Aeroacoustic Effects of a Cylinder–Plate Configuration

Michael Winkler∗ and Klaus Becker†

Cologne University of Applied Sciences, 50679 Cologne, Germany

Con Doolan‡

University of Adelaide, Adelaide, South Australia 5005, Australia

Frank Kameier§

Düsseldorf University of Applied Sciences, 40474 Düsseldorf, Germany

and

Christian Oliver Paschereit¶

Technical University of Berlin, 10623 Berlin, Germany

DOI: 10.2514/1.J051578

Aerodynamically generated noise can be amplified enormously by the insertion of a plate behind a cylinder. In this

work, the aeroacoustic sound generation of a cylinder–plate configuration placed in a steady flow has been

investigated experimentally. The amplification of the generated sound is quantified, and the condition for the

amplification is analyzed in detail. In the experiments, the distance between cylinder and plate as well as the flow

velocity were varied. A critical spacing that depends on the Reynolds number was found, for which the sound

pressure levels rise dramatically. The variation of the distance and the flow velocity also showed a hysteresis effect

regarding the occurrence of the sound-pressure amplification.

Nomenclature

CL0 = sectional rms lift coefficientCs = sound pressure coefficientd = cylinder diameter, mmg = cylinder–plate distance, mmpc = sound pressure (single cylinder), Papc�p = sound pressure (cylinder–plate configuration), PaStc = Strouhal number calculated by sound pressure spectra

of the single cylinderStc�p = Strouhal number calculated by sound pressure spectra

of the cylinder–plate configurationt = plate thickness, mmu = flow velocity, m=sV = amplification factor� = correlation length, mm

I. Introduction

S OUND generation by bodies immersed in an airstream isimportant for a wide range of industrial applications like air-

conditioning systems, wind turbines, or heat exchangers. This holdsespecially for aeronautical applications such as landing gears, forexample. Further, sound generation by the interaction of bluff bodieswith downstream bodies can be enhanced enormously under certain

circumstances. A deep knowledge of the underlying sound-generation mechanisms is therefore important.

The flowfield of bluff bodies is often dominated by flowseparations and turbulence. Because of these flow separations, awake and free shear layers are formed behind the bluff bodies. Forinstance, instabilities in thewake of a circular cylinder at relative highReynolds numbers are responsible for the development of a Kármánvortex street. The more- or less-ordered vortices are convected withthe flow and interact with the downstream bluff body. By these bluffbody interactions, the whole flowfield can be changed. For example,the resistance forces of the bodies can be manipulated by theplacement of the interacting bodies.

The interest in bluff-body interactions for the control of noise foraerospace applications can be seen by the high number ofpublications on this field of research [1–5]. Awidely used setup is thecombination of cylinders and airfoils. The experiments of Jacob et al.[6] provide interesting physical information about a rod-airfoilconfiguration. At subcritical Reynolds numbers, the instantaneousflowfield is quite different from the classical vortex street. Strongthree-dimensional effects, secondary vortices, vortex splitting, andstretching significantly distort the flowfield and are responsible forspectral broadening around the shedding frequency and itsharmonics. They are particularly strong near the leading edge. As aresult, the leading edge is the dominant source region. Greschneret al. [7] predict the unsteady flowfield generated by an airfoil in thewake of a circular rod numerically by using a detached-eddysimulation and by using a Ffowcs Williams and Hawkings acousticanalogy formulation for the computation of far-field sound. Kao [8]numerically investigated the sound generation of vortices interactingwith an arbitrary body in a low-speed flow by the method of matchedasymptotic expansions. Kao concluded that sound radiation fromvortex/bluff-body interactions is almost always lower than that fromthe vortex/airfoil interaction. The explanation lies perhaps in the flowpattern in the nose region of a bluff body, where the fluid, afterimpacting a flat surface, branches off into two streams and skirts thecorners to be away from the body. As a result, the vortex never gets achance to be very close to the surface, and there is less interaction.

Other interesting phenomena regarding the interaction of bluffbodies are hysteresis effects.Many investigators study the interactionof flexible bodies or flexible mounted bodies, which show hysteresisregarding the vibration behavior and the flow pattern (Singh andMittal [9], Brika and Laneville [10], andWanderley et al. [11]). Also,the interaction of rigid bodies experiences hysteresis effects, even if

Presented at the 17th AIAA/CEAS Aeroacoustics Conference (32ndAIAA Aeroacoustics Conference), Portland, 5–8 June 2011; received 14September 2011; revision received 26 January 2012; accepted for publication1 February 2012. Copyright © 2012 by Michael Winkler. Published by theAmerican Institute of Aeronautics and Astronautics, Inc., with permission.Copies of this paper may be made for personal or internal use, on conditionthat the copier pay the $10.00 per-copy fee to theCopyright Clearance Center,Inc., 222RosewoodDrive, Danvers,MA01923; include the code 0001-1452/12 and $10.00 in correspondence with the CCC.

∗Scientific Assistant, Institute of Automotive Engineering, BetzdorferStrasse 2.

†Professor, Institute of Automotive Engineering, Betzdorfer Strasse 2.‡Associate Professor, School of Mechanical Engineering. Senior Member

AIAA.§Professor, Institute for Sound and Vibration Engineering, Josef Gockeln

Strasse 9.¶Chair of Fluid Dynamics, Hermann Föttinger Institut, Müller-Breslau-

Strasse 8.

AIAA JOURNALVol. 50, No. 7, July 2012

1614

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

there are fewer publications. Liu and Chen [12], for example, study aconfiguration of two square cylinders in tandem arrangement. It isshown that the flow patterns are not only affected by the distance ofthe bodies; they depend on themanner inwhich the distance is varied.Tasaka et al. [13] investigate two circular cylinders in tandemarrangement and visualize the flow pattern. According to how thedistance is changed, two different flow modes are discerned. Carmoet al. [14] also investigate the possible states in the flow around twoidentical circular cylinders in a tandem arrangement. Numericalsimulations are used to study the hysteresis in the transition region offlowmodes. The relationship between three dimensional instabilitiesand hysteresis is also addressed.

In the aforementioned investigations on hysteresis effects, only theinteraction of equal-shaped bodies are investigated, and acoustics arenot considered. The aim of this investigation is to enhance theknowledge of physical effects like hysteresis for two differentinteracting bodies and their impact on the aeroacoustic sound-generationmechanisms. Therefore, a simple configuration is chosen,which consists of a circular cylinder and aflat plate. Themain issue ofthe present investigation is sound amplification, caused by placingthe plate in the wake of the circular cylinder. The prerequisites forthe sound amplification are analyzed by varying the spacing betweenthe bodies and the flow velocity. Hysteresis effects regarding thevariation of these parameters are investigated, and the amplificationis quantified in relation to the Reynolds number.

II. Experimental Setup

The experiments are carried out in the University of Adelaide’sanechoic wind tunnel, where a freejet is generated at a rectangularchannel outlet (275 � 75 mm). The test configuration, consisting ofa flat plate and a circular cylinder, is placed in the core of a freejet(Fig. 1). The plate, with its dimensions of 120 � 60 � 1 mm, is madeout of steel. It is supported by a steel rod, which is mounted to acomputer-controlled traverse system. The positional accuracy of thetraverse system is�6:25 �m. The mainly used cylinder diameter dis 3mm, but there are alsomeasurementswhere the cylinder diameteris varied from 2 mm up to 10 mm. The maximum flow velocity u is30 m=s. It is calculated using pressure measurements from a pitottube, which is mounted in the center of the outlet plane before thetests. The pressure measurements are taken by a MKS Instruments220BD Baratron differential capacitance manometer, with anaccuracy of�0:15% of the reading. Together with the random errorsin temperature and absolute-pressure measurements, the randomerror for the flow velocity is estimated to be less than 1%. The area ofthe core flow is 165 � 45 mm. The turbulence intensity, measured inthe core flow of the outlet plane, is 0.4%. Based on cylinder diameterand maximum velocity, the Reynolds number is up to about1:7 � 104, and the Mach number is below 0.09.

Acoustic data are acquired by a half-inch condenser microphoneType 4190 fromBrüel&Kjær. Themicrophone is calibrated at 1 kHzand 94 dB by the CA 106 sound calibrator from BSWATechnology.It is placed perpendicular to the cylinder axis at half-height of the testconfiguration in 0.08 m distance from the center. The measurementdata are collected using a National Instruments board at a samplingfrequency of 32,768 Hz. The resulting frequency resolutions for thecalculated spectra is 1Hz. Themaximum frequency error is therefore�0:5 Hz. Together with the random errors of the flow velocity andthe diameter of the cylinder, the estimated uncertainty of the Strouhalnumber is approximately 2%.

III. Results

A. Comparison of Configurations

The auto-power spectra of the sound pressure level (SPL)for different test configurations at a flow velocity of 15 m=s(Re� 2250) are shown in Fig. 2. In addition to the results of thecylinder–plate configuration, the results of the freejet, the plate, thecylinder, and the no-flow background noise are plotted for reference.The background noise measurement shows that there are someexternal disturbances in the frequency range around 200 Hz.However, the signal-to-noise ratio is big enough to avoid an influenceof this disturbances on the measurement results of the testconfigurations. By the noise measurements of the freejet, it can beseen that the sound pressure level below 300 Hz is mainly caused bythe freejet. Only the single plate and the cylinder–plate configurationgenerate additional noise around a frequency of approximately200 Hz. This noise is generated by vortices shedding from the rodsupporting the plate. The insertion of the plate into the freejet alsocauses an increase of the sound pressure level between 1000 and4000 Hz with broadband characteristic. In comparison to the resultsfor the single plate, the single cylinder within the freejet produces anincrease of the sound pressure level centered on 1055 Hz. Thisbehavior is caused by alternately shedding vortices from the cylinderand by the vortex street behind the cylinder. The resulting Strouhalnumber is 0.21, which is expected for a circular cylinder at aReynolds number of 3000. Furthermore, first and second harmonicsare visible. The positioning of the plate in the wake of the cylindercauses a large increase of the sound pressure level, compared to thesingle-cylinder case. In the following, such an increase is termedsound-pressure amplification. For the results shown in Fig. 2, thesound pressure level at the aeolian tone is amplified by nearly 30 dB,which is a factor of around 30 in the linear scale. The harmonics areamplified by a larger factor. There is also a change in frequency. Incomparison to the single cylinder, the main peak for the cylinder–plate configuration decreases to 959 Hz. This results in a value of0.19 for the Strouhal number. The investigation of the frequencybehavior will be discussed later in this paper.

Fig. 1 Schematic representation of the test setup (top); photographs of

the test setup (bottom).

Fig. 2 Auto-power spectra of the soundpressure levels for different test

configurations. Normalized distance g=d� 4; flow velocity u� 15 m=s;Reynolds number Re� 22500.

WINKLER ETAL. 1615

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

B. Parameter Variations

The results for the parameter-variation study were acquired bysetting the flow velocity to be constant and then increasing thenormalized distance g=d from 0 to 5. This procedure is repeated foreach flow velocity between 0 and 30 m=s with a resolution of0:3 m=s. The resolution of the distance variation is 0.25 mm. Thatresults in 6161 measurement points and gives a detailed overview ofthe system behavior (Fig. 3). Therefore, the overall sound pressurelevel, which is obtained by filtering the microphone signal between50 and 12,800 Hz and calculating its mean square, is shown. Thereare two regions to be differentiated: an amplification and anonamplification situation. Below a normalized distance of around2.75, the overall sound pressure level is significantly lower than forlarger distances. In this region, the cylinder–plate configurationgenerates less noise because the plate acts more like a splitter plateand prevents the generation of vortices behind the cylinder. Theseresults match with findings in literature, in that there is a criticalspacing [15,16]. Unal and Rockwell [17] also investigate the criticalspacing and define a pre- and post-vortex formation region. But, tothe authors’ knowledge, there are fewer investigations on thedependency of the critical spacing on the flow velocity and Reynoldsnumber as well as its effect on aeroacoustics.

The effect of the lateral edges of the plate on the acoustics isdifficult to determinewithout detailed visualizationmethods, but onecan suspect that, during the interaction, streamwise vorticeswill formclose to the edge, either from the pressure differential across the plateor stretching of the vortex shed from the cylinder as it passes over theplate.Whatever the effect of the edge is on the flow, it appears to havea small effect on the acoustics, as the main aspects of theconfiguration can be explained by two-dimensional phenomena.

The spectrogram on the right-hand side of Fig. 3 provides aninsight into the behavior of the investigated configuration. Thediagram contains the sound-pressure-level spectra of all tested flowvelocities at a normalized distance of 2.9. The data show some areasof sound pressure level rise, forwhich the relation between frequencyand velocity is approximately linear. The line of sound pressure levelrise below 400 Hz, which shows up over the whole velocity range, iscaused by shedding vortices from the support of the plate. Thesupport consists of a cylindrical rod with a diameter of 11 mm and istherefore expected to produce sound at relative low frequenciescompared to the tested cylinderwith its 3mmdiameter. Because of itslow frequency content and the relative low sound pressure levelscompared to the amplified sound pressure levels, the influence of thesupport on the investigated effects can be neglected. The actualregion of interest in the spectrogram spans from the bottom-leftcorner of the diagram to the upper-right corner.

For flow velocities below 4 m=s and frequencies less than 250 Hz,the sound pressure level of the cylinder–plate configuration is

amplified in comparison to the single-cylinder case. The amplificationof the sound pressure level can also be seen by the presence of aharmonic. For a further increase of the flow velocity, the sound-pressure amplification vanishes. The still-visible line between 4 m=sand 18 m=s has a different gradient and is less intense. This is causedbyunmodified shedding fromspanwise portion of the cylinderwithouta plate downstream. At 17:9 m=s and a frequency of around 1100Hz,the sound pressure level increases drastically. It can be seen that thesound pressure level rises over the whole frequency range and most atthe vortex-shedding frequency. In addition to that, the vortex sheddingfrequencydrops byaround100Hz.The diagram inFig. 4 is createdoutof the measurement results shown in Fig. 3a. The illustrated pointsmark the change between the amplification and nonamplificationsituation as a function of flow velocity and normalized distance. It canbe seen that the critical distance depends on the flow velocity and,consequently, the Reynolds number. At relatively highflow velocities,the critical distance decreases approximately linearly with the flowvelocity and approaches a maximum. This maximum value of 3.2 interms of normalized distance g=d is reached for a flow velocity ofaround 6 m=s (Re� 1200). Interestingly, below this velocity, thecritical distance, atwhich the soundpressure level is amplified, reducesagain. An explanation for this effect can be found in the literature.Norberg [18] investigates thevortex formation length for aflowarounda single circular cylinder and for varying Reynolds numbers. Fromthese results and according tomeasurement results of other researchers[17,19], it can be seen that thevortex formation length canvary. It has amaximum at a Reynolds number of about 1200 and decreases forlower and higher Reynolds numbers. There is a slight difference

a) b)

Fig. 3 Overall sound pressure level, band-pass-filtered between 50 Hz and 12,800 Hz, of the cylinder–plate configuration for variation of normalized

distance g=d and flow velocity u. a) Overview of all measurement points, and b) spectrogram for a normalized distance g=d� 2:9.

Fig. 4 Critical spacing for transition from nonamplification to

amplification situation, marked by � at largest sound-pressure-level

rise of data in Fig. 3.

1616 WINKLER ETAL.

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

between the absolute values of formation length and the criticalspacing of the present investigation. This difference can be attributedto slight changes in the formation of the cylinder wake because of thedownstream plate. An indication for this is the frequency variation asdiscussed for the results in Fig. 2. But, in general, it can be seen that thecritical distance for the sound-pressure-level amplification of thecylinder–plate configuration is linked to the vortex formation length ofthe cylinder wake.

This argument, that changes in the fluid dynamics with gapdistance causes variations in the sound-pressure amplification issupported by results of Ozono [20]. His investigation of a cylinderwith a detached flat plate shows that there is a critical spacing of2< g=d < 2:4 for 6700< Re < 25000 for the generation of vorticesbetween cylinder and plate. Roshko [21] and Hwang et al. [22] alsostate that, for a certain distance, the plate can inhibit the vortexgeneration. By these results, it can be seen that the critical spacing forsound amplification relies on the generation of vortices betweencylinder and plate.

C. Frequency Behavior

The relation of shedding frequency, flow velocity, and normalizeddistance g=d can be seen in Fig. 5. Here, the Strouhal number isplotted against the Reynolds number for values of g=d from 3.17 to4.92. For these normalized distances, the sound-pressureamplification exists over the whole velocity and Reynolds numberranges, respectively. In addition to that, the result for the singlecylinder is plotted. The dependency of Strouhal number andReynolds number for the single cylinder can be differentiated in threeregions by the shape of the curve. Between Reynolds numbers from500 to approximately 1250, the Strouhal number shows a steep andnearly linear increase. For higher Reynolds numbers up to 3900, theStrouhal number increases further, but the inclination is not linearanymore. From Reynolds numbers of 3900 onward, the Strouhalnumber starts to decrease in a linear manner. The changes in the runof the curve are attributed to changes in the pattern of the vortexstreet, as it is discussed byRoshko [23] and Fey et al. [24]. The curvesfor the cylinder–plate configurations show a similar behavior,although the changes are not as well pronounced. The differences inStrouhal number between the single cylinder and cylinder–plateconfiguration show that a reduction in vortex shedding frequencyoccurs when the plate is inserted behind the cylinder. The drop inStrouhal number is smallest for the largest distance between cylinderand plate. The nearer the plate approaches the cylinder, the more thevortex shedding process is altered. On the right-hand side of Fig. 5,the Strouhal numbers of the cylinder–plate configurations aredivided by the Strouhal numbers of the single-cylinder case. It can beseen that the reduction in Strouhal number depends on the Reynoldsnumber as well. The largest reduction is at Reynolds numbers of

around 1250. For increasing Reynolds numbers, the differencereduces. As discussed in the previous subsection, the length of thevortex formation region is reduced for increasing Reynolds numbershigher than 1250. Because of this, the effective distance between theleading edge of the plate and formation region increases, althoughthe normalized distance is kept constant. Therefore, the influence ofthe plate on the vortex shedding process is less intense, and theStrouhal number increases toward the value of the single cylinder.This behavior can also be seen in Fig. 6. Here, the Strouhal/Reynoldsnumber relation is shown for a range of Reynolds numbers from 500up to 1:8 � 104. The wide range of Reynolds numbers is set byvarying the flow velocity from 10 m=s to 25 m=s in increments of5 m=s and the use of different cylinders with 2, 3, 4, 5, 6, 8, and10 mm in diameter. The measurements are taken for the single-cylinder case (empty symbols) and the cylinder–plate configuration(filled symbols) for a fixed normalized distance g=d� 4. In additionto that, an empirical function by Norberg [25] for the Strouhalnumber of a circular cylinder is plotted for reference. Themeasurement data show some scatter for equal Reynolds numbers.One reason for the scatter might be the changing aspect ratio ofcylinder diameter and cylinder length, which is 17.5 for the largestdiameter cylinder and 77.5 for the smallest diameter cylinder. Onecan expect the flow at around midspan to be effectively decoupledfrom the Strouhal number, influencing end effects at some finiteaspect ratio. Norberg [26] suggests aminimum aspect ratio of around

Fig. 5 a) Strouhal number as a function of Reynolds number for single cylinder○ and different normalized distances g=d� 3:17, �; 3.42, � ; 3.67,▶;

3.92,■; 4.17,▼; 4.42,◆; 4.67,▲; 4.92,◀; b) Strouhal number reduction of cylinder–plate configuration Stc�p in relation to the Strouhal number for the

single cylinder Stc.

Fig. 6 Strouhal number as a function ofReynolds number for the single

cylinder (empty symbols) and the cylinder–plate configuration (filled

symbols) at g=d� 4. The Reynolds number is varied by four different

flowvelocities (10 m=s, 15 m=s, 20 m=s, and 25 m=s) and seven cylinderdiameters (2 mm,○ �; 3 mm,□■; 4 mm,◇◆; 5 mm,▽▼; 6 mm,▲△;

8 mm,◁◀; 10 mm,▷▶. The solid line represents the empirical formula

of Norberg [18].

WINKLER ETAL. 1617

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

50 for 600< Re < 4000 and 60–70 for 4000< Re < 104. The effectof outlet area blockage on the flow velocity by the cylinders iscorrected by means of experimentally determined correction factors.The form of the curve of themeasurement data for the single-cylindercase generally agree with the empirical function of Norberg.Presumably, the disparity between the present results and those ofNorberg [25] are combination effects related to the notabledifferences in end conditions of the cylinder, turbulence level, andaspect ratio. The comparison of the single-cylinder case with theresults for the cylinder–plate configuration show the largestdifference for small Reynolds numbers. For increasing Reynoldsnumbers, the difference is reduced. At very high Reynolds numbersof around 104, the difference is nearly constant. This complies withthe argumentation in the last paragraph. The vortex formation lengthalso reaches a nearly constant value in this range of Reynoldsnumbers (see [18]), and with this the influence of the plate on thevortex formation process stays unchanged.

D. Hysteresis Effects

For the investigations of hysteresis effects, the flow velocity is setto 12 m=s, and the distance is increased by 0.25 mm steps from 0 to15 mm, which corresponds to a normalized distance of 0 to 5. Afterthis, the plate is moved backward to zero distance. The results ofthese measurements are shown in Fig. 7. The overall sound pressurelevel is plotted as a function of the normalized distance g=d. Thepoints acquired for increasing normalized distance jump fromone state to the other at a normalized distance of nearly 3.2. For thedecreasing distance, there is no drop back to the nonamplifiedstate until a value of 2.7. The results show a clear hysteresis effect. Inthe region between the normalized distances of 2.7 to 3.2, thenonamplified (as well as the amplified state) is stable and depends onthe direction of parameter variation.

The dependencyof the sound pressure level on themanner offlow-velocity variation is analyzed for constant values of normalizeddistance. The flow velocity is increased from 0 to 24 m=s, in 0:3 m=ssteps, and then decreased to zero velocity again. The results of thesemeasurements can be seen in Fig. 8. The overall sound pressure level

is plotted against the flow velocity for three different distances. In theupper diagram, the normalized distance is set to 2.75, whichcorresponds to a distance of 8.25 mm. The sound-pressureamplification exists right from the beginning at low flow speeds. Itvanishes for slightly higher velocities and occurs again at a muchhigher flow speed. If the flow velocity is decreased again, the sound-pressure amplification vanishes at a lower flow velocity compared tothe establishing for increasing velocity. The same effect exists for thechange at lower flow speeds. The diagram in the middle of Fig. 8 isplotted for a normalized distance of 3. The comparison of increasedand decreased flow-velocity variation shows the same hysteresiseffect like for a distance of g=d� 2:75, although the changes occurat different flow speeds. The lower diagram shows the results for anormalized distance of 3.25. These measurement results do not showany great change of the sound pressure level. The sound-pressureamplification is stable for all flow speeds. All results in Fig. 8 matchwell with the findings in Fig. 3, and they show an additional aspect ofthe flow-velocity variation. The occurrence of sound-pressure-levelamplification for the cylinder–plate configuration not only dependson the flow-velocity variation, but it also depends on the manner inwhich the velocity is varied.

Hysteresis effects are not necessarily linked to the occurrence offluid structure interactions, as can be seen by the work of Inoue et al.[16] or other research on tandem cylinder flows [13,14]. For thecurrent investigation, the structure dynamic behavior of the plate hasa negligible effect on the acoustic results. This was shown in aseparate investigation (see [27]) on the basis of varied structuraldynamic parameters. The hysteresis in this study is related tononlinear fluid dynamics rather than fluid-structure interactioneffects.

E. Quantification of the Sound-Pressure Amplification

In the previous subsections, the specific conditions under whichthe sound pressure is amplified by the plate are discussed in detail.The concern of the following subsection is to quantify theamplification of the cylinder–plate configuration in comparison withthe single-cylinder case. Therefore, an amplification factor V isdefined:

V �pc�ppc

(1)

In this definition, pc�p is the sound pressure of the cylinder–plateconfiguration, and pc is that of the single cylinder, taken at thecorresponding vortex-shedding frequencies. The dependency ofthe amplification factor on the flow velocity is plotted in Fig. 9. Theresults are shown for measurements taken with a cylinder 3 mm indiameter and a normalized distance g=d� 4. The run of the curve issimilar for all the normalized distances between 3.17 and 4.92,whichresult in the sound-pressure amplification over the whole velocity

Fig. 7 Distance hysteresis of the overall sound pressure level for flow

velocity u� 12 m=s; increasing distance, ○; decreasing distance, �.

a)

b)

c)

Fig. 8 Flow-velocity hysteresis of the overall sound pressure level for

three different normalized distances; increasing velocity, ○; decreasing

velocity, �; a) g=d� 2:75; b) g=d� 3; and c) g=d� 3:25.Fig. 9 Amplification factor as a function ofReynolds number.Cylinder

diameter d� 3 mm; normalized distance g=d� 4.

1618 WINKLER ETAL.

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

and Reynolds number range, respectively. The Reynolds number isaltered by variation of the flow velocity. For a Reynolds number of500, the amplification factor starts to increase from values of around10 to 15 up to 40 for a Reynolds number of 1500. Irrespective of asmall reduction of the amplification factor at around a Reynoldsnumber of 2300, V varies between 25 and 40 for the range betweenReynolds numbers of 1500 and 3900. From there on, theamplification factor decreases to a value of 7 at Re� 6000. Thereason for the decrease of the amplification factor for higherReynolds numbers is investigated by means of Fig. 10. Here, thesound pressure level of the cylinder–plate configuration and thesingle cylinder are plotted as a function of the Reynolds number.The sound pressure levels are scaled by subtraction of the logarithmof the flow velocity to the power of 5.3. Hence, a horizontal curvedenotes that the radiated power is proportional to u5:3. The cylinder–plate configuration shows this behavior for Reynolds numbers higherthan Re� 2000. For lower Reynolds numbers, the value is less than5.3. The behavior of the single cylinder can be differentiated in threeregions as follows. Below Reynolds numbers of 1250, the exponentof the flow velocity is much lower than 5.3. Between Reynoldsnumbers of approximately 1250 and 3000, the sound pressure levelof the single cylinder behaves like the cylinder–plate configurationand varies with u5:3. For Reynolds numbers above 3000, the singlecylinder shows a different behavior. The exponent of the flowvelocity ismuch higher than 5.3, as seen by the steeply increase of thescaled sound pressure level.

The amplification factor is roughly constant in the Reynoldsnumber range between 1250 and 3000. This is caused by the nearlysimilar proportionality of the flow velocity and the radiated soundpower for the cylinder–plate configuration and the single cylinder.The drop of the amplification factor for higher Reynolds numbers iscaused by the single cylinder. The proportionality of radiated powerand flow velocity rises compared to the cylinder–plate configuration.Hence, the radiated power increases faster with Reynolds number forthe single cylinder in comparison to the cylinder–plate configuration,and therefore the amplification factor drops. The reason for thechange in sound power radiation by a cylinder can be found inthe dependence of the sound power radiation on the lift coefficient.The noise radiated by a cylinder with vortex shedding is closelyrelated to its lift coefficient, as can be seen in the theory of Phillips[28], for example. A sound pressure coefficient Cs is defined byKeefe [29] in terms of sectional rms lift coefficient CL0 , Strouhalnumber St, and normalized spanwise correlation length �=d:

Cs � CL0St�����������=d

p(2)

Deviations from a sixth-power law as it is normally expected for adipole sound source like the vortex-shedding cylinder (see Heckeland Müller [30]) will occur when Cs varies with the Reynoldsnumber. By combination of measurement data from several differentauthors, Norberg [25] shows that the sound pressure coefficient

depends strongly on the Reynolds number. For Reynolds numbersbetween 3000 and 6000, the sound pressure coefficient rapidlyincreases. Themeasurement data of Leehey andHanson [31] supportthe rapid increase, and their sound pressure measurements also showsignificant deviations from a sixth-power law. For the cylinder–plateconfiguration, the sound radiation ismainly caused by the interactionof plate with the vortices. Therefore, the lift coefficient, andconsequently the sound pressure coefficient of the plate, shows adifferent dependency on the Reynolds number compared to thecylinder.

IV. Conclusions

Aeroacoustic effects regarding the flow around a circular cylinderand a downstream flat plate have been investigated experimentally.Compared with the single-cylinder case, the positioning of the platebehind the cylinder can amplify the generated sound pressure. Theoccurrence of this sound-pressure amplification depends on the flowvelocity as well as the distance between cylinder and plate. It alsodepends on the manner in which the parameters are varied. Theresults for the variation of flow velocity as well as the variation ofdistance between cylinder and plate show hysteresis regarding theoccurrence of the sound-pressure amplification. This sound pressurerise can be quantified by a factor V, which is around 30 for lowerReynolds numbers and decreases for increasing Reynolds numbers.The Strouhal number is reduced by the insertion of the plate. Theinfluence of the plate on the Strouhal number reduces for increasingReynolds numbers.

Acknowledgments

This research project is part of the Competence Center Sound andVibration Engineering, founded by the Ministry for Innovation,Science and Research of the German federal state North Rhine-Westphalia. The first author would like to acknowledge the supportby B. Virnich, Müller-BBM VibroAkustik Systeme GmbH, for themeasurement software PAK and the University of Adelaide forproviding the test facilities.

References

[1] You, D., Choi, H., Choi, M.-R., and Kang, S.-H., “Control of Flow-Induced Noise Behind a Circular Cylinder Using Splitter Plates,” AIAAJournal, Vol. 36, No. 11, 1998, pp. 1961–1967.doi:10.2514/2.322

[2] Spiteri,M., Zhang,X.,Molin, N., andChow,L.C., “The use of a Fairingand Split Plate for Bluff Body Noise Control,” 14th AIAA/CEASAeroacoustics Conference, Vancouver, AIAA Paper 2008-2817,May 2008.

[3] Oerlemans, S., Sandu, C., Molin, N., and Piet, J., “Reduction ofLanding Gear Noise Using Meshes,” 16th AIAA/CEAS AeroacousticsConference, Stockholm, AIAA Paper 2010-3972, June 2010.

[4] Boorsma,K., Zhang,X.,Molin,N., andChow,L.C., “BluffBodyNoiseControlUsing Perforated Fairings,”AIAA Journal, Vol. 47,No. 1, 2009,pp. 33–43.doi:10.2514/1.32766

[5] Khorrami, M. R., Choudhari, M.M., Lockard, D. P., Jenkins, L. N., andMcGinley, C. B., “Unsteady Flowfield Around Tandem Cylinders asPrototype Component Interaction in Airframe Noise,” AIAA Journal,Vol. 45, No. 8, 2007, pp. 1930–1941.doi:10.2514/1.23690

[6] Jacob,M. C., Boudet, J., Casalino, D., andMichard,M., “ARod-AirfoilExperiment as a Benchmark for Broadband Noise Modeling,”Theoretical and Computational Fluid Dynamics, Vol. 19, No. 3, 2005,pp. 171–196.doi:10.1007/s00162-004-0108-6

[7] Greschner, G., Thiele, F., Jacob,M. C., and Casalino, D., “Prediction ofSound Generated by a Rod-Airfoil Configuration Using EASM DESand the Generalised Lighthill/FW-H Analogy,” Computers and Fluids,Vol. 37, No. 4, 2008, pp. 402–413.doi:10.1016/j.compfluid.2007.02.013

[8] Kao, H. C., “Vortex/Body Interaction and Sound Generation in Low-Speed Flow,” NASATM 1998-208403, 1998.

[9] Singh, S. P., and Mittal, S., “Vortex-Induced Oscillations at LowReynolds Numbers: Hysteresis and Vortex-Shedding Modes,” Journal

Fig. 10 Sound pressure level of single cylinder ◇ and cylinder–plate

configuration� at normalized distance g=d� 4, scaled to the 5.3 power of

flow velocity u.

WINKLER ETAL. 1619

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578

of Fluids and Structures, Vol. 20, No. 8, 2005, pp. 1085–1104.doi:10.1016/j.jfluidstructs.2005.05.011

[10] Brika, D., and Laneville, A., “The Flow Interaction Between aStationary Cylinder and a Downstream Flexible Cylinder,” Journal ofFluids and Structures, Vol. 13, No. 5, 1999, pp. 579–606.doi:10.1006/jfls.1999.0220

[11] Wanderley, J. B. V., Sphaier, S. H., and Levi, C., “A NumericalInvestigation of the Hysteresis Effect on Vortex Induced Vibrationon an Elastically Mounted Rigid Cylinder,” 28th InternationalConference on Offshore Mechanics and Arctic Engineering, ASMEPaper OMAE2009-79725, 2009.

[12] Liu, C. H., and Chen, J. M., “Observations of Hysteresis in FlowAround Two Square Cylinders in a Tandem Arrangement,” Journal ofWind Engineering and Industrial Aerodynamics, Vol. 90, No. 9, 2002,pp. 1019–1050.doi:10.1016/S0167-6105(02)00234-9

[13] Tasaka, Y., Kon, S., Schouveiler, L., and Le Gal, P., “Hysteretic ModeExchange in the Wake of Two Circular Cylinders in Tandem,” Physicsof Fluids, Vol. 18, No. 8, 2006, Paper 084104.doi:10.1063/1.2227045

[14] Carmo, B. S., Meneghini, J. R., and Sherwin, S. J., “Possible States inthe FlowAroundTwoCircular Cylinders inTandemwith Separations inthe Vicinity of the Drag Inversion Spacing,” Physics of Fluids, Vol. 22,No. 5, 2010, Paper 054101.doi:10.1063/1.3420111

[15] Yucel, S. B., Cetiner, O., and Unal, M. F., “Interaction of CircularCylinder Wake with a Short Asymmetrically Located DownstreamPlate,” Experiments in Fluids, Vol. 49, No. 1, 2010, pp. 241–255.doi:10.1007/s00348-010-0852-x

[16] Inoue, O., Mori, M., and Hatakeyama, N., “Aeolian Tones Radiatedfrom Flow Past Two Square Cylinders in Tandem,” Physics of Fluids,Vol. 18, No. 4, 2006, Paper 046101.doi:10.1063/1.2187446

[17] Unal, M. F., and Rockwell, D., “On Vortex Formation from a Cylinder,Part 2: Control by Splitter-Plate Interference,” Journal of Fluid

Mechanics, Vol. 190, 1988, pp. 513–529.doi:10.1017/S0022112088001430

[18] Norberg, C., “LDV-Measurements in the Near Wake of a CircularCylinder,”Advances inUnderstanding of Bluff BodyWakes andVortex-

Induced Vibration, American Society of Mechanical Engineers,Fairfield, NJ, 1998.

[19] Williamson, C.H.K., “VortexDynamics in theCylinderWake,”AnnualReview of Fluid Mechanics, Vol. 28, 1996, pp. 477–539.doi:10.1146/annurev.fl.28.010196.002401

[20] Ozono, S., “Flow Control of Vortex Shedding by a Short Splitter Plate

Asymmetrically Arranged Downstream of a Cylinder,” Physics of

Fluids, Vol. 11, No. 10, 1999, pp. 2928–2934.doi:10.1063/1.870151

[21] Roshko, A., “On the Drag and Shedding Frequency of Two-Dimensional Bluff Bodies,”NACATN 3169, 1954.

[22] Hwang, J. Y., Yang, K. S., and Sun, S. H., “Reduction of Flow-InducedForces on a Circular Cylinder Using a Detached Splitter Plate,” Physicsof Fluids, Vol. 15, No. 8, 2003, pp. 2433–2436.doi:10.1063/1.1583733

[23] Roshko, A., “On the Development of Turbulent Wakes from VortexStreets,” NACA Rept. 1191, 1954.

[24] Fey, U., Koenig, M., and Eckelmann, H., “A New Strouhal–Reynolds-Number Relationship for the Circular Cylinder in the Range47< Re < 2 � 105,” Physics of Fluids, Vol. 10, No. 7, 1998,pp. 1547–1549.doi:10.1063/1.869675

[25] Norberg, C., “Fluctuating Lift on a Circular Cylinder: Review and NewMeasurements,” Journal of Fluids and Structures, Vol. 17, No. 1, 2003,pp. 57–96.doi:10.1016/S0889-9746(02)00099-3

[26] Norberg, C., “An Experimental Investigation of the Flow Around aCircular Cylinder: Influence of Aspect Ratio,” Journal of Fluid

Mechanics, Vol. 258, 1994, pp. 287–316.doi:10.1017/S0022112094003332

[27] Winkler, M., and Becker, K., “Vibroacoustic Behavior of PlateStructures in Vortex Fields,” 11th International Symposium of Students

and Young Mechanical Engineers, Gdańsk Univ. of Technology,Gdańsk, Poland, 2008, pp. 169–178.

[28] Phillips, O. M., “The Intensity of Aeolian Tones,” Journal of Fluid

Mechanics, Vol. 1, 1956, pp. 607–624.doi:10.1017/S0022112056000408

[29] Keefe, R. T., “An Investigation of the Fluctuating Forces Acting on aStationary Circular Cylinder in a Subsonic Stream, and of theAssociated Sound Field,” Univ. of Toronto Inst. of AerophysicsRept. 76, Toronto, 1961.

[30] Heckl,M., andMüller, H. A., “Strömungsgeräusche,” Taschenbuch derTechnischen Akustik, edited by B. Stüber, C. Mühle, and K. Fritz,2nd ed., Springer, Berlin, 1994, pp. 195–196.

[31] Leehey, P., and Hanson, C. E., “Aeolian Tones Associated withResonant Vibration,” Journal of Sound and Vibration, Vol. 13, No. 4,1970, pp. 465–483.doi:10.1016/S0022-460X(70)80052-9

M. GlauserAssociate Editor

1620 WINKLER ETAL.

Dow

nloa

ded

by C

AR

LE

TO

N U

NIV

ER

SIT

Y L

IBR

AR

Y o

n Se

ptem

ber

27, 2

013

| http

://ar

c.ai

aa.o

rg |

DO

I: 1

0.25

14/1

.J05

1578