AFRREV STECH An International Journal of Science and Technology Bahir Dar, Ethiopia Vol.1 (1) April-July, 2012:

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1 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 AFRREV STECH An Internatonal Journal of Scence and Technology Bahr Dar, Ethopa Vol.1 (1) Aprl-July, 2012: ISSN (Prnt) ISSN (Onlne) 3D Flow around a Rectangular Cylnder: a revew Odesola, Isaac F. Department of Mechancal Engneerng Faculty of Technology, Unversty of Ibadan, Ibadan, Ngera E-mal: fodesola@mal.u.edu.ng or fodesola@yahoo.com Olawore, Ayode Department of Mechancal Engneerng Faculty of Technology, Unversty of Ibadan, Ibadan, Ngera Abstract Turbulent flows around three-dmensonal obstacles are common n nature and occur n many applcatons ncludng flow around tall buldngs, vehcles and computer chps. Understandng and predctng the propertes of these flows are necessary for safe, effectve and economcal engneerng desgns. Ths paper presents the revew of 3D flow around a rectangular cylnder usng large eddy smulaton as the turbulence model and the computatonal study s developed n the frame of the Benchmark on the Aerodynamcs of a Rectangular Cylnder (BARC). Dfferent smulatons around bluff bodes 128 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

2 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 were revewed and the results obtaned through dfferent methodologes are presented. The effect of change by vortex sheddng on the magntude of flud forces of rectangular cylnders are examned and reported. The aerodynamc ntegral parameters obtaned from dfferent papers are compared. Keywords: Rectangular cylnder, large eddy smulaton, BARC. Introducton The study of flow around bluff bodes of rectangular shape has a deep engneerng nterest because many cvl but also ndustral structure can be assmlate to ths shape. The flud-dynamc forces actng on a rectangular cylnder have been manly nvestgated for unbounded flow condtons. Even the boundng effect of a fxed wall occurs n many applcaton of cvl engneerng, for example n the case of brdges and/or buldngs placed n the proxmty of other structures or partcular land morphology, both n water or n ar-flow [16]. Smlarly, pers, brdge pllars, and legs of offshore platforms are contnuously submtted to the load produced by martme or fluval streams. Ths knd of flow s also found n many other techncal applcatons, especally those concernng wth thermal and hydraulc devces [11]. The geometry of bluff bodes plays a pvotal role n the flow-structure nteractons and the resultng flow and pressure felds around them [18]. The understandng of turbulent flow around a bluff body s far from mature, even f the flow s around smple geometry. Snce the Drect Numercal Smulaton (DNS) of such flow s stll not feasble for a qute long foreseeable tme, usng wall resolved Large Eddy Smulaton (LES) technque to nvestgate ths hgh Reynolds number flow would be both valuable and challengng [19]. The benchmark s orented to the flow around bluff-bodes, and they are sutable to explore the feasblty of the LES to relate engneerng problems because they show complcated flow events such as massve separatons, mpngng, transton to turbulence and formaton of vortex streets. These flow patterns are commonly found n the aerodynamc analyss of ground vehcles [10]. LES s partcularly attractve for the smulaton of bluff body flows, whch are characterzed by a complex threedmensonal and ntrnscally unsteady dynamcs that s dffcult to be accurately smulated by the RANS approach [1]. The flow around a crcular or rectangular cylnder n the unform flow s the most basc flud dynamc phenomenon. It s known that the flow around a rectangular cylnder exhbts an unsteady behavour such as full-separaton flow, alternately reattachment 129 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

3 3D Flow around a Rectangular Cylnder: a Revew AFRREV STECH, Vol. 1 (2) Aprl-July, D Flow around a Rectangular Cylnder: a Revew flow and full-reattachment flow, accompaned by a change n flud dynamc force accordng to changes n ts sde rato [15]. Nowadays, the flow around bluff bodes has been wdely nvestgated; the greater numbers of studes concern the flow past crcular cylnders. Less attenton has been dedcated to the flow around rectangular cylnders, although ths phenomenon s of great nterest for engneerng and aerodynamc applcatons, especally for the flud structure nteractons va expermentaton and numercal approach. After the frst expermental works of Okama [12] that nvestgated the Strouhal number varyng the cylnder wdth-to-heght rato (B/D) from 1 to 4 n a wde range of Reynolds numbers, some studes regardng both the lamnar and turbulent flows have been performed through numercal and expermental technques. Okama [13] nvestgated the numercal smulaton of flow around a rectangular cylnder at a wdth-to-heght rato (B/D = 1.5 to 4) on the unsteady 2D flow pattern, at zero angle of ncdence at a crtcal range Reynolds number of flows, whereas Saroglu et al [8] carred out expermental and numercal analyss of ths phenomenon at moderate Reynolds numbers. Bruno et al. [2] studed the flow around a B/D = 5 cylnder at Re = 40,000 by means of a fnte volume dscretzaton, whereas Ngro et al. [10] appled a fnte element method to the large eddy smulatons of the flow past a sharp-edged surface mounted cube at Re = 40,000. Yu and kareem [18] numercally conducted parametrc study of flow around rectangular prsms of dfferent aspect ratos at a Reynolds number of and the Naver Stokes equatons n the large eddy smulaton (LES) framework are solved usng a fnte volume method. Rokugou et al. [14] carred out three-dmensonal numercal analyss of the flow around rectangular cylnders wth varous sde ratos, D/H, from 0.2 to 2.0, for Reynolds number of 1000 by usng a mult drectonal fnte dfference method on a regular-arranged mult grd. Nakaguch et al [9] ponted out that pressure dstrbuton around the cylnder surface provdes basc knowledge of the force exerted by the flud on a body, the pressure dstrbuton varyng accordng to the B/H ratos of the secton. Turbulence models are equatons that account for turbulence of flow based on some assumptons, snce t s computatonally not practcal to thoroughly represent all the physcal characterstcs of a flow usng the current avalable computer power. The smulatons start wth the applcaton of LES to flow around a rectangular cylndrcal body wth aspect rato 5:1 [5]. The LES 130 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

4 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 approach has emerged as a more attractve scheme whch has the promse of provdng mproved results wth reasonable computatonal effort [4]. Large eddy smulaton (or LES) tres to smulate the largest scales of moton whle treatng the small scales by a model [6]. Nomenclature Re Φ f U St D U P SGS Reynolds number chord rato vortex sheddng frequency (Hz) mean velocty of the flow (m/s) Strouhal number body characterstc length (m) velocty n the streamwse drecton (m/s) pressure (Pa) flud densty (m/s) knematc vscosty of the flow (m 2 /s) characterstc spatal length of the flter dynamc vscosty(kg/ms) subgrd scale (SGS) Reynolds Stress SGS eddy vscosty S l x t u p C s stran rate tensor characterstc length scale of the unresolved moton space coordnate tme coordnate fltered velocty fltered pressure flter wdth Smagornsky constant y+ dmensonless dstance of grd ponts from the wall Flow around Rectangular Cylnders From the study of the flow around rectangular cylnders, one learns about the flow characterstcs around smlar shape bodes such as the deck secton of 131 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

5 3D Flow around a Rectangular Cylnder: a Revew AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 long span brdges. Maorty of the brdge deck sectons resemble more complex rectangular shape. Flow separates from the leadng edge corner and forms vortces that travel along the surface of the deck, whch are eventually shed from the tralng edge resultng n the vortex sheddng phenomenon. A vortex core tends to have a local mnmum pressure, so the formaton and progresson of vortces ntroduce forces on the deck surface. The same phenomenon s observed on the flow around rectangular secton wth smlar rato. Also, the Strouhal number and drag coeffcent of the flow change accordngly. Flow can be lamnar or turbulent dependng on the Reynolds number. For engneerng applcatons, most flows are turbulent n nature. Turbulence s the chaotc nature of flow n moton showng random varaton n space and tme. Turbulent flow s characterzed by ts rregularty, three-dmensonalty and dsspatve nature. Turbulence contans eddes wth dfferent szes whch are always rotatonal n moton. Dfferent scales of eddes are found n a flow. Large scale eddes are responsble for the carryng of energy and transfer of momentum n the flow. On the other hand, the smaller scale eddes, where dsspaton of energy occurs are known as the Kolmogorov scale eddes. The large eddes extract energy from the mean flow and transfer t to the smallest eddes where energy s taken out of the flow through vscosty. Naver-Stokes equatons Combnng these fundamental prncples, the physcs of flud flow s expressed n terms of a set of partal dfferental equatons known as the Naver-Stokes equatons. By solvng these equatons (contnuty equaton, momentum equaton and the energy equaton), the pressure and velocty of the flud can be predcted throughout the flow. For more explanaton on the dervaton of Naver-Stokes equatons, see Versteeg and Malalasekera (1995). Assumng that the flow s ncompressble, the followng equatons can be used to descrbe the flud flow, Naver-Stokes Equatons: (conservaton of momentum), u t u u x 1 p u x x 1 The contnuty equaton: (conservaton of mass), 132 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

6 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 u x 0 2 Large Eddy Smulaton (LES) Large eddy smulaton (LES) s classfed as a space flterng method n CFD. LES drectly computes the large-scale turbulent structures whch are responsble for the transfer of energy and momentum n a flow whle modellng the smaller scale of dsspatve and more sotropc structures. In order to dstngush between the large scales and small scales, a flter functon s used n LES. A flter functon dctates whch eddes are large by ntroducng a length scale, usually denoted as n LES, the characterstc flter wdth of the smulaton. All eddes larger than are resolved drectly, whle those smaller than are approxmated. Flterng of Naver-Stokes equatons In LES, the flow velocty U s separated nto a fltered, resolved part U and a sub-flter, unresolved part, u, U ' U u. 3 The flter dscretses the flow spatally. Applyng the flter functon to Eq. 2.2, we have, U ' ' x Gx, x U x dx... As mentoned, the flter functon dctates the large and small eddes n the flow. Ths s done by the localzed functon G (x, x ). Ths functon determnes the sze of the small scales, 4 G 1 ' 0 f x x otherwse 2 5 Varous flterng methods exst; the top hat flter s common n LES. By mposng the flter functon n the contnuty and the Naver-Stokes equatons, one obtans the fltered equatons governng the flud flow n LES, 133 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

7 AFRREV STECH, Vol. 1 (2) Aprl-July, D Flow around a Rectangular Cylnder: a Revew u... 6 x u t 0 uu x 2 1 p u x x..7 The over bar denotes the space fltered quanttes. In flud flow around an mmersed obect, shear stress occurs because not all the flud exerts forces tangentally to the wall of the obect. Ths results n the appearance of the stress terms n the equatons governng flud flow. After dvdng the Naver- Stokes Equaton nto fltered and sub-flter components, the unknown stress term uu of the flow. arses due to the nonlnearty of the equatons and the shear stress Ths term needs to be approxmated to solve the fltered Naver-Stokes Equatons. u u ' ' ' ' ' u u u u u u u u u u u u.. 8 The unknown term u comprses the resolvable scale component u 134 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne: u and the small scale component u of the flow. Thus, a relatonshp based on the nteracton among components of varous scales n the flow has been derved to estmate the unknown. Ths s wrtten as, ' ' ' ' u u uu u u uu uu.. 9 The term s known as the subgrd scale (SGS) Reynolds Stress. Physcally, the rght hand sde of Eq.9 represents the large scale momentum flux due to turbulence moton. Smagornsky model To approxmate the SGS Reynolds stress, a SGS model can be employed. The most commonly used SGS models n LES s the Smagornsky model. In a flow, t s the shear stress and the vscosty of the flow that cause the

8 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 chaotc and random nature of the flud moton. Thus, n the Smagornsky model, the effects of turbulence are represented by the eddy vscosty based on the well-known Boussnesq hypothess [17]. The Boussnesq hypothess relates the Reynolds stress to the velocty gradents and the turbulent vscosty of the flow. It s therefore assumed that the SGS Reynolds stress s proportonal to the modulus of the stran rate tensor of the resolve eddes [7], 1 3 kk 2vSGS. S vsgs. u x u x...10 Where S 1 u 2 x u x where v SGS s the SGS eddy vscosty and S s the stran rate tensor, 1 2 S S 2 S...12 The SGS eddy vscosty v SGS needs to be approxmated n order to solve Eq Based on dmensonal analyss, the followng relatonshp has been obtaned, v SGS lq SGS...13 where l s the characterstc length scale of the unresolved moton that usually takes the value of the flter wdth x y z 3. x, y and z are the grd spacngs n the x, y and z drecton respectvely. By relatng the velocty scale of the unresolved moton q SGS 1 to the gradents of the fltered velocty based on an analogy of the mxng length model, the SGS vscosty s wrtten as [20], v SGS 2 C S...14 s 135 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

9 3D Flow around a Rectangular Cylnder: a Revew AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 where C s s the Smagornsky constant that changes dependng on the type of flow. For sotropc turbulent flow, the Cs value s usually around 0.18 to Bascally, the Smagornsky SGS model smulates the energy transfer between the large and the subgrd-scale eddes. Energy s transferred from the large to the small scales but backscatter (reverse of cascade process) sometmes occurs where flow becomes hghly ansotropc, usually near to the wall. To account for backscatterng, the length scale of the flow can be modfed usng Van Drest dampng [7] y 25 s Cs1 e C...15 where y+ s the dmensonless dstance of grd ponts from the wall. Van Drest dampng accounts for the reduced growth of the small scales near the wall whch gves a smaller value of SGS vscosty n order to represent the flow more accurately. Flow modelng and computatonal approach The key features n the smulaton of the flow around rectangular cylnders s the ablty of the turbulence models to capture the changes of the flow characterstcs wth respect to the ncreasng B/H rato and the predcton of the reattachment of flow along the sde surface of the cylnders. The 3D, turbulent, unsteady flow around the cylnder s modeled n the frame of the large eddy smulaton approach to turbulence usng the classcal tmedependent fltered Naver Stokes equatons. Only flow at zero angle of ncdence has been conducted n the current study. The author s aware of the sgnfcant effect of the non-zero ncdent flow. Postve ncdent flow generates negatve cross wnd force as a consequence of the pressure dstrbuton around the cylnder, whch results n aeroelastc nstablty f the enveloped structure s free to move. Ths s very mportant n the study of the flow around a brdge deck secton. Doman sze: The computatonal doman and boundary condtons used n the smulaton for the flow around the rectangular cylnder s depcted n fgure1. The spanwse length of the computatonal doman s set equal to L/B = 1 on the bass of a short revew of the state of art. The breadth (B) to depth (D) rato s set equal to 5. Drchlet 136 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

10 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 condtons on the velocty feld and on the sub-grd knetc energy are mposed at the nlet boundares. Neumann condtons on the normal component of the stress tensor T, as well as the same Drchlet condtons on kt, are mposed at the outlet boundares. Perodc condtons are mposed on both the sde surfaces and on the upper-lower surfaces, as depcted n Fg. 1. No-slp condtons are mposed at the secton surface. Fg. 1: Computatonal doman and boundary condtons (not drawn to scale) Dscretsaton: The LES uses a second order central dfferencng scheme for space dscretsaton and a second order backward Euler scheme for the tme dscretsaton. A hexahedral grd s adopted to dscretze the spatal computatonal doman. 137 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

11 3D Flow around a Rectangular Cylnder: a Revew AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 Meshng: LES requres more globally refned mesh n order to properly resolve the eddes n the flow (fne mesh n the mesh senstvty analyss) to make sure that flow near to the wall s properly resolved. The rest of the regons where SST are actve have a coarser mesh, whch helps to save computatonal power. Tme step and convergence: Concluson The tme s non-dmensonalsed by U and D. The non-dmensonal t 510 tme-step s set equal to, whch provdes an accurate advancement n tme and a CFL number close to unt. The smulaton s extended over T = 800 non-dmensonal tme unts n order to have a long enough statstcal sample to obtan converged statstcs, after havng excluded the ntal transent. Computatons are carred out on 8 Intel Quadcore X GHz CPUs and requre about 2.5 GB of RAM memory and 15 days of CPU tme for the whole smulaton [7]. The tme step used n the smulaton s , where 50 tme steps are necessary to generate one vortex cycle n the flow. Ths s equvalent to 0.08 n term of the non-dmensonal tme step. The resduals of convergence of the soluton are mantaned at 10-4 to keep the errors at an acceptable level [5]. The study of the flow around rectangular sectons provdes fundamental understandng of the flow characterstcs around the sectons and bodes wth smlar shapes. Ths also provdes nsght nto the aerodynamc characterstcs of the flow around a brdge deck secton. Valdaton of the turbulence models (LES) on the flow around rectangular sectons wth aspect rato of 5:1 has been conducted based on the comparson of fundamental flow characterstcs wth expermental fndngs. These nclude velocty profles, pressure feld and dstrbuton of vortces, as well as the changes of Strouhal number and drag coeffcent at the aspect rato. From the work done on the LES, t was concluded that LES s a relable and an accurate model for unsteady and complex flow smulaton. Detals of eddes and vortex structures are well captured but a more refne mesh s needed. The applcaton of the prncpal component analyss (PCA) on the study of the pressure dstrbuton around the cylnders smplfed and dentfed the 138 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne: 3

12 AFRREV STECH, Vol. 1 (2) Aprl-July, 2012 domnant pressure dstrbuton on the surface of the cylnder and thus the aerodynamc forces nduced. Ths approach proved frutful and ndcated the possblty of ts applcaton on the flow around a brdge deck secton where complex flow features wth ntense vortex nteracton s nvolved. References 1. A.N. Grozescu, L.Bruno, D. Fransos, M.V. Salvett. Large-eddy smulatons of a Benchmark on the Aerodynamcs of a Rectangular 5:1 Cylnder. In BBAA VI nternatonal colloquum on bluff bodes aerodynamcs & applcatons, Mlano, Italy; (2008). 2. Bruno L, Fransos D, Coste N, Bosco A. 3D flow around a rectangular cylnder: a computatonal study. Journal of Wnd Engneerng and Industral Aerodynamcs, C. Mannn, K. Wenman, A. Šoda, G. Schewe. Three-dmensonal numercal smulaton of flow around a 1:5 rectangular cylnder. EACWE 5 Florence, Italy D. Yu, A. Kareem. Two-dmensonal smulaton of flow around rectangular prsms, Journal of Wnd Engneerng and Industral Aerodynamcs 62 (1996) Ka Fan Law, Smulaton of Flow around Bluff Bodes and Brdge Deck Sectons usng CFD; Flow around Rectangular Cylnders. Dssertaton Submtted for the degree of Doctor of Phlosophy (PhD), Unversty of Nottngham, England (2005). 6. Kshan B. Shah, Joel H. Ferzger. A flud mechancans vew of wnd engneerng: Large eddy smulaton of flow past a cubc obstacle. Journal of Wnd Engneerng and Industral Aerodynamcs 67&68 pg (1997). 7. L.Bruno, N. Coste, D. Fransos. Analyss of the separated flow around a 5:1 rectangular cylnder through computatonal smulaton. EACWE 5 Florence, Italy July Mustafa Saroglu, Tahr Yavuz. Vortex Sheddng From Crcular and Rectangular Cylnders Placed Horzontally n a Turbulent Flow. Turk J Engn Envron Sc 24, (2000). 139 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

13 AFRREV STECH, Vol. 1 (2) Aprl-July, Nakaguch H, Hashmoto K, Muto S, An expermental study on aerodynamcs drag of rectangular cylnders. J. Japan Socety of Aeronautcal and Space Sc., 1968, Vol.16, p Norberto Ngro, German Flppn, Gerardo Franck, Maro Stort and Jorge D Elıa flow around a sharp-edged surface-mounted cube by large eddy smulaton. In Mecanca Computaconal, vol. XXIV, (2005). 11. O. Almeda, S. S. Mansur, A. Slvera-Neto. On the flow past rectangular cylnders: physcal aspects and numercal smulaton. Engenhara Térmca (Thermal Engneerng), Vol. 7, No 01, p (2008). 12. Okama A, Strouhal number of rectangular cylnders. Journal of Flud Mechancs, Vol.123, p (1982). 13. Okama A, Numercal smulaton of flow around rectangular cylnders. Journal of Wnd Engneerng and Industral Aerodynamcs, vol 33, (1990). 14. Rokugou A, Okama A, Kamyama K, Numercal Analyss of Flow around Rectangular Cylnders wth Varous Sde Ratos. Japan Socety of Mechancal Engneers vol.68; no.670; page (2002). 15. S. Berrone, V. Garbero, M. Marro. Numercal smulaton of low- Reynolds number flows past rectangular cylnders based on adaptve fnte element and fnte volume methods, Computers & Fluds 40 (2011) Stefano Malavas, Ncola Trabucch, Numercal nvestgaton of the flow around a rectangular cylnder near a sold wall. In BBAA VI Internatonal Colloquum on: Bluff Bodes Aerodynamcs & Applcatons Mlano, Italy, July, (2008). 17. Sumeet Thete, Kaustubh Bhat and M. R. Nandgaonkar. 2D Numercal Smulaton of Flud Flow over a Rectangular Prsm. CFD Letters Vol. 1(1) Yu Daha, Ahsan Kareem, Parametrc study of flow around rectangular prsms usng LES. Journal of Wnd Engneerng and Industral Aerodynamcs 77&78 p (1998). 140 Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne:

14 AFRREV STECH, Vol. 1 (2) Aprl-July, Zhgang We, Ahsan Kareem. A benchmark study of flow around a rectangular cylnder wth aspect rato 1:5 at Reynolds number 1.E5. Global Center of Excellence founded by the MEXT, Japan (2009). 20. Charles Meneveau, Turbulence: Subgrd-Scale Modelng, Johns Hopkns Unversty Scholarpeda, 5(1):9489, Copyrght IAARR 2012: Indexed Afrcan Researches Revew Onlne: