787

The Enhancement of Aerodynamic Characteristics on Bluff

Bodies near a Moving Ground∗

Tae-Yoon KIM∗∗, Bo-Sung LEE∗∗∗, Yo-Cheon KU∗∗∗∗,Dong-Ho LEE† and Yasuaki KOHAMA††

In this study, passive control methods for attaching horizontal and vertical fences onthe lower surface of the cylinder near a moving ground were adopted to enhance the aero-dynamic characteristics with the changes in gap height. The horizontal fences increase thedomain where the lower separated shear layer is interfered by viscous effect on the ground.In a moving ground, this viscous effect is only slightly observed due to elimination of shearlayer induced by relative ground motion. However, vertical fences diminish the momentumprovision intended to roll up to wake region by blocking the gap flow, thereby suppressingthe vortex shedding irrespective of ground conditions. Therefore, the horizontal fences in amoving ground have the advantage of reducing averaged lift and drag though cannot suppressthe vortex-induced oscillation. Even though vertical fences have an advantage of suppressingvortex shedding past a cylinder, the existence of the vertical fences themselves causes theaveraged drag to increase above the critical gap height due to the existence of vertical fences.

Key Words: Vortex Shedding, Passive Control, Vertical & Horizontal Fences, MovingGround

1. Introduction

An understanding of the flow around a bluff bodyclose to a ground is very important in automobile, aero-nautical and wind engineering fields because of aerody-namic characteristic and instability resulting from flowseparation. It has been reported that the traffic accidentssuch as overturning or slipping induced by the abruptcross-wind at tunnel exit of highway and on the longbridge. Under such strong cross-wind conditions, it isnoteworthy that vortex shedding past bluff shape vehicles,such as sports utility vehicles, articulated lorries, large

∗ Received 6th May, 2006 (No. 05-5040)∗∗ Hyundai/Kia Motors, Whasung-Si, Gyunggi-Do and

School of Mechanical and Aerospace Engineering, SeoulNational University, Seoul 445–706, Korea

∗∗∗ Samsung SDS, Seoul 135–918, Korea∗∗∗∗ School of Mechanical and Aerospace Engineering, Seoul

National University, Seoul 151–742, Korea† School of Mechanical and Aerospace Engineering, Seoul

National University, BD 301–1213, San 56–1, Shinrim-dong, Kwanak-ku, Seoul 151–742, Korea.E-mail: donghlee@snu.ac.kr

†† Institute of Fluid Science, Tohoku University, Sendai 980–8577, Japan

buses etc. The separation from bluff bodies produces astrong loss of pressure recovery and vortex-induced oscil-lation, which result in the increase of aerodynamic dragand instability. Therefore, it is necessary to evaluate aero-dynamic characteristics at the conceptual design stage of abridge, heavy ground vehicle, or building near the ground.

For the past several decades, numerous studies onthe vortex shedding formation past a cylinder have beenperformed by Bearman(1), Huerre(2), Lyn(3), Bosch(4),Bailey(5), Martinnuzi(6), etc. Various active and passivecontrol methods have been suggested to suppress the vor-tex shedding and enhance the aerodynamic characteristic.Active control methods, such as blowing, suction, instal-lation of mechanical devices or excitation by micro wavehave been introduced. Also the passive control methodsinclude modification of trailing-edge shape, installation oftrip wires or plates, adapting ventilated and closed cav-ity, etc. Despite the fact that extensive studies have beenconducted, active control methods still have intrinsic prob-lems in that they are mechanically too complex such thatit is difficult to be applied in practice. Hence, the passivecontrol methods have been more widely adopted than theactive control methods for actual realization rather thanthe active control methods.

JSME International Journal Series B, Vol. 49, No. 3, 2006

788

Tamura et al.(7) studied the averaged and fluctuat-ing statistics of lift and drag acting on a square sectionedcylinder with sharp corners, chamfered and rounded cor-ners. With these controlled shapes of a square cylinder,the shear layers were close to the side surface. Accord-ingly reattachment was enhanced and drag forces were re-duced. Choi and Kwon(8) investigated physical mechan-ism of aerodynamic and aero-elastic instability of a bluffbody with various corner cuts and attack angles experi-mentally. They claimed the corner cut method showedbetter performance for the galloping but could not sup-press the vortex shedding. Duell et al.(9) investigated theeffect of the mounted cavity in the base region experimen-tally. They reported that the mean base pressure was in-creased to 4% and 11% when the ratio of depth and heightof cylinder (D/H) were 0.2 and 0.8 respectively. Take-mori et al.(10) reported that the drag could be reduced byinstalling upper and lower corner vanes in the wake re-gion, and these wake control vanes were found to be at-tractive and effective for drag reduction. Khalighi et al.(11)

reported that the presence of the plates in the wake re-gion reduces the intensity of the re-circulating velocity ofthe base region, which in turn reduces the vortex shed-ding and increases the pressure at the base region. B. Leeet al.(12) reported the passive control attached the verticaland horizontal fences in the lower surface of the cylindercan suppress the vortex shedding past a cylinder.

Even though numerous studies have been conductedon cylinders placed near a stationary ground, only a fewstudies have been investigated on the bluff body placednear a moving ground. Arnal et al.(13) performed a nu-merical simulation of square cylinder under the condi-tion of the free-stream, fixed and sliding wall conditionswith changes in the Reynolds number. They claimedthat the presence of the fixed wall reduced the Strouhalnumber where the periodic vortex shedding occurred. Incontrast, the sliding wall at the free-stream velocity re-sulted in vortex shedding which was extremely periodic.Kim and Geropp(14) investigated flow around some two-dimensional bluff bodies with wind tunnel experimentsequipped by moving-belt and reported that a larger liftforces and longer wakes was apparent with decreasingclearance. Bhattacharyya and Maiti(15) performed a nu-merical simulation at the square cylinder placed on amoving ground in laminar Reynolds number range belowRe = 1 000. Therefore, the results showed that the aver-aged drag experienced by moving ground was higher thanthe corresponding stationary case. Even though numer-ous studies have been conducted on bluff bodies near aground, there is little information on the square cylindernear a moving ground in turbulent Reynolds number re-gion as O(104).

Therefore, the objective of this study is to provideadditional information of the flow-field around a square

cylinder on a moving as well as stationary ground withgap heights. So, based on this investigation, we will dis-cuss the effects of the horizontal and vertical fences near amoving ground in connection with the enhancement of theunsteady aerodynamic characteristics and stability. To thisend, two-dimensional Reynolds-averaged Navier-Stokesequations were used to investigate the flow characteris-tics such as the Strouhal number, aerodynamic coefficientsand vortex formation mechanism past a square cylinderaccording to the change in the gap height at a Reynoldsnumber of 20 000.

2. Governing Equations and Numerical Approaches

The governing equations used in this study arethe two-dimensional unsteady incompressible Reynolds-averaged Navier-Stokes equations. To calculate incom-pressible flow-field for efficiency, the continuity equationwas transformed into the pressure equation by the pseudo-compressibility scheme(16). The governing equations canbe written in dimensionless form as∂p∂tc=−β∂ui

∂xi(1)

∂ui

∂tc+∂uiu j

∂x j=− ∂p∂xi+∂

∂x j

[(ν+νt)

(∂ui

∂x j+∂uj

∂xi

)]− ∂ui

∂t

(2)

All geometric variables in Eqs. (1) and (2) are non-dimensionalized by the height of the cylinder D, staticpressure p by the pressure of free stream p∞, and veloc-ity u, v by the free stream velocity u∞, respectively, andtime by D/u∞. The third-order upwind biased schemewas employed for the discretization of convection terms,and the central difference scheme for the viscous terms.To calculate the time-dependent flow-field, a dual timestepping method was used, where the physical time termswere treated as the source on the right hand side as shownin Eq. (2). Then, sub-iterations were performed for thepseudo time ∆tc until the right hand side of Eq. (2) con-verged with physical time ∆t kept constant. Parallel com-puting was adopted to analyze effectively the unsteadyflows by dividing the physical domain into several sub-domains through the domain decomposition technique.Data Parallel Symmetric Gauss-Seidel method(17) whichwas developed to conduct efficient parallel computing wasemployed for temporal integration. Also, in order to accu-rately predict the large separated flow fields such as a bluffbody, the ε-SST turbulence model(18), which is a modifi-cation of the Menter’s SST model(19), was used. The per-formance and applicability of the ε-SST turbulence modelare well illustrated in the previous researches of the au-thors(20).

2. 1 Grid system and boundary conditionIt is difficult to generate a single block grid around a

square cylinder. In the case of a sequential solver, a multi-block grid system is the most appropriate choice due to its

Series B, Vol. 49, No. 3, 2006 JSME International Journal

789

Fig. 1 Grid distribution of a cylinder

cost-efficient computation. However, there exists a loadbalancing problem that arises in parallel solver. There-fore, in this study, the solver adopted the H-type singleblock structured grid system with blanked cells(21). Thisapproach can be seen as a kind of Chimera grid tech-nique(22). In the domain, the cells in the cylinder aremarked as zero and the outer cells are marked as one.The only additional memory requirement is for the arrayneeds to denote which cells are blanked. Furthermore,only minimal modifications need to be made to the so-lution algorithm. In the computation process, the cellsmarked as zero are automatically excluded, and the wallboundary conditions are applied during the calculation offluxes. Figure 1 shows the geometry of the cylinder andcomputational grid, where D and B denote the height andwidth of the cylinder, respectively, and G means the gapheight from the ground. In this study, the aspect ratio(B/D) was fixed as 1. The gap height (G/D) was variedfrom 0.2 to 1.0, the Reynolds number Re=U∞D/νwas setas 20 000. The first grid spacing from the cylinder surfaceand ground was set as ∆xi/D = 0.005 for ∆x+i < 5 for thewhole surface of the cylinder and the ground. To accom-modate the unsteady flows, physical time step was set as∆t= 0.05 and the sub-iterations were performed to obtainthe converged solutions at the fixed physical time. At theinflow, 1/7 power law with adequate boundary layer thick-ness (δ/D= 4) was imposed at 6.7D, in front of the cylin-der. At the outlet, flow properties were extrapolated andsymmetry boundary conditions were imposed on the upperboundaries. No-slip boundary condition was imposed onthe cylinder wall surface and stationary ground cases, butthe same inflow speed was imposed on the moving ground.To investigate the effects of the grid size and the first gridspacing on the numerical solutions, grid refinement testswere carried out with 398×298 grid, where the first gridspacing ∆xi/D= 0.002 5, 198×148 where ∆xi/D = 0.005,and 98×73 where ∆xi/D = 0.01. The effect of the physi-cal time step on the unsteadiness of the solution was alsoinvestigated with ∆t = 0.025, 0.05, 0.1 cases in 198×148grid. Table 1 summarizes the preliminary grid refinementtest results. Based on this, we concluded that the 198×148grid and ∆t = 0.05 can be used for the following numeri-

Table 1 Numerical parameters and results with various gridsand time steps

(a) No vortex shedding (b) Vortex shedding

(c) Blocked upwash byhorozontal plates

(d) Blocked upwash byvertical plates

Fig. 2 Schematic diagrams of vortex shedding mechanism andpassive control methods

cal experiments in view of the fact that they are almostidentical with the Strouhal numbers and aerodynamic co-efficients from 198×148 and 398×298 grid.

2. 2 Passive control methodIn order to suppress vortex-induced oscillation for

reducing aerodynamic drag of a cylinder near stationaryground, B. Lee et al.(12) suggested installing vertical andhorizontal fences under the lower surface of the cylinder.Generally, the decrease in gap height or the increase in as-pect ratio makes the periodic vortex shedding to be sup-pressed. When the vortex shedding is suppressed, theonly long recirculation zone is found in Fig. 2 (a), whilethe vortex shedding can be induced by the interaction ofthe upper and lower shear layers above the critical gapheight as shown in Fig. 2 (b). This vortex shedding canbe suppressed by installing horizontal and vertical fencesat the lower surface of the cylinder, the vortex sheddingcan be suppressed. This is because horizontal fences actlike to increase aspect ratio of cylinder and vertical fencesprevent the momentum provision from the gap region tothe wake region in Fig. 2 (c) and (d) respectively. In thisstudy, investigated whether horizontal and vertical fenceshave the same influence in terms of suppressing the vor-tex shedding in a moving ground. From the preliminarystudies related with fence lengths and gap heights, the twofences having the length of 0.1D and thickness of 0.07D,respectively, were installed horizontally and vertically on

JSME International Journal Series B, Vol. 49, No. 3, 2006

790

Fig. 3 Controlled geometry with horizontal and vertical fences

the front and rear lower surface of the square cylinder asshown in Fig. 3.

3. Results and Discussion

3. 1 Strouhal numberFigure 4 shows the Strouhal numbers (St = Df /u∞)

according to gap heights (G/D). The shedding frequencywas determined by FFT for the time history of lift coef-ficient. In the case of a stationary ground, the criticalgap height of baseline, where the periodic vortex shed-ding occurs, exists around G/D = 0.55. However in thecase of moving ground, it is at G/D = 0.35. This sug-gests that the cylinder near moving ground is more likelyto experience higher instability and aerodynamic drag dueto unsteady wind loading than a stationary ground. TheStrouhal number in the case of stationary ground showsa peak value immediately after the critical gap height dueto the ground effect(20), and decreases to the value of freestanding cases as the gap height increases. However, incase of moving ground, the Strouhal number rapidly in-creases at G/D = 0.3∼0.45 but remains almost constantthereafter. In the case of controlled shapes, vortex shed-ding at G/D = 0.55 is suppressed by both horizontal andvertical fences in a stationary ground. Meanwhile, in amoving ground, only vertical fences can suppress oscil-lation at G/D< 0.45, while horizontal fences cannot sup-press and instead show similar pattern with baseline.

Figure 5 shows the variation of lift and drag coeffi-cients at G/D = 0.55 in a stationary ground and at G/D =0.35 in a moving ground respectively. The amplitude oflift and drag coefficient in the case of moving ground atG/D= 0.35 is larger than stationary ground at G/D= 0.55.In a stationary ground, the oscillation of lift and drag issuppressed by horizontal and vertical fences as shown inFig. 5 (a) and (c). The lift and drag of vertical fencesare higher than the case of horizontal fences. This canbe described as installed vertical fences, perpendicular tothe flow direction. However, horizontal fences in a mov-ing ground make aerodynamic oscillations more amplifyrather than baseline. Otherwise, vertical fences can reduceaveraged drag as well as suppress the vortex shedding inFig. 5 (b) and (d). It is worthy to note that in a stationaryground, two dominant shedding frequencies are observed,

Fig. 4 Strouhal numbers according to Gap heights; a)Stationary Ground, b) Moving Ground (�: Baseline, �:Horizontal Fence, ♦: Vertical Fence)

whereas in moving ground, there is no second sheddingfrequency due to absence of separated shear layer on theground(12), (20).

3. 2 Vortex shedding mechanismFigure 6 shows the instantaneous vorticity contours

of cylinder when has maximum lift. When the squarecylinder approaches stationary ground, there are three sep-arated shear layers: two clockwise separated shear layerswith negative vorticity that develop on the upper of cylin-der and the ground, and another counter-clockwise sep-arated by shear layer generated on the lower surface ofthe cylinder with positive vorticity(15). For periodic vor-tex shedding, there must be interaction between the upperand lower separated shear layers in wake region. How-ever in a stationary ground, the clockwise separated shearlayer from the ground cancels the vorticity concentrationof counter-clockwise shear layer on the lower surface ofthe cylinder. Consequently, this prevents rolling up toin wake region. In addition, both horizontal and verti-cal fences attached to the lower surface of cylinder rein-force that mechanism and suppress the vortex-induced os-

Series B, Vol. 49, No. 3, 2006 JSME International Journal

791

Fig. 5 Time evolution of Aerodynamic Coefficients; a) Lift in Stationary Ground at G/D=0.55, b) Lift in Moving Ground at G/D = 0.35, c) Drag in Stationary Ground atG/D= 0.55, d) Drag in Moving Ground at G/D= 0.35 (—: Baseline, ♦: HorizontalFence, �: Vertical Fence)

cillation. On the other hand, though the cylinder movescloser to the ground than the case of stationary ground inFig. 6 (b), strong vortex shedding may occur due to the ex-istence of the very weak shear layer on a moving ground.Figure 6 (c) and (d) shows the effects of horizontal fences.The horizontal fences have similar role as in that it in-creases the aspect ratio of cylinder, hence extending thedomain where the lower separated shear layer is interferedby viscous effect from the ground. As the viscous effect isstrong in a stationary ground, the longer horizontal fencesis more effective in suppressing make the vortex sheddingmore efficiently suppressed, but the viscous effect does notexist in a moving ground where shear layer induced by rel-ative ground motion is almost eliminated. However, ver-tical fences can suppress the vortex shedding irrespectiveof ground conditions, because they diminish the momen-tum provision to the wake region by blocking the gap flowactually in Fig. 6 (e) and (f).

Figure 6 (b) and (d) shows that vortex on a movingground is detached from ground, and pushed out horizon-tally downward. However, the separated shear layer fromthe stationary ground at G/D = 0.55 in Fig. 6 (a) is con-nected to the upper separated shear layer interrupted bythe lower shear layer in the wake region behind a square

cylinder, and together sheds downward.Figure 7 shows instantaneous streamline distributions

in an oscillation cycle. In a stationary ground at G/D =0.55 in Fig. 7 (a), the vortex generated past a cylinderis connected to separation bubble on the ground, sepa-rated from the ground directly. This phenomenon pro-duces secondary shedding frequency in the wake regionpast a square cylinder as mentioned in Fig. 6. However,in cases of baseline and horizontal fences on a movingground in Fig. 7 (b) and (d), strong vortex is generated inthe wake region without any interference of the shear layeron the ground. Only a large recirculation zone is found inFig. 7 (c), (e) and (f), due to vortex shedding which is sup-pressed by passive control devices.

3. 3 Aerodynamic characteristicsFigure 8 shows the time-averaged streamwise x-

directional velocity distributions measured at the exit re-gion of gap between a square cylinder and ground for var-ious gap heights. Time-averaged parameters were calcu-lated by averaging the computational results over an entireshedding cycle. In cases where the vortex shedding occursin a moving and stationary ground, the higher momentumprovided to the wake region than the cases without vortexshedding. Also, the position (y/G) where maximum ve-

JSME International Journal Series B, Vol. 49, No. 3, 2006

792

Fig. 6 Vorticity contour at maximum Lift; a) Stationary Ground at G/D=0.55, b) MovingGround at G/D=0.35 (solid line: clockwise, dotted line: counter-clockwise)

Fig. 7 Instantaneous Streamline in a cycle of Oscillation; a), c), e) Stationary Ground atG/D=0.55, b), d), f) Moving Ground at G/D=0.35

Series B, Vol. 49, No. 3, 2006 JSME International Journal

793

Fig. 8 Averaged x-directional velocity profiles for various gap heights (��♦�©: Suppression,����•: Vortex shedding); a), c), e) Stationary Ground, b), d), f) Moving Ground

locity denoted as (u/u∞)max was measured can be seen tomove closer to the lower surface of the square cylinder. Incase of a moving ground, a higher momentum is observedwhich is due to weak wall boundary layer than stationarycases at the same gap height. A square cylinder locatednear a stationary ground, the reattached flow at the lowersurface of cylinder makes the position of maximum ve-locity move closer to the ground. The gap flow, like a jetflow, does not roll up the wake region but expands alongthe ground. This deters interaction between the upper sep-arated shear layer and the gap flow, consequently resultingin the suppression of the vortex shedding below the criti-cal gap height. In cases of horizontal fences near a station-ary ground in Fig. 8 (c), the gap velocity is large interferedand canceled by viscous effects from the ground. But, theviscous effect becomes negligible in a moving ground as

shown in Fig. 8 (d). This confirms that the vertical fencesdiminish momentum provision to the wake region, moreso than the baseline and horizontal fences and irrespectiveground conditions.

Figure 9 shows the Y-directional velocity profiles ingap region. In both cases of stationary and moving ground,the Y-directional velocity in the periodic vortex sheddingis higher than in the suppression cases. Also, as the gapheight increase, the position (y/G) where maximum veloc-ity denoted as (v/u∞)max located closer to the lower surfaceof the square cylinder as Fig. 8. For the periodic vortexshedding, the gap flow has to roll up behind a square cylin-der, then the vortex core location approaches closer to thelower surface of a square cylinder, which is supported bythe results illustrated in Figs. 8 and 9.

Figure 10 shows the time-averaged pressure coeffi-

JSME International Journal Series B, Vol. 49, No. 3, 2006

794

Fig. 9 Averaged y-directional velocity profiles for various gap heights (��♦�©: Suppression,����•: Vortex shedding); a), c), e) Stationary Ground, b), d), f) Moving Ground

cient along the surface of the cylinder with the passivecontrol methods and ground condition. The stagnationpoint where located at the center of front face (A-B) hashigh pressure. The pressure of the cases where vortexshedding is suppressed is a higher than shedding cases,and also, an adverse pressure gradient at gap region (B-C)is found. The averaged pressure at the top and lee side ofcylinder is uniformly distributed and is almost the samewith the exception of baseline and horizontal fences in amoving ground where vortex shedding occurs. This resultis qualitatively similar with the experimental finding per-formed by Martinuzzi et al.(6) at stationary ground withG/D = 0.6. The pressure distribution of vertical fences atG/D = 0.35 in a moving ground is very similar to casesat G/D= 0.55 in a stationary ground. There is no signifi-

cantly difference between stationary and moving ground atfront side (A-B), except that the moving ground show thelower pressure recovery in wake region (C-D) than caseof a stationary ground. Consequently, the difference in thepressure distribution in the wake region causes the aerody-namic drag of cylinder near a moving ground to increaseas shown in Fig. 11.

Figure 11 shows the averaged lift and drag coeffi-cients for various gap heights. Concerning with the av-erage coefficients, horizontal fences in both ground con-ditions show good performance in terms of the reduc-tion of the aerodynamic lift and drag all gap heights ir-respective of vortex shedding. At 0.3<G/D< 0.4 for thecase of a moving ground, vertical fences showed a goodperformance of aerodynamic drag and stability as vor-

Series B, Vol. 49, No. 3, 2006 JSME International Journal

795

tex shedding can be suppressed by only vertical fences.The drag of baseline and horizontal fences in a movingground rapidly increases until G/D< 0.4, and then remain

Fig. 10 Averaged Pressure Coefficient along the surface ofsquare cylinder (� � �: Vortex shedding, ��©:Suppression) (Stationary Ground for G/D=0.55 inSolid line, �: Baseline �: Horizontal Fence, �:Vertical Fence in; Moving Ground for G/D= 0.35in Dash line, �: Baseline, �: Horizontal Fence, ©:Vertical Fence)

Fig. 11 Averaged Lift and Drag Coefficient for various gap heights with Stationary and Mov-ing Ground (�: Baseline, �: Horizontal Fence, ♦: Vertical Fence)

almost constant like Strouhal number distributions there-after as shown in Fig. 4. As a cylinder is brought closer toa ground the lift coefficient initially decrease. Then as theflow accelerated in the gap between the cylinder and theground causs the pressure on the lower side of cylinderdrop and lower the lift. The downward force of cylinderis maximized around G/D=0.3 in both cases of a movingand stationary ground. Furthermore the horizontal fencesmake this Venturi effect stronger, preventing the horizontalfences in a moving ground from suppressing the vortex-induced oscillation. Despite this, it still has the advantageof reducing averaged lift and drag. On the other hand, ver-tical fences have a strong point of suppression of vortexshedding past a cylinder, but the averaged drag increasesabove the critical gap height.

4. Conclusion

In this study, passive control methods which attachhorizontal and vertical fences on the lower surface of thecylinder near a moving ground were investigated. The hor-izontal fences enlarge the domain where the lower sep-arated shear layer is interfered by viscous effect on theground. No effect is observed in moving ground due to

JSME International Journal Series B, Vol. 49, No. 3, 2006

796

elimination of shear layer induced by relative ground mo-tion. However vertical fences actually block the gap flowand diminish the momentum provision to the wake region,can suppress the vortex shedding irrespective of groundconditions. In conclusion, the horizontal fences in a mov-ing ground have the advantage of reducing averaged liftand drag without suppressing the vortex-induced oscilla-tion. Whereas the vertical fences have a strong point ofsuppressing vortex shedding past a cylinder, but the dragincreases above the critical gap height. Therefore, it isimportant to choose between horizontal or vertical fencesat the design stage in accordance with the objective andapplication.

Acknowledgement

This work was supported by “the Brain Korea 21Project in 2005” and “the Sixth Strategic SupercomputingSupport Program in KISTI.”

References

( 1 ) Bearman, P.W. and Zdravkovich, M.M., Flow arounda Circular Cylinder near a Plane Boundary, J. FluidMech., Part 1, Vol.89 (1978), pp.33–47.

( 2 ) Huerre, P. and Monkewits, P.A., Local and Global In-stabilities in Spatially Developing Flows, Annual Re-view of Fluid Mechanics, Vol.22 (1990), pp.473–537.

( 3 ) Lyn, D.A., Einav, S., Rodi, W. and Park, J.H., A Laser-Doppler Velocimetry Study of Ensemble-AveragedCharacteristics of the Turbulent near Wake of a SquareCylinder, J. Fluid Mech., Vol.304 (1995), pp.285–319.

( 4 ) Bosch, G., Kappler, M. and Rodi, W., Experiments onthe Flow Past a Square Cylinder Placed near a Wall,Exp. Thermal Fluid Sci., Vol.13 (1996), pp.292–305.

( 5 ) Bailey, S.C.C., Kopp, G.A. and Martinuzzi, R.J., Vor-tex Shedding form a Square Cylinder near a Wall, J.Turbulence, Vol.003 (2003), pp.1–18.

( 6 ) Martinuzzi, R.J., Bailey, S.C.C. and Kopp, G.A., In-fluence of Wall Proximity on Vortex Shedding from aSquare Cylinder, Experiments in Fluids, Vol.34 (2003),pp.585–596.

( 7 ) Tamura, T. and Miyagi, T., The Effect of Turbulence onAerodynamic Forces on a Square Cylinder with Vari-ous Corner Shapes, J. Wind Eng. Ind. Aerodyn., Vol.83(1993), pp.135–145.

( 8 ) Choi, C.K. and Kwon, D.K., Aerodynamic Stability forSquare Cylinder with Various Corner Cuts, Wind andStructure, Vol.2, No.3 (1999), pp.173–187.

( 9 ) Duell, E.G. and George, A.R., Experimental Study of aGround Vehicle Body Unsteady near Wake, SAE Paper

1999-01-0812, (1999).(10) Takemori, Y., Kato, S., Masumitsu, Y., Kaya, Y. and

Mizutani, T., Drag Reduction of Bluff-Based Bodyby Wake Control Vanes (Effective Utilization of Un-der Floor Flow), Seoul FISITA World AutomotiveCongress, F2000G357, (2000).

(11) Khalighi, B., Zhang, S., Koromilas, C., Balkanyi, S.R,Bernal, P., Laccarino, G. and Moin, P., Experimentaland Computational Study of Unsteady Wake Flow be-hind a Bluff Body with a Drag Reduction Device, SAEPaper 2001-01-1042, (2001).

(12) Lee, B.S., Kim, T.Y. and Lee, D.H., Control of Vor-tex Shedding behind a Rectangular Cylinder near theGround, Numerical Heat Transfer, Part A, Vol.47, No.8(2005), pp.787–804.

(13) Arnal, M.P., Goering, D.J. and Humphrey, J.A.C., Vor-tex Shedding from a Bluff Body Adjacent to a PlaneSliding Wall, J. Fluid Eng., Vol.113 (1991), pp.384–398.

(14) Kim, M.S. and Geropp, D., Experimental Investigationof the Ground Effect on the Flow around Some Two-Dimensional Bluff Bodies with Moving-Belt Tech-nique, J. Wind Eng. Ind. Aerodyn., Vol.74-76 (1998),pp.511–519.

(15) Bhatacharyya, S. and Maiti, D.K., Vortex Sheddingfor Flow over a Square Cylinder Close to a Mov-ing Ground, IUTAM Symposium, New Jergey, USA,(2003).

(16) Rogers, S.E. and Kwak, D.C., An Upwind Differ-encing Scheme for the Time-Accurate Incompress-ible Navier-Stokes Equations, AIAA Journal, Vol.28(1990), pp.113–134.

(17) Lee, B.S. and Lee, D.H., Data Parallel SymmetricGauss-Seidel Algorithm for Efficient Distributed Com-puting, Proc. 38th AIAA 97-2138, (1997).

(18) Kim, T.Y., Lee, B.S. and Lee, D.H., Study of the Un-steady Wakes Past a Square Cylinder near a Wall, J.Mech. Sci. Tech., Vol.19, No.5 (2005), pp.1169–1181.

(19) Menter, F.R., Two-Equation Eddy-Viscosity Turbu-lence Models for Engineering Applications, AIAAJournal, Vol.32, No.8 (1994), pp.1598–1605.

(20) Kim, T.Y., Passive Control of the Flow Field around aSquare Cylinder near a Ground, Ph.D. Thesis, (2005).

(21) Kim, T.Y., Lee, B.S., Lee, D.H. and Lee, D.H., AStudy on Vortex Shedding around a Bluff Body nearthe Ground, SAE Paper 2003-01-1652, Detroit, (2003).

(22) Steger, J.L., Doughty, F.C. and Beneck, J.A., AChimera Grid Scheme, Advances in Grid Generation,FED, Vol.5, Edited by Ghia, K.N., (1983), pp.59–69,ASME, NewYork.

Series B, Vol. 49, No. 3, 2006 JSME International Journal