Effects of splitter plates and Reynolds number on the aerodynamicloads acting on a circular cylinder

Y. Qiu a, Y. Sun a,b,n, Y. Wu a,b, Y. Tamura c

a School of Civil Engineering, Harbin Institute of Technology, Heilongjiang, Harbin 150090, Chinab Key Lab of Structures Dynamic Behavior and Control, Harbin Institute of Technology, Ministry of Education, Heilongjiang, Harbin 150090, Chinac Tokyo Polytechnic University, 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan

a r t i c l e i n f o

Article history:Received 21 October 2013Received in revised form19 February 2014Accepted 19 February 2014Available online 13 March 2014

Keywords:Circular cylinderReynolds numberSemi-cylindrical roofSplitter plateVortex shedding

a b s t r a c t

Many studies have been undertaken aimed at reducing drag forces and suppressing vortex sheddingfrom circular cylinders, mainly focusing on the influence of the splitter plate in the wake of the airflow.In this study, a circular cylinder with diameter D (0.4 m) with splitter plates has been used to investi-gate the aerodynamic differences between a bare cylinder and a semi-cylindrical roof. Wind tunnelexperiments, with simultaneous multi-pressure measurements on cylinders with frontal, wake andbilateral splitter plates, have been undertaken for a range of Reynolds numbers from 6.90�104 to8.28�105. It was found that a frontal splitter plate, with plate length to cylinder diameter ratio of L/D¼3,has produced a postcritical flow at relatively low Reynolds numbers by the generated disturbances in theapproaching flow. For the semi-cylindrical roof, that can be approximated as a circular cylinder withbilateral plates under similar flow conditions, the vortex shedding is suppressed by a splitter plate(L/D¼3) in the wake. The results reveal that the transition of separated shear layer around a semi-cylindrical roof occurs in the Reynolds number range 6.90�104 to 1.66�105. The mean and fluctuatingpressure distributions become relatively stable when Re41.66�105.

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1. Introduction

Unsteady flow around bluff bodies, especially circular cylinders,has been studied extensively for various engineering applications,such as buildings, bridge cables, risers in marine engineering, etc.A strong dependence of the aerodynamic behavior on Reynoldsnumber has been shown for two primary reasons: the first isthe position of the flow separation point, which is associated withthe state of the surface boundary layer and hence the Reynoldsnumber; the second is the strength of vortex shedding due to theinteraction of separated shear layers, which affects the magnitudeof wake suctions and generates large unsteady forces. Since vortexshedding in the wake has the potential to damage the integrity ofcylindrical structures, and also dependent on Reynolds number,the suppression of vortex shedding has been one of the mostactive topics of research for many decades due to its significancefor engineering applications. Zdravkovich (1981) proposed somepassive control devices for suppressing vortex shedding, including

surface protrusions (e.g. helical strakes, wires, studs or spheres,etc.), shrouds, and near-wake stabilizers such as splitter plates.

A rigid splitter plate, as one of most frequently used suppres-sion devices, can inhibit the formation of vortices or disrupt theirformation. Previous investigations by Roshko (1953, 1954) foundthat placing a splitter plate of length 5D (D is the cylinderdiameter) in the wake can inhibit the periodic vortex formationand increase the base pressure considerably. The experiment wascarried at a subcritical Reynolds number of 1.45�104. Gerrard(1965a) also conducted an experimental investigation on the flowpatterns around a circular cylinder with splitter plates of differentlengths up to a maximum of 2D at a Reynolds number of 2.0�104.He verified a phenomenon that the shedding frequency is inver-sely proportional to the length scale of the vortex formationregion. Apelt et al. (1973) and Apelt and West (1975) system-atically studied the effects of wake splitter plates on circularcylinders with Reynolds numbers in the range 104oReo5�104.It was found that splitter plates longer than 2D in the wake of acircular cylinder can progressively modify the drag and vortexshedding up to a plate length/diameter ratio of L/D¼3; while nofurther changes occur with L/D43 and with no vortex shedding.Adachi et al. (1990) used three wake splitter plates (L/D¼1/6,1 and 3) to investigate their effects on the drag and vortexshedding of a circular cylinder in a Reynolds number range of

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Journal of Wind Engineeringand Industrial Aerodynamics

http://dx.doi.org/10.1016/j.jweia.2014.02.0030167-6105 & 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: School of Civil Engineering, Harbin Institute ofTechnology, Heilongjiang, Harbin 150090, China. Tel.: þ86 451 86282080.

E-mail address: sunnyhit@hit.edu.cn (Y. Sun).

J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50

5�104oReo107. The results proved that the drag forces can beremarkably reduced in the subcritical regime, and that the wakesplitter plate serves to suppress the separation bubble in thesupercritical regime.

This brief review shows that most works aim to develop flowcontrol devices by using fixed rigid splitter plates in the wake tosuppress the vortex shedding of slender structures such as tallbuildings. However, unsteady flow around a semi-cylindrical roofhas received limited attention, and such structures are found to besensitive to Reynolds number due to the curved surface. A studyby Johnson et al. (1985) revealed that the separation point of thesemi-cylindrical roof showed a strong Reynolds number depen-dency in the range 1.0�104 to 4.75�105, and thus the meanpressure distributions varied significantly with Re. Toy and Tahouri(1988) experimentally studied the surface pressure distributionson semi-cylindrical structures in a turbulent boundary layerat a Reynolds number of 6.6�104. Some other key aerodynamicparameters, such as fluctuating force coefficients and vortexshedding behavior, are not yet fully understood. Compared withan isolated cylinder, the semi-cylindrical roof can be characterizedby the upstream and downstream ground boundary conditions.Some authors may believe that for a semi-cylindrical structure,if recognized as a cylinder attached with very long wake splitterplate, the vortex shedding can be ceased by the downstreamboundary condition, which would be expected to influence theReynolds number sensitivity. Nevertheless, more detailed aero-dynamic force characteristics should be experimentally providedto confirm these points, especially for a wide range of Reynoldsnumbers which have not yet been tested. In this study, a splitterplate with the ratio of plate length to cylinder diameter ofL/D¼3 was employed as a surface boundary condition instead ofa ground boundary condition. Thus, the semi-cylindrical roof canbe practically approximated as a circular cylinder with attachedsplitter plates placed at the front and rear of the body, as shownin Fig. 1.

The objective of the present study is to enhance our under-standing of the aerodynamic differences between a bare cylinderand a semi-cylindrical roof, including pressure and force charac-teristics as well as vortex shedding suppression. For this, windtunnel tests with simultaneous multi-pressure measurementswere conducted for the range of Reynolds numbers 6.90�104–8.28�105. Both subcritical and supercritical flows around a barecylinder were taken into account. Three types of splitter plateswith L/D¼3 were considered: (a) frontal plate, which affects theapproaching flow; (b) wake plate, which prevents the interactionof separated shear layers and (c) cylinder with bilateral plates. Inaddition, tests on a horizontal semi-cylindrical roof were con-ducted to investigate the aerodynamic similarity between a semi-cylindrical roof and a cylinder with bilateral plates and thecorresponding transition Re regime was addressed.

2. Wind tunnel experiments

The present experiments were conducted in a closed-circuit-type wind tunnel located at Harbin Institute of Technology, China,which has a maximum wind speed of 50 m/s. The dimensions ofthe wind tunnel test section are 25.0 m long, 4.0 m wide and3.0 m high.

2.1. Circular cylinder

A schematic of the circular cylinder models and the pressuretap layout is shown in Fig. 2(a). A fiberglass-reinforced plastic(FRP) cylinder with a diameter D of 0.4 m and a height H of 2.7 mwas vertically mounted on the wind tunnel floor as a bare cylinderor with splitter plates installed. The flow velocity U for themeasurements was controlled from 6 to 30 m/s. At the modellocation, the maximum thickness of the boundary layer developedon the smooth wind tunnel floor was about 0.3 m. The cylindermodel was instrumented with a pressure tap ring located 1.35 mfrom the tunnel floor. The pressure tap ring consisted of 36 orificesspaced every 101 around the circumference of the cylinder. TheReynolds numbers, based on the cylinder diameter, ranged from1.66�105 to 8.28�105. This covered both subcritical and super-critical flows around a bare cylinder (Schewe, 1983). The free-stream turbulence intensity of the smooth approaching flow wasmeasured to be within 0.5%, which is sufficient to check modifica-tion of the wake structure behind bluff bodies (Gerrard, 1965b).The maximum blockage ratio of the cylinder was about 8.2% andMaskell's theory (1963) was applied to correct the value of thedrag coefficient for the blockage effect. The aspect ratio H/D of thecylinder is 6.75, which is large enough to obtain a relatively stabledistribution of local drag coefficient (Gould et al., 1968; Okamotoand Yagita, 1973), and a small variation of fluctuating lift coeffi-cient with Re over the central part of the cylinder (Szepessy andBearman, 1992).

A wooden plate was employed as a splitter plate and arrangedparallel to the free-stream direction. The thickness of the splitterplate was 0.02 m and the chord length used was 1.2 m with theratio of plate length to cylinder diameter being L/D¼3. As seen inFig. 2(b), (c) and (d), three positions of the splitter plate wereinvestigated in this study, referred to as frontal plate, wake plateand bilateral plates, respectively. The cylinder model with a frontalplate is considered to disturb the approaching flow, which gen-erates a flat-plate turbulent boundary layer with a maximumthickness δ, about 80 mm, in the studied Reynolds number range,as shown in Fig. 3. Note, the velocity measurements were taken at1.2 m from the leading edge of a two-connected splitter platewithout the presence of cylinder model. The wake plate aimsto prevent the interaction of the separated shear layers. Thecombined influence of frontal and wake plates is attained in the

splitter plate

∞

Wind

ground

Fig. 1. Schematics of the bare cylinder (a), circular cylinders with frontal plate (b), wake plate (c) and bilateral plates (d), semi-cylindrical roof (e).

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50 41

bilateral plate case. Instantaneous wind pressures acting onthe cylinder surface were measured using a DSM3400 pressurescanner system. A sampling frequency of 625 Hz was employedand the measurement duration was 100 s. In addition a hot wireprobe, used for the vortex shedding frequency measurements, waspositioned in the neighborhood of the cylinder, 0.5D downstreamas shown in Fig. 2(a).

The drag coefficients for a bare cylinder were first calculatedfrom the pressure distributions and compared with the results ofprevious research in Fig. 4. It can be seen that the present barecylinder data agree well with the results from the previous work.The best correlation is with the work of Schewe (1983) andAchenbach and Heinecke (1981) at Reynolds numbers in thesubcritical regime. However, in the supercritical regime theexperimental data are appreciably higher, which may be a resultof the differences in turbulence levels.

2.2. Semi-cylindrical roof

A horizontal semi-cylindrical roof model was used to examinethe effects of Reynolds number in a relatively low Re range, andto investigate the aerodynamic similarity between the semi-cylindrical roof and the cylinder with bilateral plates. Fig. 5 showsthe model of the semi-cylindrical roof. A base plate elevated 0.5 mfrom the floor was used to minimize the effect of boundary layerover the wind tunnel floor. The base plate has a thickness of0.02 m, with a width of 2.4 m and a length of 4.8 m. This is longenough to ensure that the separated flow reattaches to the platesurface. The diameter d of the semi-cylindrical roof is 0.2 m, andthe corresponding Reynolds number varies from 6.90�104 to3.31�105. In order to obtain similar flow conditions, the roofmodel is placed at a position of 0.6 m from the leading edge of thebase plate, which amounts to half the chord length of the splitter

H

L=1.2m

H

L=1.2m L=1.2m

H

θ =10

Hot-wire

D/2

z

y

Fig. 2. Experimental models: (a) bare cylinder and pressure tap layout, (b) cylinder with frontal plate, (c) wake plate, and (d) bilateral plates.

0.2 0.4 0.6 0.8 1.00

0.1

0.2

0.3

0.4

0.5u* Iu Re (×10 )

L=3D

u

z

U

Iu (%)

z (m

)

u* = u /U

δ = 0.08 m

3 6 9 12 15

1.66 3.31 5.52 8.28

Fig. 3. Variations of the normalized velocity un and turbulence intensity Iu in theflat-plate turbulent boundary layer as a function of height z.

105 1060

0.4

0.8

1.2Delany & Sorensen,1953

Schewe, 1983

Achenbach & Heinecke,1981

Scruton, 1981Wieselsberger, 1922

Shih et al, 1993

Present data

Cd

Re

Fig. 4. Drag coefficients for the bare cylinder compared with data from publishedworks (Delany and Sorensen,1953; Scruton,1981; Shih et al., 1993;Wieselsberger, 1922).

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–5042

plate. It should be noted that the flat-plate turbulent boundarylayer generated by the base plate was not used to simulate theatmospheric turbulent boundary layer, but only to investigate itsinfluence on the Reynolds number sensitivity of the aerodynamicsof the semi-cylindrical roof. The blockage ratio of the semi-cylindrical roof with a length of 2.4 m is about 2.3%, and thusthe blockage effect can be ignored. Eleven rows of pressure tapswere arranged across the middle of the model to obtain a time-averaged value of the pressure coefficient, and the spacingbetween two neighboring taps was 91. The sampling conditionand data processing methods were the same as those for thecircular cylinder case.

3. Experimental results and discussion

3.1. Mean pressure and force coefficients

The wind pressure coefficients used in this article are calculatedusing Eq. (1). Δp is the instantaneous pressure difference between thesurface pressure and reference pressure in the wind tunnel, and0.5ρaU2 is the mean dynamic pressure. The mean and fluctuatingpressure coefficients are ensemble averages of 5 samples.

Cp ¼ Δp0:5ρaU

2 ð1Þ

Fig. 6 shows the mean pressure distributions of the bare cylinder andthe cylinders with splitter plates for different Reynolds numbers. Thedata for the bare cylinder are shown in Fig. 6(a). The changes in thepressure distributions, with Reynolds number changes from subcriticalto supercritical, are abrupt and dramatic. In the Re range from1.66�105 to 3.04�105, the pressure distributions are symmetricand can be characterized by a wide wake region. However, at thecritical Reynolds number Re¼3.31�105, the pressure coefficients atthe lateral sides of cylinder suddenly increase and exhibit a distinctasymmetric pattern. Schewe (1983) has pointed out that in the criticalflow regime, the boundary layer becomes turbulent at the separationpoint and this occurs only at one side of the cylinder, which causes anasymmetric pressure distribution and non-zero mean lift on thecylinder. When Re increases into supercritical regime, from 3.59�105 to 8.28�105, the pressure distributions become relatively stableand present a narrow wake region.

Fig. 6(b) shows the experimental data for the cylinder with afrontal plate, which was intended to generate a flat-plate turbulentboundary layer in the free-stream direction. It is interesting tonote that the pressure distributions tend to be symmetric andare insensitive to changes of Reynolds number in the range1.66�105–8.28�105. Compared to the bare cylinder, the cylinderwith a frontal plate seems to exhibit relatively large suctions onthe cylinder sides. It is widely known that the state of boundarylayer over the cylinder surface is significantly related with the flowconditions. Basu (1986) revealed that small-scale turbulence in theapproaching flow can penetrate the surface boundary layersaround the cylinders and cause the premature transition of the

separated shear layer from laminar to turbulent, and consequentlyinfluence the pressure distribution.

Fig. 7 shows mean pressure distributions which correspond toRe¼1.66�105 and 8.28�105 for cylinder with frontal plate, andthe mean pressure distributions as measured by Roshko (1961)and Jones et al. (1969) acquired at Re¼8.4�106 and 8.3�106

respectively. It can be seen that, except in the windward regionwhere a flat-plate boundary layer directly influences, the experi-mental data show good agreement with the mean pressuredistributions on a smooth bare cylinder measured in the post-critical flow. This may reveal that the disturbances generated bythe frontal plate have produced a turbulent boundary layer, andachieved a type of flow separation associated with postcriticalregime at relatively low Reynolds numbers from 1.66�105 to8.28�105. A similar effect can also be obtained by changing thesurface roughness of a bare cylinder. As shown in Fig. 7, the Cpdistribution on a bare cylinder attached with strips (Jenkins et al.,2006) also exhibits a good agreement with the data from currentand previous studies, at Re of 1.66�105 and relative roughness isabout 5.2�10�3. Similar to the effects produced by frontal plate,increasing surface roughness can generate a turbulent boundarylayer upstream of the flow separation, which has been widelystudied and used, and is efficient in allowing the establishment ofthe postcritical regime at relatively low Reynolds numbers.

In order to avoid the oscillation of the wake plate, the measure-ments on the cylinder with a wake plate were only carried out atReynolds numbers up to 3.31�105, and with a lower limit of8.28�104. The pressure distributions at three Reynolds numbers upto 1.38�105 are first plotted in Fig. 8 to verify the current data. Thisshows a good agreement with results from Apelt and West (1975),Adachi et al. (1990) and Gu et al. (2012). It should be noted that theexperimental and literature-cited data were derived from cylinderswith the same ratio of plate length to cylinder diameter. As shown inFig. 6(c), typical subcritical pressure distributions can be observed inthe Reynolds number range from 8.28�104 to 2.76�105. Asymmetricpressure distributions occur again at Reynolds numbers of 3.04�105

and 3.31�105. This phenomenon may reveals a transition from oneReynolds number regime to another, has seen with the bare cylinder.This is also in agreement with the experimental results for the cylinderwith awake plate (L/D¼3) investigated by Adachi (1990). The pressurecoefficients for the cylinder with bilateral plates in the Reynoldsnumber range from 1.66�105 to 8.28�105 are shown in Fig. 6(d).Similar pressure patterns and conclusions can be obtained as thoseobserved with the frontal plate. These findings imply that a frontalsplitter plate has a more significant influence on the state of thesurface boundary layer before and after separation than the splitterplate in the wake.

Drag and lift forces acting on the cylinder model have beenevaluated from the middle section instrumented with pressuretaps. These are calculated by the numerical integration of thepressure Cp distributions and given as

Cd ¼R 2π0 Cp cos θ dθ; Cl ¼

R 2π0 Cp sin θ dθ ð2Þ

z

θ =9º

2.4 m 4.2 m

0.5 m

Semi-cylindrical roof

x

d

pressure tap

0.6 m

Fig. 5. Experimental model for the semi-cylindrical roof and a sketch of the pressure tap layout.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50 43

where θ is the angle between the pressure coefficient and free-stream direction. Fig. 9 shows the variation of the mean dragcoefficients Cd as a function of Reynolds number for the barecylinder and the cylinders with splitter plates. It can be seen thatCd for the bare cylinder drops in the critical regime remarkably.This is due to the narrowing of the wake width as a consequ-ence of the downstream movement of the separation point(Zdravkovich, 1997). Similar to the bare cylinder case, the meandrag coefficient of the wake plate case also shows a remarkabledrop in the Re range of 3.0�105�3.31�105. In addition, with awake splitter plate of L/D¼3, the Cd for the cylinder was reducedto approximately 83% of the bare cylinder value in the subcriticalregime. However, the drag coefficient Cd for the cylinders withfrontal and bilateral plates monotonously increases in the range0.35 and 0.5, and Cd clearly reduces when Reo3.0�105.

0 60 120 180 240 300 360-3

-2

-1

0

1

1.66×105

1.93×105

2.48×105

3.04×105

3.31×105

3.86×105

4.14×105

4.97×105

5.52×105

6.07×105

6.62×105

7.18×105

8.28×105

θ /degree

C p

0 60 120 180 240 300 360-3

-2

-1

0

1

1.66×105

1.93×105

2.48×105

3.04×105

3.31×105

3.86×105

4.14×105

4.97×105

5.52×105

6.07×105

6.62×105

7.18×105

8.28×105

θ /degree

Cp

0 60 120 180 240 300 360-3

-2

-1

0

1

8.28×104

1.10×105

1.38×105

1.66×105

1.93×105

2.21×105

2.48×105

2.76×105

3.04×105

3.31×105

θ /degree

Cp

0 60 120 180 240 300 360-3

-2

-1

0

1

1.66×105

1.93×105

2.48×105

3.04×105

3.31×105

3.86×105

4.14×105

4.97×105

5.52×105

6.07×105

6.62×105

7.18×105

8.28×105

θ /degree

Cp

Fig. 6. Mean pressure distributions for bare cylinder (a) and cylinders with frontal plate (b), wake plate (c) and bilateral plates (d).

0 30 60 90 120 150 180

-2

-1

0

1

Cp

θ /degree

Re=8.4×10 , Roshko (1961) Re=8.3×10 , Jones et al. (1969) Re=1.66×10 , Jenkins (2006),

Bare Cyl. with Strips Re=1.66×10 , Experiments Re=8.28×10 , Experiments

Fig. 7. The mean pressure distributions for cylinder with frontal plate comparedwith the data collected from references.

0 30 60 90 120 150 180-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

Cp

θ /degree

Re=1.0×10 , Apelt & West (1975) Re=1.04×10 , Adachi (1990) Re=5.0×10 , Gu, et al (2012) Re=8.28×10 , Experiments Re=1.10×10 , Experiments Re=1.38×10 , Experiments

Fig. 8. The mean pressure coefficients of the cylinder with wake plate (L/D¼3) insubcritical Re regime.

105 1060

0.5

1.0

Schewe, 1983 bare cylinder frontal plate wake plate bilateral plates

Cd

Re

Fig. 9. The mean drag coefficients of cylinders with and without splitter plates atvarious Reynolds numbers.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–5044

The absolute values of the mean lift coefficient Cl versus Re areplotted together with the results of Schewe (1983) in Fig. 10. It wasfound that |Cl| for cylinders with frontal or bilateral plates, remainsnearly zero due to the influence of approximately symmetricpressure distributions around the cylinder. However, the value of|Cl| for bare cylinders and wake plate cases is particularly high inthe critical regime between 3.0�105 and 3.5�105. The variationof lift coefficient in the critical regime is mainly caused by thechange from symmetric to asymmetric flow, which essentiallyreflects the beginning of one-side transition of separated shearlayer to turbulence.

3.2. Unsteady pressure patterns at critical Re

The transition of boundary layer from laminar to turbulent on acylinder surface can happen in different regions, as a functionmainly of Re. In the particular critical regime, the boundary layertransition generally occurs close to the separation point for asmooth bare cylinder in a low turbulence level flow (Zdravkovich,1997). As is well known, it is possible to identify different regimesbased on specific aerodynamic characteristics such as the Cd – Reand Strouhal number – Re curves. For a bare cylinder with smoothsurface, three Re regimes can be determined from the mean dragcoefficient distributions (see Fig. 9), and it is not difficult torecognize the subcritical (1.66�105oReo3.0�105) and super-critical flows (3.5�105oReo8.28�105). However, in the criticalregime (3.0�105oReo3.0�105), a transition from symmetric toasymmetric flow can generally be observed around the cylinder.

Fig. 11 shows the Cp time histories of two opposite lateralpressure taps near the separation point at critical Re of 3.31�105.It is seen that the pressure coefficients change alternatively on thetwo sides of the cylinder with jumps of about ΔCp¼0.6. Besides,two mean pressure distributions are plotted in Fig. 12 correspond-ing to the different time intervals A and B, which show oppo-site asymmetric pressure distributions. Roshko (1954) and Schewe

(1983) suggested a general sense that, in the critical regime, theseparated shear layer is turbulent at one side of the cylinder andlaminar at the other side, resulting in a non-zero mean lift andsudden drop in Cd of the cylinder. On the other hand, the side atwhich the separation is turbulent alternates from one side to theother occasionally, and thus results in strong pressure instabilitiesnear the separation point.

Fig. 13 shows the Cp time histories of a lateral pressure tap(Tap-26) at Re¼3.31�105 for cylinders with splitter plates. As shownin Fig. 13(a), at Re of 3.31�105, remarkable pressure instabilitiesnear the separation point can be observed with ΔCp jumps ofabout 0.85. This reveals a phenomenon of one single separationbubble attached to the surface, through which the separatedshear layer undergoes asymmetric transition to turbulence. It isof interest to note that, although a wake splitter plate can inhibitthe vortex shedding, a transition of the separated shear layer canstill be observed in the same critical regime. Whereas, in Fig. 13(b)and (c), the Cp time histories of cylinders with frontal and bilateralplates are characterized as stationary processes. Extensive inves-tigations showed that this feature is prevailing for all the surfacepressure taps in the studied Re range 1.66�105 to 8.28�105.

3.3. Wind force power spectra and Strouhal number

Power spectra analysis is used to reveal the frequency domainfeatures of fluctuating pressures and forces as well as vortexshedding. Fig. 14 illustrates the relationships between the powerspectra of the fluctuating forces, with velocity being recorded inthe downstream region and pressures measured near the separa-tion point for the bare cylinder. At the subcritical Re¼2.48�105,as shown in Fig. 14(a), it is well known that there is a clear sharppeak in the spectra of the lift fluctuation and time-series obtainedby a hot-wire anemometer in the wake at the Strouhal numberSt�0.2. Also the spectrum of the drag fluctuation has a peak at 2St,which is clearly evident as pointed out by Nishimura and Taniike(2001). At critical Reynolds number of 3.31�105, sharp peaksare observed in the spectra of both lift and drag fluctuations asshown in Fig. 14(b). This particular phenomenon is considered toresult from the one-sided transition of the separated shear layerto turbulence and asymmetric formation of the lee-wake vortices.In Fig. 14(c), the power spectrum of the lift fluctuation is char-acterized by a remarkably narrow peak at St�0.45 in thehigh frequency range at the supercritical Reynolds number of4.14�105. In addition, it is clear that a sharp peak at St can alsobe observed in the power spectrum of wind pressure fluctua-tions near the separation point, which suggests that the vortexshedding influences the pressure fluctuations over the surface ofthe cylinder.

Fig. 15 shows the direct comparisons of the lift and drag powerspectra for the cylinders with splitter plates. For the cylinder witha frontal plate, it can be clearly observed that the power spectrumfor lift fluctuations has an evident sharp peak at the Strouhal

105 106

0

0.5

1.0

1.5 Schewe, 1983 bare cylinder frontal plate wake plate bilateral plates

Transition|Cl |

Re

Fig. 10. The mean lift coefficients plotted against Reynolds number.

sec

20 40 60

-1.0

-0.5

0

20 40 60

-1.0

-0.5

0

Tap-12Cp

Tap-26

Interval-BInterval-A

sec

Fig. 11. Time histories of two opposite lateral pressure taps (Tap-12 and Tap-26) atcritical Re of 3.31�105 for the bare cylinder.

Interval-A Interval-B

Tap-12

Tap-26

Tap-12

Tap-26

U U

Fig. 12. The mean pressure distributions on the bare cylinder measured in the twodifferent time intervals at Re¼3.31�105.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50 45

number but the drag spectrum has a wide bandwidth. However,for the cylinder models with wake and bilateral plates, there areno particular peaks in either the lift or the drag power spectra. Inaddition, spectral analysis of the time-series derived from the hot-wire anemometer measurements in the wake, do not exhibit anydominant frequencies for any of the cylinders or Reynolds num-bers investigated in these experiments. This suggests that vortexshedding from the cylinder is eliminated by the existence of awake splitter plate (L/D¼3), which is consistent with the resultsobtained by Apelt and West (1975).

Fig. 16 shows the variations of the lift power spectra withReynolds number for the bare cylinder and the cylinder modelwith a frontal plate. Simply, the Strouhal number is defined as thesharp peak reduced frequency in the power spectra of lift fluctua-tions. The variation of the Strouhal number with Re is shown inFig. 17. For the bare cylinder, the distributions of St are consistentwith the results obtained by Schewe (1983). In the subcriticalregime with Re ranging from 1.66�105 to 3.04�105, the Strouhalnumber amounts to St¼0.2, with regular vortex shedding from thecylinder. At supercritical Re from 3.31�105 to 8.28�105, Stremains nearly constant, at about 0.45. However, the variation ofthe Strouhal number for the cylinder with a frontal plate slightlyincreases with Re in a range from 0.20 to 0.25. It is well knownthat in postcritical regime, the St generally ranges between 0.2 and0.3 (Holmes, 2001). Thus, the observed shedding frequencies mayprovide further evidence of the frontal splitter plate in producingpostcritical flow on the cylinder at relatively low Reynolds num-bers in a range of 1.66�105–8.28�105.

3.4. Aerodynamic similarity analysis

In Section 3.1, it was found that the mean pressure distribu-tions on the circular cylinders with bilateral plates vary slightlywith Reynolds number and show a stable wind load pattern in theRe range from 1.66�105 to 8.28�105. Since the splitter plateswith L/D¼3 installed at the front and rear of the circular cylinderwere employed to approximate the ground boundary conditionof semi-cylindrical roof, a premature transition of the separatedshear layer to turbulence may also be observed for the semi-cylindrical roof in the same Re regime. Thus, as an extendedinvestigation, a semi-cylindrical roof model was tested in a

relatively low Re range to prove these points and to determinethe transition Re regime. Another aim of this test model is to find aload pattern which is Reynolds number independent to be used asthe reference of future experimental investigations.

The Reynolds numbers corresponding to the semi-cylindricalroof case range from 6.90�104 to 3.31�105. To validate theconsistency and continuity of these two test cases at variousReynolds numbers, Fig. 18 shows the mean pressure distributionsderived from the semi-cylindrical roof model and circular cylindermodel with bilateral plates at the same Reynolds numbers. It canbe seen that the pressure distributions match well, indicatingsimilar flow patterns between these two models. The pressuredistribution shows little sensitivity to Reynolds number over thesmall range from 1.93�105 to 3.31�105. Note that, the slightdiscrepancy between the two models may be associated with theeffects of a higher blockage ratio for the circular cylinder model.

Fig. 19(a) shows the mean pressure distributions along thecenter meridian in a Reynolds number range from 6.90�104 to8.28�105. It should be noted that this figure includes combinedmeasured data from the semi-cylindrical roof model and thecircular cylinder model with bilateral plates, since an aerodynamicsimilarity between the two test models has been shown to bevalid at the same Reynolds numbers, (as seen from Fig. 18). AtRe¼6.90�104, a peak suction pressure coefficient of Cpmin¼�1.0is observed at about 721, and the negative pressure graduallyincreases with Re and then reaches a stable value at about 1081.Here, the separation angle θs¼1081 can be approximately deter-mined in which the leeward pressure distribution becomes uni-form indicating the beginning of the wake region (Nishimura andTaniike, 2001). In the Re range from 6.90�104 to 1.66�105, thepeak suction pressure coefficient gradually increases with Re from�1.0 to �1.7, and the separation point gradually moves towardsthe downstream region from about 1081 to 1171. With Reynoldsnumber increasing from 1.66�105 to 8.28�105, the peak suctionpressure coefficient near the cylinder apex becomes approxi-mately constant at about 811, and the θs remains nearly stable atabout 1171. In addition, the wake pressure shows a relatively slightvariation with Re in a range from �0.45 to �0.30.

The RMS pressure distributions along the center meridian atvarious Reynolds numbers are shown in Fig. 19(b). It can be clearlyobserved that the Reynolds number has a significant influence on

0 5 10 15 20 25 30 35 40 45 50 55 60-2.0

-1.5

-1.0

-0.5

0

Time (s)

Cp

0 10 20 30 40 50 60-1.5

-1.0

-0.5

0

Time (s)

C p

0 10 20 30 40 50 60-1.5

-1.0

-0.5

0

Time (s)

C p

Tap-26

Tap-26 Tap-26

Fig. 13. Cp time histories of the lateral pressure taps (Tap-26) at Re¼3.31�105 for the cylinders with (a) wake plate, (b) frontal plate and (c) bilateral plates.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–5046

the distribution of fluctuating pressure coefficients Cp0 in the nega-

tive pressure region, especially in the downstream region after theseparation point. In the range of Re¼6.90�104–1.66�105, Cp

0

gradually decreases with Re and a dual-peak phenomena can beobserved at about θ¼991 and 1171 in the region before/near theseparation point. This suggests that fore-separation bubble formedat this stage and a transition of separated shear layers occurred(Cheng and Fu, 2010). When Re41.66�105, there remains onlyone peak for Cp

0 at θ¼1171 and the values slightly decrease withthe increasing Re. This indicates that the separation point and theboundary of the wake region became stable.

Fig. 20 shows the variations of lift and drag coefficients withReynolds number. This is calculated from the pressure along the

center meridian of each test model. Here, the force coefficients forthe cylinder with bilateral plates are evaluated based on thepressure distribution around the half-cylinder, and Cd can also beapproximately substituted by the values determined by Eq. (2)due to the symmetric pressure patterns. It can be observed thatthe Cd continuously decreases, whilst the Cl rapidly increases asthe Reynolds number increases, up to about 1.66�105. With theReynolds number further increasing from 1.66�105 to 8.28�105,the Cl and Cd slightly vary with Re and gradually show relativelystable values. Thus, these experimental data indicate that thetransition of separated shear layer occurs in a Re range in between6.90�104 and 1.66�105, and the pressure distribution becomesrelatively stable thereafter.

hot-wire

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

Pressure

StSt

Velocity

DragLift

2St

f D/U

f S( f

)/σ2

St

Tap-14

D/2

f D/U f D/U

hot-wire

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

Pressure

StSt

Velocity

Drag

Lift

f D/U

St

Tap-14

D/2

f D/U f D/U

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

hot-wire

Pressure

StSt

Velocity

Drag

Lift

f D/U

St

Tap-14

D/2

f D/U f D/U

f S( f

)/σ2

f S( f

)/σ2

Fig. 14. Relationships between the power spectra of fluctuating wind force, velocity and wind pressure for the bare cylinder at (a) subcritical Re¼2.48�105, (b) criticalRe¼3.31�105 and (c) supercritical Re¼4.14�105.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50 47

4. Conclusions

The characteristics of wind loads acting on a circular cylinderwith attached splitter plates at the front and/or rear of the cylinderhave been investigated experimentally to study the aerodynamicdifferences between bare cylinders and semi-cylindrical roofs.Reynolds numbers in the present study were varied from6.90�104 to 8.28�105. For the cylinder model with a frontalsplitter plate, Cd was remarkably reduced when Reo3.0�105 andmonotonously increased in the range 0.35 to 0.5. Compared withthe results of a bare cylinder for Re from 1.66�105 to 8.28�105, itwas found that the frontal splitter plate, by generating the flat-plate turbulent boundary layer, caused the premature transitionof the separated shear layer, and stable shedding frequenciesin a range from 0.20 to 0.25 were determined. These observed

aerodynamic features suggested that the cylinder with a frontalplate has produced a post-critical flow at relatively low Reynoldsnumbers. The vortex shedding from the cylinder can be sup-pressed effectively by a splitter plate (L/D¼3) in the wake, whichessentially isolates the separated shear layers on the sides of thecylinder. However, the separated shear layer transition was stillobserved in a Re range of 3.0�105–3.5�105, which was consis-tent with the results for a bare cylinder.

The aerodynamic similarity between the semi-cylindrical roofand the cylinder with bilateral plates was then examined for thesame Re. It was verified that the semi-cylindrical roof could beapproximated as a circular cylinder with bilateral plates undersimilar flow conditions. For the semi-cylindrical roof with Revarying from 6.90�104 to 8.28�105, the vortex shedding wasinhibited and the wake suctions were reduced in a narrow range

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

LiftDragDrag

LiftRe=4.14×105Re=3.31×105Re=2.48×105

StSt

Drag

Lift

f D/U

f S( f

)/σ2

St

f D/U f D/U

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

LiftLift

DragDrag

Re=3.31×105Re=2.48×105Re=1.38×105

Drag

Lift

f D/U

f S( f

)/σ2

f D/U f D/U

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

10-1 10010-3

10-2

10-1

100

101

Lift DragDrag

Re=4.14×105Re=3.31×105Re=2.48×105

DragLift

f D/U

f S( f

)/σ2

f D/U f D/U

Lift

Fig. 15. Power spectra of the fluctuating wind forces at three Reynolds numbers for the cylinders with (a) frontal plate, (b) wake plate and (c) bilateral plates.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–5048

from �0.45 to �0.30, which would be expected to reduce theReynolds number sensitivity to some extent. However, the peaksuction pressure coefficient clearly increased with Re and a down-stream movement of separation point was still observed in theRe range from 6.90�104 to 1.66�105. The pressure distribu-tions became relatively stable when Re41.66�105. Finally, the

transition of separated shear layer around the semi-cylindricalroof was identified in the Reynolds number range in between6.90�104 and 1.66�105.

The wind tunnel tests for the semi-cylindrical roof model werecarried out in a shallow flat-plate turbulent boundary layer, thusthe results are not appropriate to be used for building design.

St =0.45

10-3 10-2 10-1 100 101

Re=8.28×105

Re=6.07×105

Re=4.14×105

Re=3.31×105

Re=2.48×105

Re=1.66×105

St =0.2

f D/U

St =0.2

10-3 10-2 10-1 100 101

Re=8.28×105

Re=6.07×105

Re=4.14×105

Re=3.31×105

Re=2.48×105

Re=1.66×105

f S( f

)/σ

f D/U

f S( f

)/σ2 2

Fig. 16. Variations of the power spectra of the fluctuating lift forces with different Reynolds numbers for (a) bare cylinder and (b) cylinder with a frontal plate.

105 1060.0

0.2

0.4

0.6 Schewe, 1983 bare cylinder frontal plate

Transition

St

Re

Fig. 17. Variations of the Strouhal number with Re for the bare cylinder and cylin-der with the frontal plate.

30 60 90 120 150 180

-2

-1

0

1

θ /degree

Circular cylinder Semi-cylindrical (bilateral plates) roof

Re=1.93×105 : Re=2.21×105 : Re=2.48×105 : Re=3.31×105 :

Cp

Fig. 18. Comparison of the mean pressure distributions on center meridians of semi-cylindrical roof and circular cylinder with bilateral plates at the same Reynoldsnumbers.

30 60 90 120 150 180-2.0

-1.5

-1.0

-0.5

0

0.5

1.0 6.90×104

8.28×104

1.10×105

1.38×105

1.52×105

1.66×105

2.48×105

3.31×105

4.14×105

5.52×105

6.62×105

8.28×105

θ /degree

Cp

Re

30 60 90 120 150 1800

0.05

0.10

0.15

0.20

0.25 6.90×104

8.28×104

1.10×105

1.38×105

1.52×105

1.66×105

2.48×105

3.31×105

4.14×105

5.52×105

6.62×105

8.28×105

θ /degree

C ′p

Re

Fig. 19. Variations of pressure coefficients with Re on center meridians of the twowind tunnel models: (a) mean pressure coefficient Cp, (b) fluctuating pressurecoefficient Cp

0 . Key: solid symbol, semi-cylindrical roof; empty symbol, cylinderwith bilateral plates.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–50 49

Further studies are planned to consider the effects of the atmo-spheric turbulent boundary layer in a wide Reynolds numberrange, which is expected to influence the aerodynamic loads onthe semi-cylindrical roof.

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China under Grant nos. 91215302, 51278160and 51378147, the Natural Scientific Research Innovation Founda-tion in Harbin Institute of Technology HIT.NSRIF.2009098. The firstauthor expresses his many thanks to Prof. Yukio Tamura, TokyoPolytechnic University, for his scientific advice regarding theexperimental data processing.

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2.0x105 4.0x105 6.0x105 8.0x1050

0.2

0.4

0.6

0.8

1.0

Semi-cylindrical Circular cylinder roof (bilateral plates)Lift coefficient: Drag coefficient:

Forc

e co

effic

ient

s

Reynolds number

Fig. 20. Variations of the lift and drag coefficients as a function of Re for the twowind tunnel models.

Y. Qiu et al. / J. Wind Eng. Ind. Aerodyn. 127 (2014) 40–5050