EVALUATION OF FORCE COEFFICIENTS FOR A 2-D ANGLE SECTION USING REALIZABLE k-ε TURBULENCE MODEL

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1 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan EVALUATION OF FORCE COEFFICIENTS FOR A -D ANGLE SECTION USING REALIZABLE k-ε TURBULENCE MODEL S. Chra Ganapah, P. Harkrshna, A. Abraham, S. Arunachalam and N. Lakshmanan 3 Scens, Drecor Grade Scens, 3 Proec Advsor Srucural Engneerng Research Cenre, Councl of Scenfc and Indusral Research, CSIR Campus, Taraman, Chenna 6003, Inda, har@sercm.org ABSTRACT Lace owers such as ransmsson lne owers and communcaon owers use L-angle secons as prmary as well as secondary members. Whle consderable research has been repored for wnd nduced loads on regular shaped buldngs and srucural componens, sudes on L-angle secons were scarce. In he presen sudy, mean drag and lf force coeffcens for a -D L-angle secon were numercally obaned under low urbulen upsream flow usng Realzable k ε urbulence model avalable n FLUENT sofware. The resuls for dfferen wnd angles of aack were compared wh he expermenal resuls avalable n leraure. Furher, he force coeffcens under urbulen flow wh a urbulence nensy of 0% have been evaluaed. KEYWORDS: ANGLE SECTION, DRAG, LIFT, FORCE COEFFICIENT, TURBULENCE MODEL Inroducon Angle secons are frequenly used n he consrucon of engneerng srucures such as hgh volage ransmsson lne owers, anenna mass and brdges. These are ncorporaed as prmary as well as, secondary members. Whle here s consderable research on cubcal and cylndrcal srucures, only a few earler research sudes consdered rregular shapes. [Mod and Slaer (983)] conduced sudes on wake-body neracons for a wo dmensonal srucural angle member under saonary and vorex nduced oscllaory condons usng a convenonal low urbulence wnd unnel. [Sahopoulos and Zhou (993)] have examned he wnd loads for L-shaped plan vew as well as for L-shaped cross secon (sepped-roof buldng) hrough a numercal sudy. [Lel e al. (997)] used FLUENT for smulang he flow and dsperson of gases around a U- shaped buldng and he numercal resuls were compared wh wnd-unnel measuremens. [Gomes e al. (005)] carred ou wnd unnel model ess on rregular shapes (manly on L and U shaped models) for measurng pressure dsrbuon under unform flow. Furher, CFD code was used o compare he numercally obaned flow paern and pressure dsrbuons wh wnd unnel resuls. [Meroney e al. (999)] explaned a numercal smulaon procedure of flow and dsperson of gases for rregular shapes by usng FLUENT and FLUENT/UNS usng he sandard k ε, he RNG k ε, and he Reynolds-sress urbulence closure approxmaons. They have found good agreemen beween numercally and expermenally obaned resuls for normal wnd ncdence. In he presen sudy, drag and lf force coeffcens for a -D L-angle shaped secon were numercally obaned under low urbulen upsream flow usng Realzable k ε urbulence model avalable n FLUENT sofware. The resuls for dfferen wnd angles of aack were compared wh he wnd unnel measuremens [Mod and Slaer (983)]. In addon, he force coeffcens under urbulen flow wh a urbulence nensy of 0% have been evaluaed.

2 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan Governng Equaons The followng are he governng dfferenal equaons for Reynolds Averaged Naver-Sokes Smulaon (RANS) modelng. Connuy equaon: = 0, =,,3 for x, y, z drecons () Momenum equaon: where + u p = ρ u = mean velocy componens p = mean pressure = knemac vscosy of he flud τ ' = Reynolds sress ensor wh ( u u' ρ = densy of ar + ' = u ' u' ) + + τ ' In Eddy Vscosy Model (EVM), he Reynolds sresses ( τ ' () ) are expressed as proporonal o mean velocy gradens n analogy o he vscous sresses n lamnar flows as gven below τ ' = u ' u' = u u + k δ (3) x x 3 where δ = kronecker dela funcon = (for = ) or 0 (for ) = knemac urbulen (or) eddy vscosy k = urbulen knec energy Unlke knemac or molecular vscosy ( ) whch s a flud propery, he knemac urbulen or eddy vscosy ( ) depends on he flow. The knemac urbulen or eddy vscosy can be expressed as lo / τ o (4) where l o = he urbulen lengh scale τ = he urbulen me scale o In sandard k-ε model, he urbulen lengh scale (l o ) and he urbulen me scale (τ o ) are obaned from he urbulen knec energy (k) and he urbulen energy dsspaon rae (ε), and he knemac urbulen or eddy vscosy ( ) s expressed as k = C µ (5) ε where C µ = 0.09 The sandard k-ε model s found o perform poorly n hghly sraned flows wh hghly curved sreamlnes (e.g. swrlng / roang flows) near bluff bodes and n ansoropc urbulen flows. I also does no srcly sasfy he realzably (mahemacal) consrans whch are conssen wh he physcs of urbulen flows [FLUENT 6.3 (006)]. To sasfy he realzably consrans, he coeffcen, C µ, used for evaluang knemac eddy vscosy,, (Eq. 5) has been made as a funcon of sran and roaon parameers nsead of a consan value of In he presen sudy, Realazable k-ε urbulence

3 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan model avalable n he FLUENT sofware (verson 6.3.6) [FLUENT 6.3 (006)] has been used. As per [FLUENT 6.3 (006)], C µ has been defned as gven below: Cµ = (6) ku * A0 + As ε A 0 = 4.04 A = 6 cosφ (7) s φ = cos ( 6W ) (8) 3 S S k S k W = ~ (9) S S ~ = S S (0) S = + () ~ ~ U * = S S + ΩΩ () Ω ~ = Ω ε ω (3) k k k k Ω = Ω ε ω (4) Ω = Here, he urbulen knec energy (k) and he urbulen energy dsspaon rae (ε) are obaned from he respecve derved dfferenal ranspor equaons as gven below, k k k + u = + + τ σ ' k ε (6) ε ε ε ε + u + ε σ = + C S C ε k + ε (7) where σ k =.0; σ ε =.; C =.9 η C = max 0.43, η + 5 (8) k η = S ε (9) S S S (0) The followng numercal schemes were used n he presen sudy: a) Second order mplc scheme for unseady formulaon, b) Second order upwnd dfferencng scheme for momenum, k and ε ranspor equaons and c) SIMPLE (Sem-Implc Mehod for Pressure- Lnked Equaons) algorhm for couplng he pressure and velocy erms. Evaluaon of Force Coeffcens for a -D Angle Secon In hs sudy, numercal smulaons were carred ou for an equal angle secon wh varous wnd angles of aack. The wdh of he equal angle secon (b) s m and he hckness () s 0.07 m. (5)

4 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan Compuaonal Doman and Mesh Sze of he compuaonal doman for wnd drecon (θ = 0 0 ) normal o a flange has been chosen as b n wnd drecon and 5b n perpendcular o wnd drecon (Fgure ). For wall bounded urbulen flows, he frs grd pon from he wall surface has o be a a prescrbed dsance dependng upon he mehod of near wall reamen. In he presen sudy, sandard wall funcon has been used for he near wall reamen. For sandard wall funcon, each wall-adacen cell's cenrod should be locaed whn he log-law layer for whch he frs grd pon needs o be a a dsance correspondng o a wall un (y + ) of beween 30 and 300 (FLUENT 6.3). The wall un y + s defned as, + Yu * y = () where Y = dsance of he frs grd pon from he wall surface (n he presen case, he surface of he angle secon) u* = shear frcon velocy Here, u* depends upon he Reynolds number of he flow. Hence for a gven flud flow smulaon, he y + depends upon he dsance of he frs grd pon from he wall surface and he Reynolds number. In he presen sudy, hs dsance corresponds o 0.0b for Reynolds number equal o 50,000 [Mod and Slaer (983)]. The compuaonal doman has been meshed by choosng he wdh of he frs cell near he walls of he angle secon as 0.0b. The dsance of he oher grd lnes from he angle secon face o oher boundares s vared wh a geomerc seres usng a srechng rao. The maxmum srechng of successve mesh cells s lmed o. for smooh varaon [Bosch and Rod, (998)]. The mesh has been generaed usng a srechng rao of abou.. Symmery Boundary θ b b Inle Boundary 5b Oule Boundary b Symmery Boundary Fgure : Compuaonal Doman wh Mesh for Wnd Drecon Normal o a Flange (0 0 )

5 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan Boundary Condons [Mod and Slaer (983)] expermenally obaned drag and lf force coeffcens for an equal angle secon a a Reynolds number of 50,000 and under low urbulence levels. Hence, a he nle boundary condon, he mean velocy ( u ), was gven as m/s wh he urbulence nensy ( I u = ( u ' u' ) / / u ) of 0.%. The oule boundary was chosen a a dsance of 5b from he rear face (leeward face) of he angle a whch he dervaves of all he flow varables n he flow drecon were se equal o zero. The symmery (free-slp) boundares were chosen a a dsance of 7b from he sde faces of he angle a whch he velocy n he drecon normal o he boundary was se equal o zero and also he dervaves of all he flow varables n he drecon normal o he boundary were se equal o zero. Wall (no-slp) boundares were chosen for all he sdes of he bluff body a whch he veloces n he flow and normal o flow drecons were se equal o zero. Resuls Unseady flow smulaons were carred ou wh a me sep ( ) of 0.00 s for dfferen wnd drecons. The evaluaed mean drag ( C d ) and lf ( C l ) force coeffcens for a few wnd drecons were summarzed n Table. I s o be noed ha he symmery axs for he angle secon corresponds o wnd drecons (θ) of 35 0 and 35 0 ( 45 0 ). The numercally obaned force coeffcens compared well wh he expermenal values for wnd drecon of In addon, he force coeffcens for urbulen flow wh 0% of urbulence nensy were also gven n Table. The C d values were observed o be sgnfcanly reduced under urbulen flow for wnd drecons 0 0 and However, he C l values were observed o be sgnfcanly ncreased under urbulen flow for wnd drecons 0 0 and Parameers Table : Comparson of Numercal and Expermenal Force Coeffcens Expermenal values [Mod and Slaer (983)] Wnd drecon (θ) / ( 45 0 ) C d (.964) C l ( 0.548) Numercal values Wnd drecon (θ) / ( 45 0 ) 0.9 (0.944).93 (.4).355 (.897).39 (.9).75 (.458) (0.00) Noe: Values gven n bracke correspond o urbulen flow wh 0% urbulence nensy..0 (.) 0.0 (0.07) Fgure compares he numercally evaluaed C d values under low urbulen flow (0.%) and hgh urbulen flow (0%) condons wh he expermenal values [Mod and Slaer (983)] and he codal values as per [AS/NZ 70. (00); NRC-CNRC (995); IS 875 (Par 3) (987)]. Smlarly, he numercally evaluaed C l values under low urbulen flow ( I u = 0.%) and hgh urbulen flow ( I u = 0%) condons are compared wh he expermenal values [Mod and Slaer (983)] and he codal values as per [AS/NZ 70. (00); NRC-CNRC (995); IS 875 (Par 3) (987)] n Fgure 3.

6 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan C d Wnd drecon (deg) Numercal (Low Turbulen) Numercal (Hgh Turbulen) Expermenal Codal Fgure : Comparson of C d Values 3 C l Numercal (Low Turbulen) Numercal (Hgh Turbulen) Expermenal Codal Wnd drecon (deg) Fgure 3: Comparson of C l Values I can be seen from Fgure ha he numercally evaluaed C d values under low urbulen flow condon compared well wh he expermenal values a θ of 45 0 only and are observed o be over predced for all wnd drecons (θ) compared o codal values. However, he C d values under hgh urbulen flow condon compared well wh he codal values. Fgure 3 shows ha he numercally evaluaed C l values under low urbulen condon compared well wh he expermenal values excep for θ = However, he C l values under hgh urbulen condon compared well wh he codal values.

7 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan The Srouhal number (S ) s he reduced vorex sheddng frequency, defned as: n b S = () s u where n s = vorex sheddng frequency Fgure 4 compares he numercally evaluaed Srouhal numbers under low urbulen flow and hgh urbulen flow condons wh he expermenal values. I can be seen ha he numercally evaluaed S values under low urbulen flow condon compared well wh expermenal values excep for θ = I can be observed ha he Srouhal number reduced under hgh urbulen flow condon for all wnd drecons (θ) by 0 o 0% Srouhal Number Numercal (Low Turbulen) Numercal (Hgh Turbulen) Expermenal Wnd drecon (deg) Fgure 4: Comparson of Srouhal Number Values Conclusons Numercal smulaons have been carred ou o evaluae mean drag and lf force coeffcens for a -D L-angle secon under low urbulen flow ( = 0.%) and hgh urbulen flow ( I u = 0%) condons wh a Reynolds number of 50,000 usng Realzable k ε urbulence model. The C d values were observed o be sgnfcanly reduced under hgh urbulen flow for wnd drecons 0 0 and However, he C l values were observed o be sgnfcanly ncreased under hgh urbulen flow for wnd drecons 0 0 and The numercally obaned C d values under low urbulen flow condon compared well wh he expermenal values [Mod and Slaer (983)] only for θ = Excep for θ = 90 0, he numercally obaned C l values under low urbulen flow condon compared well wh he expermenal values [Mod and Slaer (983)]. The numercally obaned C d and C values under hgh urbulen flow condon compared well wh he codal values. l I u

8 The Sevenh Asa-Pacfc Conference on Wnd Engneerng, November 8-, 009, Tape, Tawan The Srouhal number was observed o be reduced under hgh urbulen flow condon for all wnd drecons (θ) by 0 o 0% as compared o he values correspondng o low urbulen flow condon. Acknowledgemens Ths paper s beng publshed wh he knd permsson of Drecor, Srucural Engneerng Research Cenre, CSIR, Chenna, Inda. References AS/NZ 70. (00), Ausralan/New Zealand Sandard, Srucural Desgn Acons, Par : Wnd Acons, Sandards Ausrala & Sandards New Zealand. Bosch, G. and Rod, W. (998), Smulaon of Vorex Sheddng Pas a Square Cylnder wh Dfferen Turbulence Models, Inernaonal Journal for Numercal Mehods n Fluds, 8, FLUENT 6.3 (006), User s Gude, ANSYS Fluen Inc, Lebanon, USA. Gomes, M.G., Rodrgues, A.M. and Mendes, P. (005), Expermenal and Numercal Sudy of Wnd Pressures on Irregular-plan Shapes, Journal of Wnd Engneerng and Indusral Aerodynamcs, 93(0), IS 875 (Par 3) (987), Code of Pracce for Desgn Loads (oher han Earhquake) for Buldngs and Srucures Par 3 Wnd Loads, Bureau of Indan Sandard, New Delh. Lel, B.M., Klen, P.K., Rau, M. and Meroney, R.N. (997), Concenraon and Flow Dsrbuons n he Vcny of U-shaped Buldngs: Wnd-unnel and Compuaonal Daa, Journal of Wnd Engneerng and Indusral Aerodynamcs, 67-68, Meroney, R.N., Lel, B.M., Rafalds, S. and Schazmann, M. (999), Wnd-unnel and Numercal Modelng of Flow and Dsperson abou Several Buldng Shapes, Journal of Wnd Engneerng and Indusral Aerodynamcs, 8(-3), Mod, V.J. and Slaer, J.E. (983), Unseady Aerodynamcs and Vorex nduced Aero Elasc Insably of a Srucural Angle Secon, Journal of Wnd Engneerng and Indusral Aerodynamcs,, NRC-CNRC (995), Naonal Buldng Code of Canada, Naonal Research Councl Canada, Onaro, Canada. Sahopoulos, T. and Zhou, Y. (993), Numercal Smulaon of Wnd-nduced Pressures on Buldngs of Varous Geomeres, Journal of Wnd Engneerng Indusral Aerodynamcs, 46-47,