Effect of Downstream Flapping Plate on the Flow Field Characteristics behind a Circular Cylinder

Transcription

1 Poceedings of the 3 d Intenational Confeence on Fluid Flow, Heat and Mass Tansfe (FFHMT 16) Ottawa, Canada May 2 3, 2016 Pape No. 169 Effect of Downsteam Flapping Plate on the Flow Field Chaacteistics behind a Cicula Cylinde Roam Simenthy, Vasudevan Raghavan, Shaligam Tiwai Depatment of Mechanical Engineeing Indian Institute of Technology Madas, Chennai , India oamsimenthy@gmail.com; aghavan@iitm.ac.in; shaligt@iitm.ac.in Abstact - Two-dimensional numeical investigations of flow chaacteistics behind a cicula cylinde in the pesence of a flapping plate mounted in the wake have been caied out in the pesent study. The flapping fequency of the plate has been vaied in the ange fom 0.6 to 1.4 times the votex shedding fequency behind single stationay cicula cylinde in the pesence of a stationay plate. The gap between the cylinde and the plate is consideed to be 1D, 2D and 3D. The maximum amplitude of the tip of the plate has been fixed to be 0.3D (D being the diamete of the cylinde) fo each of the fequency atio fo fixed value of Reynolds numbe (Re) equal to 100. The length of the plate has been chosen equal to cylinde diamete. The dynamic effects and the behaviou of votex shedding behind the cylindes have been studied elaboately. Effect of fixed amplitude and vaying fequency atio of the cylinde on wake flow behaviou has been pesented in the fom of voticity contous, lift, dag and Stouhal numbe (St) plots. The dynamic foces as well as the flow stuctue behind the plate ae found to be modified in the pesence of the flapping plate. Keywods: Cicula cylinde, flapping plate, gap atio, votex shedding, lift and dag. 1. Intoduction The effective contol of the votex shedding behind the cylindes becomes an impotant issue due to thei wide ange of pactical applications like flow past heat exchanges, buildings, suspension bidges, oad vehicles to name a few. The votex shedding the bluff bodies can sometimes be catastophic due to the fact that the fequency of the votex shedding fom the cylinde matches with the esonance fequency of the stuctue. The will finally lead to the damage of the stuctue. Fom the past itself eseaches have consideed this as a classic eseach topic and made a lot of effot to suppess the votex shedding by flow contol, which is meant to contol the votex shedding fom the cylinde. Methods of contolling the shedding have been classified as active and passive methods. Among the two types of methods used fo contolling the votex shedding, the active contol is found to be moe effective. Pesence of a wake splitte is one of the effective passive contol method used fo wake stabilization and dag eduction. The concept of flapping motion is obtained fom the motion of a tadpole fo its locomotion, fom which it is seen that by popely choosing the fequency and the amplitude of flapping the dag of the cylinde can be achieved. Ali et al. [5] studied the modification of the wake stuctue of a squae cylinde due to the pesence of a downsteam plate which is placed at vaying gap distance between the plate and the cylinde fo Reynolds numbe (Re) = 150. They identified two flow egimes at citical gap distance of 2.3D and obseved that thee is no significant effect of the plate on the geneation of von Kaman voticies beyond a gap distance of 5.6D. Kwon and Choi [4] obseved that when the length of the attached splitte plate is lage than a citical length the votex fomation behind the cylinde vanishes and this citical length is a function of Re. Wu and Shu [2] conducted numeical simulation of lamina flows aound a stationay cylinde attached with a flapping plate at its ea side. They showed that the flow stuctue behind the cylinde and flapping plate is geatly affected by the flapping amplitude, fequency of plate and length of the plate. They obseved two votex inteaction modes namely constuctive and destuctive and explained thei effect on the dag foce. Bao and Tao [7] numeically analyzed the effect of a steam wise oscillating foil to contol the votex shedding of a cicula cylinde. They noticed that the dynamic inteaction between the main shea laye and oscillatoy bounday layes ae esponsible fo wake stabilization. They identified thee flow egimes based on wake stabilization and obseved that the incease in oscillation 169-1

2 amplitude and fequency of the foil augments the wake suppessing effect of the system. Seson et al. [1] pefomed 2D and 3D simulations fo a cicula cylinde in the pesence of a splitte plate to obseve the wake tansition in the flow aound the cylinde. They noticed that, when the gap between the splitte plate and the cylinde is inceased the Stouhal numbe (St) values showed a discontinuous incease in its value. Hwang et al. [3] studied and explained the flow physics elated to the eduction in flow - induced foces happening in the cicula cylinde in the pesence of a wake splitte plate having a length same as that of the cylinde. They obseved a gadual eduction of the flow-induced foces on the cylinde and the subsequent sudden incease ove a citical gap atio between the cylinde and the plate. Fom thei obsevations, they concluded that the significant eductions of dag and lift fluctuation achieved in unsteady flows using a detached splitte plate ae stongly elated to suppession of the votex shedding nea the cicula cylinde. Xiao et al. [6] examined the wake inteaction between an undulation NACA0012 foil placed in the wake of a D-sectional cylinde to study the paametic effects such as Re, the elative size of the foil to the cylinde, the foil undulating fequency, the wavelength and the gap between the cylinde and the foil affect the cylinde dag, lift foce as well as foil thust. They showed that when the foil was popely placed at a paticula location at the downsteam of the cylinde with its chod length equal to the cylinde diamete, suppession of cylinde votex shedding and an impovement in downsteam foil populsion can be achieved. Qiu et al. [8] expeimentally investigated the chaacteistics of wind loads acting on a cicula cylinde with splitte plates attached at the font and/o ea of the cylinde. They obseved that the cylinde with a fontal plate has poduced a post-citical flow at elatively low Re. Futhe they noticed that the votex shedding is suppessed by a splitte plate ( ) in the wake fo a semi-cylindical oof, that can be appoximated as a cicula cylinde with bilateal plates unde simila flow conditions. L/ D 3 2. Poblem Definition The computational domain chosen fo the pesent study is shown in Fig. 1. The length and width of the domain ae chosen as 40D and 16D, espectively. Ai at 1 atm and 298 K is consideed as the woking fluid. The position of the cicula cylinde is fixed at 10D fom the inlet and the position of the plate is vaied such that the gap between the cylinde and the plate, which is measued fom the ea side of the cylinde and the font tip of the plate ae chosen as 1D, 2D and 3D. The length of the plate is consideed to be hinged at the font end and is foced to otate hamonically in the tansvese diection elative to the diection of the incoming flow, such that, sint whee is the angle of otation about z axis and is the fequency of cylinde oscillation. The value of amplitude of flapping ( A ) chosen fo the pesent study is 0.3D. The fequency atio is vaied fom 0.6 to 1.4. The fequency atio ( f fe / fo ) is the atio of the excitation fequency of the flappe to the fequency of votex shedding behind the isolated cylinde. All the computations have been caied out fo a fixed value of Re = 100. z Fig. 1: Schematic of the computational domain

3 3. Govening Equations and Bounday Conditions 3.1. Govening equations The govening equations fo incompessible and unsteady flow that ae equied to be solved ae those of mass and momentum consevations. Fo an incompessible flow, the mass consevation equation is used in pessue-velocity coupling fo coecting the pessue field using SIMPLE algoithm. The non-dimensional govening equations in tenso fom ae given as u x i i 0 ( ) 2 u uu i i j p 1 u i, t x j xi Re x j x j (1) (2) whee u i is the velocity component along x i -coodinate diection and p is the non-dimensional pessue. Fo a two-dimensional Catesian coodinate system, Eq. (2) collectively epesents the x and y-components of the momentum equation fo the coesponding velocity components u and v, espectively. The flow velocity at the inlet (U ) is consideed as the chaacteistic velocity and the diamete (D) of the cicula cylinde is chosen as the chaacteistic length. Accodingly, the flow Reynolds numbe is given by U D Re (3) Hee is the density of the fluid at standad conditions of the fee steam and is its dynamic viscosity. The nondimensionalized static pessue at any location is given as, P P p (4) U Bounday conditions Inlet: Unifom velocity in x-diection, u 1.0 andv 0 Outlet: Pessue outlet, p 0 Top and bottom walls: Fee-slip condition and impemeable, u 0; v 0 y Cicula cylinde suface: no-slip and impemeable bounday, i.e., uv 0 Plate: u 0; z cost, whee z, the otational velocity of the plate about z-axis, is the angula amplitude of the plate measued fom the mean position. 4. Gid Geneation and Numeical Technique 4.1. Gid geneation Hybid gid have been used to divide the entie flow domain into discete finite volumes. The gid geneation has been done in such a way that the gids ae nea the cylinde suface and the egion outside the flapping plate is quadilateal type. A egion with tiangula gid is geneated in ode to accommodate the motion of the plate. A gid independence study has been pefomed to optimize the numbe of gids such that best accuacy can be achieved with optimum 169-3

4 computational time. The esults fom the gid independence study have been pesented in Table 1. The vaiations of mean dag, RMS lift coefficient and Stouhal numbe obtained fo an isolated cicula cylinde using diffeent gids ae also shown in Table-1. Finally, a gid mesh having 160 gid points on the cylinde suface is chosen fo all the computations because no significant vaiation is found in the computed values of above quantities with futhe efinement. The validation of the esults obtained fo the cylinde in the pesence of plate has been pesented in the following section. Table 1: Gid independence study fo isolated stationay cylinde. No. of gid points on the cylinde RMS Lift coefficient (C l,ms) Mean dag coefficient (C d,mean) Stouhal numbe (St) Numeical technique As mentioned ealie, the govening equations ae solved using the commecial softwae ANSYS Fluent 14.0 based on the finite volume method. The softwae uses SIMPLE (Semi Implicit Method fo Pessue Linked Equations) algoithm is used fo pessue-velocity coupling. Fo discetization unsteady tem, fist ode accuate implicit time maching scheme has been used. Convective tems ae discetized using second ode upwind scheme, while the diffusive tems ae discetized using the cental diffeence scheme. The hamonic otational motion of the plate is incopoated with the help of a Use Defined Function (UDF) and by using the dynamic meshing capability of ANSYS Fluent 14.0, which takes cae of the e-meshing when the plate is displaced at each time step. 5. Results and Discussion Computations have been caied out fo flow past a cicula cylinde with a flapping plate mounted at the downsteam. The spacing between the cylinde and flappe as well as amplitude and fequency of oscillation of the flappe ae vaied. The font end of the plate is hinged and the angle of otation of the plate is chosen such that the ea tip of the plate eaches a maximum amplitude of 0.3D fom the mean position, i.e. the centeline of the cylinde in hoizontal position. The validation of the computed esults has been fist caied out fo a single stationay cicula cylinde followed by the plate when it is stationay. Using the validated model, lift and dag fluctuation as well as voticity contous ae simulated and pesented in the following subsections Validation Fig. 2: Validation of pedicted value of Stouhal numbe at diffeent gap spacing fo a stationay plate with esult fom liteatue

5 Figue 2 shows the vaiation of St with diffeent gap spacing between the cylinde and the plate, when the plate is stationay at a fixed value of Re = 100. The esults ae validated with that of Hwang et al. (2003) and shows a good ageement Flow chaacteistics behind cicula cylindes due to flapping motion of the plate Vaiation of mean dag coefficient ( ) with fequency atio ( ) is shown in Fig. 3. Solid lines epesent the C d, mean dag values fo the cylinde when the plate is flapping and dashed lines epesent the coesponding values when the plate is kept stationay. Fo G/ D 1 the dag values show a gadual incement up to and then stats deceasing. It is noted that the pesence of the plate is obvious in this spacing and the votex shedding fequency of the cylinde is same as that of the flapping fequency of the plate fo all values of. Similaly fo, the intefeence effect of the flappe is visible fo f 0.6 f f f 1.0 G/ D 2 f values highe than 0.8 and shows incement in dag values up to f 1.0 and then stats deceasing. Fo and 0.8, the dag values ae same as that of stationay values. Futhe when the gap between the cylinde and plate is inceased such that, the dag values ae compaatively highe fo and 0.8 and then thee is a sudden dop in the value fo f 0.9, which is lowe than the stationay value. Then the value again ises up to f 1.1 and then stats to decease such that at the dag coefficient dops to a value lowe than its stationay configuation. Thus fo all the values of flapping fequency and the gap atios consideed, dag eduction is obseved at fo and 1.4. f 1.4 f 0.6 f 0.9 (a) (b) Fig. 3: Vaiation of (a) mean dag coefficient (b) RMS lift coefficient with fequency atio and fo diffeent values of spacing. Figue 3 (b) shows the vaiation of RMS lift coefficient ( C same tend as that of C d, mean. Fo G/ D 1, the l, ms ) with f. The vaiation of C l, ms also follows the C l, ms value is always highe than that of the stationay value fo all values of f, which implies that the effect of flapping of the plate tends to ceate moe fluctuation in the vetical foces acting on the cylinde. When the gap between the plate and the cylinde is inceased to a value G/ D 2, fo lowe values of f such as f 0.6 and 0.8 and fo highe values of f like f 1.2 and 1.4, Cl, ms values ae close to thei stationay values as depicted in the figue. The maximum values of C occus at f 0.9 fo G/ D1and f 1 fo G/ D 2. Futhe when the spacing is inceased to, l, ms C values ae consideably educed fo f 0.9 and 1.4 as simila to that l, ms 169-5

6 obseved fo C d, mean and oscillated at. The dynamic foces acting on the cylindes can be consideably educed when the plate is placed at f 0.9 and 1.4 at A = 0.3. Thus it can be affimed that thee is a significant effect of amplitude and fequency of oscillation of the plate on the flow - induced foces acting on the cylinde. Figue 4 shows the compaison of Stouhal numbe (St) values fo the cicula cylinde due to the pesence of flappe. It is clealy seen that at spacing values of 1D and 2D, the votex shedding behind the cylinde is influenced by the cylinde such that the shedding fequency matches with the flapping fequency of the plate. On the othe hand, at, fo all the values of except fo and 1.4, the shedding fequency ( fom that of the flapping fequency and is found to be a constant value. But fo the above two cases, matches with the excitation fequency of the flappe ( and 3. f f 0.9 f e ) as obseved in the case of G/ D 2 f s ) of the cylinde is diffeent f s Fig. 4: Compaison of pedicted value of St at diffeent values of spacing fo cicula cylinde in the pesence of flapping plate. Instantaneous voticity contous fo have been pesented in Fig. 5. As seen fom the plots of C d, mean and, the values ae lowe than thei coesponding stationay values fo f 0.9 and 1.4 as shown in Fig.5(b) and 5(d). In both the cases, votex shedding behind the cylinde is suppessed due to the flapping motion of the plate. Whee as in the othe two cases, i.e. fo f 0.6 and 1.1, the votex shedding takes place in the gap between the cylinde and the plate. Thus the eduction of flow-induced foces acting on the cylinde may be attibuted to the suppession of votex shedding due to the flapping motion of the plate. It is also noted that eduction in the foces is moe pedominant in the case of f 1.4 than f 0.9 because the dag eduction is moe in the fome case. Fo the othe cases, the votices shed fom the cylinde ae able to inteact with each othe and this in tun poduces compaatively lage fluctuating foces in the hoizontal and vetical diections. This is due to the fact that at lowe values of f, the votices shed fom the cylinde ae compaatively smalle in size and the inteaction between the shea layes becomes much stonge. At highe values of f, the sizes of the votices ae slightly highe and they almost hit the font side of the plate. This deceases the inteaction of votices in the gap of the cylinde and the plate and thus esults into educed magnitudes of foces. Fom the analysis of St data, it is obseved that the egula votex shedding fequency also gets affected due to oscillation of the plate. C l, ms 169-6

7 (a) (b) (c) (d) Fig. 5: Instantaneous voticity contous fo cicula cylinde in the pesence of the flapping plate at its mean position fo G/D = 3 and (a) f 0.6 (b) f 0.9 (c) f 1.1 (d) f Conclusion The effect of downsteam flapping plate on a cicula cylinde has been investigated fo diffeent values of spacing between cylinde and plate and vaying fequency atios fo plate oscillation, at a fixed value of Re. The fluid dynamic foces acting on the cylinde ae consideably educed than the coesponding value fo stationay case when the plate is placed at and oscillated at f 0.9 and 1.4. The votex shedding fom the cylinde is also found to get suppessed at these values of f. Thus thee is a significant effect of amplitude and fequency of oscillation of the plate on the flow-induced foces acting on the cylinde. Fom the St data it is obseved that the egula votex shedding fequency is affected due to the oscillation of the plate. Moeove, at, the shedding fequency and the flapping fequency of the plate ae diffeent, wheeas both the fequencies become same at all othe value of spacing. Refeences [1] D. Seson, J. R. Meneghini, B. S. Camo, E. V. Volpe, and R. S. Gioia., Wake tansition in the flow aound a cicula cylinde with a splitte plate, J. Fluid Mech., vol. 755, pp , [2] J. Wu and C. Shu, Numeical study of flow chaacteistics behind a stationay cicula cylinde with a flapping plate, Phys. Fluids., vol. 23, no , [3] J. Y. Hwang, K. S. Yang, and S. H. Sun, Reduction of flow-induced foces on a cicula cylinde using a detached splitte plate, Phys. Fluids., vol. 15, no. 8, [4] K. Kwon and H. Choi, Contol of lamina votex shedding behind a cicula cylinde using splitte plates, Phys. Fluids, vol. 8, no. 479, [5] M. S. M Ali, C. J. Doolan, and V. Wheatley, Low Reynolds numbe flow ove a squae cylinde with a detached flat plate, Int. J. Heat Fluid Flow, vol. 36, pp , [6] Q. Xiao, W. Liu, and J. Hu, Paametic study on a cylinde dag eduction using downsteam undulating foil, Eu. J. Mech B-Fluid, vol. 36, pp , [7] Y. Bao and J. Tao, Active contol of a cylinde wake flow by using a steamwise oscillating foil, Phys. Fluids, vol. 25, no , [8] Y. Qiu, Y. Sun, Y. Wu, and Y. Tamua, Effects of splitte plates and Reynolds numbe on the aeodynamic loads acting on a cicula cylinde, J. Wind Eng. Ind. Aeodyn., vol. 127, pp ,