the three velocity components and the turbulent kinetic energy. However, the anisotropy ofturbulence is also considered. Additionally, visualizations using a laser light section were performed toobtain an overview of the flow structures which can be found for the different geometries.

The aim of the investigations is to correlate the measured flow fields with the above-mentioned acousticmeasurements. By this means we want to find which properties of the flow have an influence on the acousticfar field. In particular, it is studied if the values of the turbulent kinetic energy directly influence the acousticsound pressure level. The investigations are meant to provide a deeper insight into the complex mechanismsof aeroacoustics which are still not fully known. Furthermore, the experimental data are used forcomparisons with numerical simulations which were carried out at the Institute [2].

The measurements provide very satisfactory results. The visualization using a laser light section clearlyshows the relevant flow structures. The wall near horseshoe vortices can be seen, in addition to the flowbehavior of the flow over the top of the cylinder. The laser Doppler-based velocity data confirm these resultsand give even more detailed information. Furthermore, the measured distributions of the turbulent kineticenergy lead to the conclusion that turbulent kinetic energy is not necessarily a basic paramter for the acousticsound pressure level generated by the flow. In fact, the size of coherent fluctuating flow domains and theanisotropy of turbulence have a strong influence on the flow-induced sound.

Nomenclature

CAA Computational aeroacoustics

cD Drag coefficientD Cylinder side length

L Cylinder length

LDA Laser Doppler anemometer

LES Large eddy simulation

RANS Reynolds averaged Navier-Stokes

ReD Reynolds number based on the cylinder side lengthD

SAS Scale adaptive simulation

SPL Sound pressure level

U Inflow velocity

U, V, W Velocity components in cartesian coordinatesx, y, z Cartesian coordinates


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The motivation for this work was to analyze the flow field around different cylinder geometries

to gain a better understanding of aeroacoustic sound generation. It was to be checked which

properties or structures of the flow field have an influence on the radiated acoustic field. Because of

the above-mentioned lack of data in the literature, the flow field around the geometries displayed in

figure 2a, 2b and 2c was to be evaluated using experimental methods. Furthermore, these data can

be used for comparisons with the results of numerical studies that have also been carried out at the

Institute [2].The setup and the measurement equipment used for the experimental investigations are described

in Section 2. The results of the measurements are presented in Section 3 and a comparison between

numerical and experimental investigations is given in Section 4. Section 5 contains a short summary

of this work.

2. Setup and measurement equipment

The studied geometries are displayed in figure 4, including the dimensions of their cross-sections

in mm. The basic stump geometry is a square cylinder with a side lengthD of 20 mm and a lengthL

of 120 mm (figure 4c). Two additional geometries are investigated. First an elliptical body isinserted into the recirculation area behind the square cylinder (figure 4a) and second a wedge is

placed in front of the cylinder (figure 4b). The selection was done based on the aeroacoustic resultsand represents, in addition to the basic geometry, the test cases for the quietest and loudest cylinder

Figure 3: Ranking of geometries referring to the acoustic sound pressure

level (U

= 30 m/s)

Figure 4: Geometries used for LDA measurements: a) elliptical afterbody; b)

wedge in front of the cylinder; c) unmodified cylinder (dimensions in mm)


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configuration.

The investigations of the flow fields were carried out in the aerodynamic wind tunnel of the

Institute. It is a closed return type of tunnel with an open measuring section. The two fans installed

provide a maximum power of 400 kW and allow speeds of up to approximately 45 m/s. The

rectangular cross-section of the nozzle (contraction ratio 5:1) has dimensions of 1.87 m in the

horizontal direction and 1.4 m in the vertical direction. The turbulence level of the tunnel is about

Tu = 0.12%.

The cylinder stump geometries are not placed directly on the floor of the wind tunnel. Instead,

they are mounted in the center of a plate with a thickness of 12 mm which is located about 0.5 m

above the tunnel floor and extends 1 m in the streamwise direction and 0.6 m in the lateral direction(see figure 5). At the leading edge of the plate a NACA 0001 profile is attached. The leading edge

of the plate is located 0.5 m downstream of the nozzle exit. These measures guarantee similar

conditions to those for the acoustic measurements which were done in the aeroacoustic wind tunnel

of the Institute. Moreover, the boundary layer is much smaller than when the cylinder is directly

mounted on the tunnel floor.

In order to obtain reliable measurements in the recirculation zone of the wake flow close to the

cylinder, laser Doppler anemometry (LDA) is applied as the measurement technique. In the present

study, a special design of a two-component LDA probe is used. This probe is specially designed for

applications in low-speed wind tunnels. At an outer diameter of 60 mm, it creates a measuring

volume approximately 75 m in diameter at a working distance of about 400 mm. The detection of

scattered light is in the direct backscatter mode. In order to reduce the probes frontal area exposedto the flow, the beam path is deflected with a 45 mirror. The LDA probe is attached to a high-

precision traverse system that allows three-dimensional movement of the probe. An illustration of

the general setup during the measurements is shown in figure 6.

Since the velocity components and the turbulent fluctuations in all three coordinate directions are

of interest, each measuring point has to be sampled twice. First the Uand Wvelocity components

were recorded, then the probe was rotated by 90 in order to obtain the third component V.

To obtain results of high accuracy, approximately 15000 samples per measuring point are

necessary in regions with high turbulence intensities. At a sampling rate of about 100-150 Hz,

which can be achieved by the LDA setup under good conditions, the measuring time is about 2 min

per point. Although the sampling rate was partially lower than 100 Hz and longer times would

always be desirable, 2 min per point was chosen since the measuring grid of each geometry consists

of some thousands of points. Following also the procedure outlined [12] for a 95% confidence

Figure 5: Measurement setup in the

aerodynamic wind tunnel


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interval, the statistical uncertainty of the mean velocity in the outer flow (far from the cylinder

model) is less than 0.01% of the local mean velocity. Within the wake of the wall-mounted

cylinder, where mean velocities can approach zero and turbulence intensities are very high, an

estimate of the mean velocity measurement uncertainty is rather arbitrary. An order of magnitude

estimate for the calculated 95% confidence interval is 1% for the mean and 1.5% for the RMS

value. The LDA system measures turbulence intensities as small as 0.8% in the outer flow region.

This value represents a lower threshold for the measured turbulence intensity and includes all

inaccuracies due to the measurement technique, wind tunnel fluctuations and traverse system

vibrations.

Measurements were carried out at U = 10 m/s for all three geometries and for the plain square

cylinder additionally at U = 30 m/s. With the cylinder side length D these speeds result in

Reynolds numbers ReD of 12.5104

and 37.6104

considering air as the medium of the flow. When

carrying out measurements at a flow speed of 30 m/s, a tripping tape is placed near the upstream

end of the plate in order to create a well-defined turbulent boundary layer. The inflow boundary

profile is measured at a distance of 10D upstream of the center of the cylinder. For a flow speed of

10 m/s, a displacement thickness of 0.788 mm and a momentum thickness of 0.357 mm areobserved, which lead to a shape factor H12of about 2.21, representing a laminar inflow. At a flow

speed of 30 m/s, the displacement thickness is 0.449 mm and the momentum thickness 0.360 mm.

The shape factor H12 is calculated as 1.25, which is fairly near the reference value of 1.4 for a

turbulent boundary layer.

3. Results

Figure 7 illustrates the three-dimensional flow field of the studied geometries. In all three cases,

the horseshoe vortex system caused by the adverse pressure gradient of the stagnation point can be

seen in front of the cylinder. The recirculation zone and the wake behind the cylinder are also

typical flow features. The behavior of the flow over the top of the cylinder is rather different for the

three cases. For the plain square cylinder, the flow separates at the top leading edge and does not

Figure 6: LDA probe during the measurements


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reattach any more. With the elliptical body mounted on the back side of the cylinder, the flow


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separates at the top leading edge also, but reattaches at the top trailing edge. In the case of the


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coefficient is calculated by the momentum loss based on a comparison of the distribution of the

mean velocity in different planes in front of and behind the cylinder geometries. The results are

summarized in table 1. The value of the drag coefficient correlates with the values of the turbulent

kinetic energy k, which is also displayed in figure 7. The highest amount of turbulent kinetic energy

kand the largest drag coefficient cD are observed for the flow around the unmodified cylinder. The

lowest values for both the turbulent kinetic energy and the drag coefficient are found for thecylinder with the wedge in front of it. At the same time, the configuration with the wedge is the

most silent one (see table 1 and figure 3). However, this does not mean that a reduction in the

turbulent kinetic energy or the drag coefficient automatically causes a reduction in the sound

generated by the geometry, since the configuration with an elliptical afterbody also shows a

reduction in the turbulent kinetic energy and the drag coefficient in comparison with the unmodified

square cylinder, but a rise in the sound pressure level. To understand this physical phenomenon, one

has to look in more detail at the measured flow fields, which is done in the following.

For the interpretation of the velocity fields, just one y-z plane at a distance of 2D behind the back

side of the unmodified cylinder and the center plane (x-z) is used. Figure 8 displays the distribution

of the mean velocity in the mentioned y-z plane for the unmodified cylinder. The velocity vectors in

the center plane for the same geometry are shown in figure 9. The velocity distribution issymmetrical in the y-z plane. Vortex cores are obtained due to the periodic flow separation at the

geometry SPL (dB) cD

elliptical afterbody 78.9 0.9

square cylinder 65.3 1.9

wedge in front 58.9 0.4

Table 1: Sound pressure level (U

= 30 m/s) and drag

coefficient (U

= 10 m/s) for the different geometries

Figure 8: Mean velocity in the streamwise

direction of the unmodified cylinder at U = 10m/s in the y-z plane

Figure 9: Vector plot and streamlines for the unmodified

cylinder at U = 10 m/s (center plane)


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The velocity field of the third investigated geometry (wedge in front of the cylinder) is shown in

figures 12 and 13. In this case, the flow field is no longer symmetrical in the y-z plane (both mean

and fluctuating field). Responsible for this flow characteristic is the sharp edge of the wedge. This

edge produces an instability point in front of the cylinder. Usually, the oncoming flow in the wind

tunnel experiments cannot be perfectly homogeneous and symmetrical with respect to the center

plane. Therefore, small disturbances or inhomogeneities at the instability point or line cause non-

uniform incoherent vortex formations. Furthermore, no flow separation occurs at the upper leadingedges of the wedge. A roof vortex of slightly smaller size than in the case of the unmodified

Figure 12: Mean velocity in the streamwise

direction of the cylinder with a wedge in front atU

= 10 m/s in the y-z plane

Figure 11: Vector plot and streamlines for the cylinder with

an elliptical aferbody at U

= 10 m/s (center plane)

Figure 13: Vector plot and streamlines for the cylinder with

a wedge in front at U = 10 m/s (center plane)


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cylinder is present in the wake of the cylinder nevertheless. Turbulence levels found downstream of

the cylinder are the lowest of all three geometries. The fluctuations of all velocity components are

of about the same magnitude.

It can be summarized that the level of turbulent kinetic energy is not a measure of the radiated

sound. Moreover, conclusions cannot be drawn from the drag coefficient. The investigations show

that two-dimensional flow structures of a large size, as found in an undisturbed vortex street behindthe cylinder geometry, result in higher sound pressure levels. Once the influence of the flow over

the top becomes stronger, the vortex street is disturbed and coherent vortex structures become

smaller. This effect can be clearly seen if the wedge is added in front of the square cylinder. Thenthe flow field is highly three-dimensional and smaller vortices are obtained. Furthermore, if the

flow field is highly three-dimensional, the fluctuations in all three coordinate directions are of about

the same level (configuration with wedge in front of the cylinder). Although the magnitude of the

turbulent kinetic energy is nearly equal in the case of the configuration with the elliptical afterbody

and the configuration with the wedge in front of the cylinder, the second one is more silent as the

fluctuations are isotropic. In the case of the elliptical afterbody, one component of the fluctuations

is dominant.

4. Comparison with numerical results

In addition to the described experimental investigations, numerical studies of the same test cases

were carried out at the Institute [2]. Simulations were done using the commercial software ANSYS-

CFX. With ANSYS-CFX, different RANS approaches and a simulation using the SAS turbulence

modeling were carried out.

Comparisons between experimental and numerical data for the three averaged velocity

components in the case of the unmodified square cylinder are shown in figure 14. The comparisons

are done in the center plane in a distanceD behind the center of the cylinder. It is evident that only

the unsteady SAS model guarantees a good match between measurements and numericalinvestigations. For the RANS approaches, the differences are much higher.

5. Summary and Conclusion

In this work, the flow fields around different wall-mounted cylinder stump geometries were

experimentally evaluated and studied in detail. The analysis allows conclusions to be drawn about

the acoustic behavior of the investigated cases. It is found that the level of turbulent kinetic energy

is not necessarily responsible for the amount of radiated sound. Also, the drag coefficient of the

Figure 14: Comparison of experimental and numerical results for the averaged velocities U, Vand Win the center

plane at a distanceD behind the center of the cylinder (U

= 10 m/s)


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bodies cannot offer valuable clues about the sound pressure level caused. In fact, the size of

coherent vortex structures and in consequence the correlation length are important indicators of the

amount of radiated sound. Also, isotropy of turbulence plays a decisive role. If the fluctuations of

all three velocity components are of about the same magnitude, the detected sound pressure level is

lower compared with anisotropic cases.

It can be summarized that the investigations presented not only allow a better understanding ofthe mechanisms taking place in the generation of aeroacoustic sound but also provide data for

comparisons with computational fluid dynamics. The second point is important as computational

aeroacoustics (CAA) fail without being based on good numerical data on the flow field.

References

[1] Becker, S.; Kaltenbacher, M.; Ali, I.; Hahn C. and Escobar, M.: Aeroacoustic Investigation of the Flow Around Cylinder Geometries - a Benchmark Test Case. In

Proceedings of the 13th AIAA/CEAS Aeroacoustics Conference, number 3511 in AIAA-

2007, May 21-23 2007, Rome, Italy

[2] Escobar, M.; Ali, I.; Hahn, C.; Kaltenbacher, M. and Becker, S.: Numerical and Experimental Investigation on Flow Induced Noise from a Square Cylinder. In 10th

AIAA/CEAS Aeroacoustics Conference, Manchester, number 2004-3004, 2004

[3] Blake, W. K.:Mechanics of Flow-Induced Sound and Vibration. Vol. 1, Academic Press,1986

[4] Zdravkovich, M. M.: Flow Around Circular Cylinders. Oxford University Press, 1997[5] Norberg, C.: Fluctuating Lift on a Circular Cylinder: Review and New Measurements.

Journal of Fluids and Structures, Vol. 17, pp. 57-96, 2003

[6] Norberg, C.: Flow Around Rectangular Cylinders: Pressure Forces and WakeFrequencies. Journal of Wind Engineering and Industrial Aerodynamics, Vol. 49, pp. 187-

196, 1993[7] Dutta, S.: Influence of the Orientation of a Square Cylinder on the Wake Properties.

Experiments in Fluids, Vol. 34, pp. 16-23, 2003

[8] Fujita, H.:Experimental Investigations and Prediction of Aerodynamic Sound Generatedfrom Square Cylinders. AIAA-98-2369

[9] Wang, H. F.: Flow Structure Around a Finite-Length Square Prism. 15th AustralasianFluid Mechanics Conference, September 13-17 2004, University of Sydney, Australia

[10]Sakamoto, H.: Vortex Shedding from a Rectangular Prism and a Circular Cylinder PlacedVertically in a Turbulent Boundary Layer. Journal of Fluid Mechanics, Vol. 126, pp. 147-

165, 1983

[11]Becker, S.; Lienhart, H. and Durst, F.: Flow Around Three-Dimensional Obstacles in

Boundary Layers. Journal of Wind Engineering, Vol. 90, pp. 265-279, 2002[12]Bendat, J.S., and Piersol, A. G., Random Data Analysis and Measurement Procedures,

John Wiley & Sons, New York, 1986

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