2 MODELS A typcal hgh-sded artculated lorry, whch was nvestgated extensvely by Baker and hs colleagues n wnd tunnels and later used n the dynamc analy

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1 The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7) Shangha, Chna; September 2-6, 2012 Determnaton of aerodynamc characterstcs of a vehcle mmerged n the wake of brdge tower usng computatonal flud dynamcs Bn Wang a, You-Ln Xu a, Le-Dong Zhu b, Yong-Le L c a Department of Cvl and Structural Engneerng, The Hong Kong Polytechnc Unversty, Hong Kong, Chna b Department of Brdge Engneerng, Tong Unversty, Shangha, Chna c Department of Brdge Engneerng, Southwest Jaotong Unversty, Chengdu, Chna ABSTRACT: The runnng safety analyss of a vehcle subected to crosswnds s one of the ssues concerned n wnd engneerng. Partcularly as a vehcle moves passng by a brdge tower, the sheldng effect of the tower on wnd forces of the vehcle occurs, whch leads to a sharp change of aerodynamc forces on the vehcle n danger. To explore the aerodynamc forces actng on the vehcle passng by the brdge tower, the flows around the vehcle mmerged n dfferent postons to the brdge tower are smulated usng the computatonal flud dynamcs (CFD) technque n ths study. The aerodynamc forces measured n the wnd tunnel are used to confrm the smulaton results. Meanwhle, the aerodynamc characterstcs of the vehcle mmerged n the wake of the brdge tower and the flow feld features are explored n detal. KEYWORDS: vehcle, brdge tower, crosswnds, aerodynamcs, computatonal flud dynamcs 1 INTRODUCTION Vehcle behavor under crosswnds s one of the ssues concerned n wnd engneerng. The runnng safety analyss of a vehcle subected to crosswnds probably started from the Baker s work n 1986 (Baker 1 ). Snce then, several studes on the safety of a vehcle subected to crosswnds have been carred out. Partcularly as a vehcle moves passng by a brdge tower, the sheldng effect of the tower on wnd forces of the vehcle occurs, whch leads to a sharp change of aerodynamc forces on the vehcle n danger. The safety of a vehcle runnng through a tower regon s therefore concerned. The aerodynamc forces of a vehcle n the wake of a brdge tower should be studed to make sure the runnng safety of the vehcle. Wnd tunnel tests are a common method to obtan the aerodynamc forces on a vehcle. Charuvst et al. 2 tested the transent aerodynamc sde force and yawng moment on a vehcle when t passed by a brdge tower subected to crosswnds. Argentn et al. 3 carred out wnd tunnel tests to measure the aerodynamc forces and the surface pressure dstrbutons of the statonary vehcle model. Wth the rapd development of computer hardware, computatonal flud dynamcs (CFD) can be employed as an alternatve tool, practcally n the flow vsualzaton whch cannot be acheved easly by wnd tunnel tests. In ths study, the flows around a brdge tower and a vehcle n dfferent postons behnd the brdge tower are smulated usng the CFD technque. The aerodynamc forces measured n a wnd tunnel are used to confrm the smulaton results. Then, the aerodynamc characterstcs of the vehcle mmerged n the wake of the brdge tower and the flow feld features are explored n detal. 1719

2 2 MODELS A typcal hgh-sded artculated lorry, whch was nvestgated extensvely by Baker and hs colleagues n wnd tunnels and later used n the dynamc analyss of wnd-vehcle-brdge systems (Xu & Guo 4, Ca & Chen 5, Chen & Wu 6 ), s selected as the reference vehcle. The geometrc scales of the vehcle are shown n Fg.1. A long span hghway brdge s also selected. It s a cable-stayed brdge of double towers wth a man span of 688m (see Fg.3). The tower composes of a par of sde by sde legs and a transverse beam to support and restran the deck (see Fg.2). The tower legs are nclned from the heght of deck to both the ends wth a chamfered rectangle secton. The transverse beam connected the two legs wth a rectangle cross secton. A flat box grder wth sde farng s selected as the brdge deck, as seen n Fg.4. The cross secton of the deck was 34.0m wde and 3.5m hgh carryng a dual two-lane hghway on the upper surface. Two lnes of handral, four lnes of protecton ral and two lnes of I-shape mantenance trace are mounted on the brdge deck. Both the vehcle and brdge models are scaled wth a length rato of 1:25. Under the crosswnds, the vehcle runnng on the upwnd frst lane s mpacted by the brdge tower more serously than the one runnng on the other lanes. Therefore the vehcle s arranged on the upwnd frst lane n ths study. Because of the complex flow feld around the tower, the vehcle n dfferent locatons wth reference to the tower may suffer dstnct wnd flow. To reflect the nfluence of dstance from the tower, three dfferent postons of the vehcle n the wake of brdge tower are consdered. They are (1) the vehcle mmerged behnd the tower entrely (poston Xd1 n Fg.5), (2) half-length of the vehcle mmerged behnd the tower (poston Xd3 n Fg.5), and (3) the vehcle ust gettng rd of the tower (poston Xd5 n Fg.5). Aerodynamc forces of the same vehcle model were tested n the TJ-3 wnd tunnel of the State Key Laboratory for Dsaster Reducton n Cvl Engneerng at Tong Unversty n Manland Chna. The models mounted n the wnd tunnel are shown n Fg.6. Fgure 1. Dmensons of vehcle model (unt: mm) Fgure 2. Dmensons of brdge tower (unt: cm) 1720

3 The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7) Shangha, Chna; September 2-6, 2012 Fgure 3. Elevaton of the selected brdge (unt: cm) Wnd Protecton ral Hand ral Protecton ral Protecton ral = = Lane 1 Lane 2 Lane 3 Lane 4 Protecton ral Hand ral Sde farng Mantenance trace Sde farng Mantenance trace Fgure 4. Cross secton of brdge deck (unt: mm) Fgure 5. Vehcle locatons Fgure 6. Wnd tunnel tests of vehcle 3 NUMERICAL METHOD 3.1 Governng equatons In order to explore the flow characterstcs around and the aerodynamc forces on the vehclebrdge system, the large eddy smulaton (LES) method s adopted for ths study. In LES, turbulent flows are decomposed nto large and small scales of turbulence by means of a hghpass flter n space. The large-scale turbulence flows can then be computed accurately by usng the LES governng equatons whle the effect of the small-scale turbulence can be estmated through the subgrd-scale (SGS) model wth the understandng that the small scales of turbulence tend to more homogeneous and unversal, and less affected by the boundary condtons than the 1721

4 large-scale ones. A box flter expressed by Eq. (1) s used for performng the spatal scale separaton and a fltered varable s expressed by Eq.(2). G ϕ (2) ' ( x, x ) ' 1 V, x v = ' 0, x v ' ' ' ( x) = G( x, x ) ϕ( x ) dx v where G s the flter functon; ϕ s the varable before flterng; ϕ s the varable after flterng; v denotes the computatonal cell; and V s the computatonal volume. By applyng the flterng operaton to the momentum and contnuty equatons, the LES governng equatons can be derved as u ρ t u + ρ = 0 ( u u ) 2 p u = + μ τ where μ (=1, 2, 3) s the fltered velocty component n the Cartesan coordnates; p s the fltered pressure; ρ s the flud densty; μ s the dynamc vscosty coeffcent; and τ s the subgrd-scale stress expressed by τ = ρu u ρu u The subgrd-scale stress must be modeled, and the subgrd-scale turbulent model employed n ths study s based on the Boussnesq hypothess. 1 τ = 2μt S + τkkδ 3 S 1 u u = + 2 where μ s the subgrd-scale turbulence vscosty; τ t kk s the sotropc part of the subgrd-scale stress. The subgrd-scale turbulence vscosty can be determned by usng the Smagornsky-Llly model. The Smagornsky constant equal to 0.1. (1) (3) (4) (5) (6) (7) 3.2 Numercal models In the smulaton, only one wnd drecton (wnd perpendcular to the brdge deck) s consdered. Fg.7 shows the computatonal flow doman when the vehcle s located at Xd3. The entre computatonal doman s a box shape enclosed by sx boundary faces. B, BV and BT represent the wdth of the deck, the length of the vehcle and the wdth of tower, respectvely. The heght of the computatonal doman s 7m whch leads a blockage rato at the level of the wnd tunnel 1722

5 The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7) Shangha, Chna; September 2-6, 2012 tests. All those szes determnng the computatonal flow doman are optmzed through parameter studes. (a) (b) Fgure 7. Computatonal doman sketch: vehcle-brdge system 3.3 Boundary condtons The nput boundary face s set as flow nlet wth a unform velocty of 10m/s, whch leads to a Reynolds number of n terms of the heght of the vehcle. The output boundary face s specfed as flow outlet wth zero pressure. The other boundares are all defned n such a way that the gradents of flow varables (ncludng velocty and pressure) normal to those boundary faces are zero. The surfaces of the vehcle and the brdge are all modeled as nonslp wall boundares. 3.4 Meshng The characterstc szes of components of the vehcle-deck-tower system vary from the sze of rals to the sze of tower greatly. The complex geometrc shape and the large varaton of characterstc sze lead to a complcated flow feld around the system n space. In order to obtan a relatve adequate spatal dscretzaton grd system correspondng to the ablty of the current usng PC, the grd optmzaton s acheved. Snce the smulaton wth the LES method s tmeconsumng for the flow around three-dmensonal complex geometrc body, steady RANS equatons enclosed wth SST two-equaton turbulence model are solved durng the process of grd optmzaton. 3.5 Computatonal scheme The LES governng equatons are dscretzed usng a three-dmensonal fnte volume method. The convectve and dffusve terms are approxmated by the bounded central dfferences of second-order accuracy and central dfference respectvely. The tme ntegraton s performed usng the second-order mplct method. Pressure and velocty are solved wth the SIMPLEC algorthm. 1723

6 4 SIMULATION RESULTS 4.1 Aerodynamc forces and coeffcents The numercal smulaton provdes the pressure dstrbuton over the surfaces of the vehcle. The aerodynamc forces actng on the vehcle can then be acqured by ntegratng the pressures over the surface. The aerodynamc forces and coeffcents dscussed below refer to the mean values. There are sx aerodynamc force components on the vehcle n the Cartesan coordnate system: lft force FL, drag force FD, sde force FS, ptchng moment MP, yawng moment MY and rollng moment MR, as shown n Fg.8. The non-dmensonal aerodynamc coeffcents are defned by C L FL = C qa ; D FD = C qa ; S FS = qa (8) M P M Y CP = ; CY = ; CR = qal qal M R qal (9) q 2 = 0.5ρU (10) where ρ s the ar densty; U represents the mean wnd speed at the nlet boundary of the computatonal doman; A s the frontal proect area of the vehcle wthout wheels and t refers to the proect area n the X-Y plane n ths study as shown n Fg.8; and L represents the maxmum length of the vehcle n the Z-Y plane as shown n Fg.8. The aerodynamc force coeffcents of the vehcle at dfferent postons are lsted n Table 1 for wnd perpendcular to the length of the vehcle. From the comparatve results of aerodynamc forces between the smulaton and the wnd tunnel texts, t can be seen that the smulated aerodynamc coeffcents agree well wth the experment n general. The smulated coeffcents demonstrate the same trend wth the change of the vehcle locaton as the wnd tunnel tests. The lft force coeffcents are senstve to the expermental condtons (Coleman & Baker 7 ) and the calculated lft force coeffcents are a slghtly larger than the test values for all three locatons. Compared wth the test results, the calculated sde force coeffcents are a slghtly larger whle the calculated ptchng moment coeffcents are lower than the test results. When the vehcle moves out of the sheldng area of the tower (from Xd1, Xd3 to Xd5), ts sde force, drag force, ptchng and rollng moment all ncrease whle ts lft force decreases. The yawng moment decreases frst and ncreases late. M Y FL Y Gravty Center X M R Z MP F S F D Fgure 8. Defntons of aerodynamc forces 1724

7 The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7) Shangha, Chna; September 2-6, 2012 Table 1. Aerodynamc Coeffcents of Vehcle Xd1 Xd3 Xd5 Experment LES Experment LES Experment LES C S C L C D C P C Y C R Flow felds The vsualzaton ablty of CFD smulaton s used here to analyze the flow felds around the vehcle. The nstantaneous flow structures n terms of vortcty magntude and the averagng flow structures n terms of proected streamlnes and velocty contours are ncluded. Sectons shown as 1-1 and 2-2 n Fg.1 are selected to present the characterstc flow structures around the vehcle. The nstantaneous contours of vortcty magntude around the vehcle at dfferent locatons from the tower n the selected sectons are shown n Fg.9, Fg.10 and Fg.11. Influenced by the tower, the flow envronment becomes more and more complex from Xd5 to Xd1. At Xd5, the vortex street n the wake of vehcle-deck s dsturbed slghtly by the tower. At Xd3, the vortex street n the wake of vehcle-deck s nterfered by the flow around the tower obvously. At Xd1, the selected vehcle secton s mmerged nto the flow regon of tower totally. (a) secton 1-1 (b) secton 2-2 Fgure 9. Contours of nstantaneous vortcty magntude for vehcle at Xd1 (unt: s-1) (a) secton 1-1 (b) secton 2-2 Fgure 10. Contours of nstantaneous vortcty magntude for vehcle at Xd3 (unt: s-1) 1725

8 (a) secton 1-1 (b) secton 2-2 Fgure 11. Contours of nstantaneous vortcty magntude for vehcle at Xd5 (unt: s-1) The averagng proected streamlnes and velocty contours of the vehcle at dfferent locatons are dsplayed n Fg.13, Fg.14 and Fg.15. Dfferent flow structures are formed. Flow separates at the upwnd tower leg. At Xd1, the vehcle s almost totally mmerged n the separatng wake of the upwnd tower leg whle the separated flow from the tower pushes on the tal part of the vehcle. The symmetrc flow feature around the tower s dsturbed slghtly by the vehcle. At Xd3, the accelerated flow around the upwnd tower leg pushes to the vehcle. The separated flow around the vehcle n Secton 1-1 reattaches to the brdge deck agan. At Xd5, the vehcle nearly gets rd of the mpact of the wake of the tower. The separated flow around the vehcle n Secton 1-1 does not reattach to the brdge deck. (a) secton 1-1 (b) secton 2-2 Fgure 12. Proected streamlnes and velocty contours for vehcle atxd1 (unt: m/s) (a) secton 1-1 (b) secton 2-2 Fgure 13. Proected streamlnes and velocty contours for vehcle at Xd3 (unt: m/s) 1726

9 The Seventh Internatonal Colloquum on Bluff Body Aerodynamcs and Applcatons (BBAA7) Shangha, Chna; September 2-6, 2012 (a) secton 1-1 (b) secton 2-2 Fgure 14. Proected streamlnes and velocty contours for vehcle at Xd5 (unt: m/s) 4.3 Surface pressure dstrbutons on vehcle The mean pressure dstrbutons over the surfaces of the vehcle under the three condtons are computed and dsplayed n Fg.16 for the case of wnd perpendcular to the vehcle. The flow acts on the upwnd sde surface of the vehcle drectly and some stagnaton areas are formed. All the surfaces except the upwnd one are n the flow separate regon of the vehcle wth negatve pressure due to the flow separatons around these surfaces. Compared wth Xd5, the stagnaton area for Xd3 moves to the head part whle the area for Xd1 focuses on the tal part of the vehcle. (a) vehcle at Xd5 (b) vehcle at Xd3 (c) vehcle at Xd1 Fgure 15. Mean pressure dstrbuton on vehcle (unt: Pa) 1727

10 5 CONCLUSIONS By usng large eddy smulaton method, the aerodynamc characterstcs of a vehcle across a brdge tower have been nvestgated. The smulated aerodynamc coeffcents agreewth the expermental results n general. The smulated coeffcents demonstrate the same trend wth the change of the vehcle locaton as the wnd tunnel tests. When the vehcle moves out of the sheldng area of the tower, ts sde force, drag force, ptchng and rollng moment ncrease whle ts lft force decreases. The yawng moment decreases frst and ncreases later. The nstantaneous contours of vortcty magntude show a complex flow envronment around the vehcle due to the tower. The averagng proected streamlnes and velocty contours show dfferent flow separaton phenomena around the vehcle at dfferent locatons. The flow acts on the upwnd sde surface of the vehcle drectly and some stagnaton areas are formed. All the surfaces except the upwnd one are n the flow separate regon of the vehcle wth negatve pressures. 6 ACKNOWLEDGEMENTS The authors wsh to acknowledge the fnancal supports from the Research Grants Councl of the Hong Kong (PolyU 5311/07E), The Hong Kong Polytechnc Unversty through a PhD studentshp, and the State Key Laboratory for Dsaster Reducton n Cvl Engneerng of Chna (2006-A-01). 7 REFERENCES 1 C. J. Baker, A smplfed analyss of varous types of wnd-nduced road vehcle accdents, J. Wnd Eng. Ind. Aerodyn, 22(1986) S. Charuvst, K. Kmura, Y. Funo, Expermental and sem-analytcal studes on the aerodynamc forces actng on a vehcle passng through the wake of a brdge tower n cross wnd, J. Wnd Eng. Ind. Aerodyn, 92(2004) T.Argentn et al., Cross-wnd effects on a vehcle crossng the wake of a brdge pylon, J. Wnd Eng. Ind. Aerodyn, 99(2011) Y. L. Xu, W. H. Guo, Dynamc analyss of coupled road vehcle and cable-stayed brdge systems under turbulent wnd, Eng. Struct, 25(2003) C. S. Ca, S. R. Chen, Framework of vehcle brdge wnd dynamc analyss, J. Wnd Eng. Ind. Aerodyn, 92(2004) S. R. Chen, J. Wu, Performance enhancement of brdge nfrastructure systems: Long-span brdge, movng trucks and wnd wth tuned mass dampers, Eng. Struct, 30(2008) S. Coleman, C. Baker, An expermental study of the aerodynamc behavour of hgh sded lorres n cross wnds, J. Wnd Eng. Ind. Aerodyn, 53(1994)