DETERMINATION OF AERODYNAMIC FORCES OVER TREE MODELS USING CFD AND PARALLEL PROCESSING TECHNIQUES

Transcription

1 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl DETERMINATION OF AERODYNAMIC FORCES OVER TREE MODELS USING CFD AND PARALLEL PROCESSING TECHNIQUES Alexandre Lus Braun, João Rcardo Masuero, Armando Mguel Awruch, Graduate Program n Cvl Engneerng (PPGEC) Federal Unversty of Ro Grande do Sul (UFRGS) Av. Osvaldo Aranha, nº 99, o andar, CEP 95-9, Porto Alegre/RS, Brasl Abstract. In the present work the evaluaton of aerodynamc forces actng on tree models s performed usng numercal smulatons based on the Fnte Element Method and parallel processng technques. Damages nduced by the wnd acton over trees n urban areas may lead to serous mplcatons, such as nterruptons n the energy supply and communcaton systems and rsk to the safety of pedestrans. The falure mechansm of trees under wnd acton s ususally assocated to breakage of the stem owng to excessve compresson, root pullout and overturnng due to excessve moments, whch may be also assocated to the mechancal behavor of the sol. Therefore, aerodynamc loads are a key parameter for determnng the occurrence of damages n trees. In the present paper, dealzed tree models are utlzed to determne aerodynamc coeffcents and flow felds around the tree locaton. The numercal model s based on the ncompressble flow approach usng the pseudo-compressblty hypothess. Turbulence s taken nto account consderng Large Eddy Smulaton (LES) wth the dynamc sub-grd model. The system of governng equatons s solved employng an explct two-step Taylor-Galerkn scheme, where spatal approxmatons are performed usng the Fnte Element Method (FEM) wth lnear hexahedral elements and one-pont quadrature. In order to solve the large system of equatons assocated to the flow problem effcently, parallel processng wth MPI mplementaton s adopted. Results obtaned wth the numercal smulatons carred out here are compared to expermental and numercal predctons presented by dfferent authors and the performance of the parallelzaton technques utlzed n the present work s also verfed. Keywords: Tree Aerodynamcs, Computatonal Flud Dynamcs (CFD), Large Eddy Smulaton (LES), Fnte Element Method (FEM), Parallel Processng.. INTRODUCTION Tree plantng s one of the most mportant human actons to mprove the urban envronment today. The nfluence of trees on the urban envronment s manly related to reducton of thermal effects through weakenng of radaton and the mpact of transpraton on the latent heat equlbrum (Lang et al., 6). In addton, trees alter sgnfcantly the ar flow n the street canyons of large ctes by reducng the flow velocty and ncreasng the turbulence level. In response to the wnd acton, trees adapt ther stem and roots n order to resst to overturnng moments, breakage of the stem or root pullout, whch may be also assocated to the mechancal behavor of the sol. Some of these falure mechansms may be nduced on the tree structure by strong wnds, leadng to serous mplcatons such as nterruptons n the energy supply and communcaton systems and rsk to the safety of pedestrans. Therefore, accurate reproducton of aerodynamc effects on trees s very sgnfcant for predctng wnd loads on buldngs and wnd envronment n urban areas. Wnd Engneerng s a tradtonal and well establshed research feld developed through extensve expermental tests performed over several structures and bodes submtted to the wnd acton, whch are characterzed wth devces specally desgned for wnd tunnel studes. Many advances and mprovements were obtaned wth aerodynamc and aeroelastc analyses carred out over cvl structures such as brdges and buldngs. In addton, wnd envronmental, pollutant and thermal condtons n urban areas have been also assessed by studyng representatve models n specalzed wnd tunnels. However, owng to advances observed n computers technology and numercal methods, expermental analyses n wnd tunnels have been gradually replaced by numercal smulatons performed wth numercal models based on Computatonal Wnd Engneerng (CWE), whch s a relatvely new branch of Computatonal Flud Dynamcs (CFD) adapted for specfc analyss n Wnd Engneerng. CWE nvolves some of the most challengng subjects on numercal nvestgaton appled to aerodynamc and aeroelastc phenomena: turbulence modelng, flud-structure nteracton, boundary layer flows ncludng separaton and reattachment and, consequently, dense fnte element meshes. Therefore, numercal analyss of trees under wnd acton can be also carred out usng CWE technques. Recent nvestgatons may be found, for nstance, n Lang et al. (6), Mochda et al. (8) and Endalew et al. (9). An mportant restrcton related to numercal analyss of -D flows usng the Fnte Element Method (FEM) s referred to the number of fnte elements utlzed by the spatal dscretzaton procedure (see a Braun and Awruch, 9). It s observed that some mllons of elements are usually needed n order to obtan a well defned mesh where the boundary layer and vortex tral regons can be adequately represented. Obvously, such a task can be only accomplshed employng dfferent approaches, ncludng hgh performance computatonal systems and specal programmng technques. Formerly, scalar seral codes used to be modfed by usng vectorzaton to run n supercomputers wth

2 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl vector processors and shared memory. However, supercomputers are very expensve and requre specal mantenance procedures. Therefore, ths opton has been replaced by an alternatve approach, where clusters of personal computers are utlzed wth hgh performance networks and parallelzaton technques. Parallelzaton s a programmng procedure where some statements are ncluded n the code n order to permt the problem to be solved wth several processors workng under parallel processng. A specal feature assocated to clusters of personal computers s concerned to the operaton and mantenance processes, whch are made wth very low costs when compared to other alternatves. A parallel program s generally wrtten usng some hgh level language such as Fortran, where parallelzaton lbrares are also ncluded n order to permt the processors to work synchronously. The most common APIs (Applcaton Programmng Interface) utlzed by a parallel code are OpenMP (Open Mult Processng) and MPI (Message Passng Interface). OpenMP lbrares are employed by parallel systems wth shared memory. On the other hand, MPI lbrares are usually ndcated for parallel processng wth dstrbuted memory (Masuero, 9). In the present work, the Naver-Stokes equatons and the mass conservaton equaton are solved usng an explct two-step Taylor-Galerkn model (see Kawahara and Hrano, 98; a Braun and Awruch, 9). The Fnte Element Method (FEM) s employed for spatal dscretzatons usng the eght-node hexahedrcal soparametrc element wth one-pont quadrature. Turbulent flows are analyzed usng LES wth the dynamc model for sub-grd scales (see Smagornsky, 96 and Llly, 99). Some smple tree models are nvestgated n order to determne aerodynamc coeffcents and flow felds around the tree locaton and the respectve results are compared wth numercal and expermental predctons performed by other authors. All smulatons are carred out usng a cluster wth 8 machnes featurng four core processors and dstrbuted memory archtecture. The numercal algorthm was wrtten employng the MPICH verson..5, whch s a MPI lbrary developed by Argonne Natonal Laboratory.. THE NUMERICAL MODEL In the Computatonal Wnd Engneerng practce, wnd flows are usually characterzed by adoptng the followng assumptons ( a Braun and Awruch, 9): ) Natural wnd streams are consdered to be wthn the ncompressble flow range; ) Wnd s always flowng wth a constant temperature (sothermal process); ) Gravty forces are neglected n the flud equlbrum; ) Ar s consdered as a Newtonan flud. Consderng the propertes presented above and n the absence of structural moton (aerodynamc analyss), the flow governng equaton are defned n a classcal Euleran knematcal descrpton by the followng expressons: a) Momentum balance equatons: v v p τ f + vj = + (, j =,,) n Ω () t xj ρ xj ρ xj b) Mass balance equaton for pseudo-compressble flows (see Braun and Awruch, 5 for further detals) the contnuty equaton: p p v j f + vj + ρc = ( j =,,) n Ω () t xj xj c) Consttutve equaton for Newtonan fluds: v v j vk σ = pδ + τ ; τ = µ + + λ δ (, j, k =,,) () xj x xk where v are components of the velocty vector n the drecton, x j are components of the Cartesan coordnates vector n the j drecton, t ndcates the tme doman, p s the thermodynamc pressure, ρ s the flud s specfc mass, c s the sound speed n the flud feld and Ω f Tf s the flow s spatal doman, whch s bounded by Γ, δ are components of the Kroenecker s delta ( δ = for = j; δ = for j ) and µ and λ are the dynamc and volumetrc vscostes of the Tf flud, respectvely. Neumann and Drchlet boundary condtons must be specfed on Γ to solve the flow problem, whch are gven by the followng expressons: v v = v ( =,,) on Γ () p p = p on Γ (5) p µ v v j λ v σ k nj σ δ nj = = S (, j, k =,,) on Γ (6) ρ ρ xj x ρ xk ρ v p where Γ (boundary wth prescrbed values v for the flud velocty feld), Γ (boundary wth prescrbed values p for the pressure feld) and Γ σ (boundary wth prescrbed values S for the flud boundary tractons) are complementary Tf Tf v p subsets of boundary Γ, such that Γ =Γ +Γ + Γ σ. In Eq. (6) n j are components of the unt normal vector n at

3 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl boundary Γ σ. Intal condtons for the pressure and velocty felds must be also specfed at t = to start up the flow analyss. Atmospherc boundary layer flows may be reproduced consderng the power law as nflow boundary condtons mposed on the velocty feld. The power law s usually descrbed as: p z U( z) = UH (7) H where U H s the reference wnd speed correspondng to the reference heght H, z s the heght coordnate and p s an emprcally derved coeffcent assocated to roughness characterstcs of the ground (see Smu and Scanlan, 996). In order to avod excessve computatonal efforts to descrbe the smaller turbulence scales, LES s adopted n the present work (see Mochda and Lun, 8 for detaled nformaton on turbulence modelng). Consequently, the governng equatons should be rewrtten as follows: v v p τ SGS f + vj = + + τ (, j =,,) n Ω (8) t xj ρ xj ρ x j p p v j f + vj + ρc = ( j =,,) n Ω (9) t xj xj SGS where τ are components of the Reynolds sub-grd stress tensor (whch s assocated to unsolved sub-grd terms that must be modeled) and overbars ndcate large scale varables. The Reynolds sub-grd tensor s usually approxmated accordng to the Boussnesq assumpton: SGS τ = ρ vv = µ S () ( ) j t where commas ndcate sub-grd scale varables, S are components of the large scale stran rate tensor and µ t s the eddy vscosty, whch s obtaned n ths work employng the dynamc sub-grd scale model (see Germano et al., 99 and Llly, 99) as shown below: µ t = ρc( x, t) S () where C( x, t) s the dynamc coeffcent (wth x and t ndcatng space and tme dependences), S s the fltered stran rate tensor modulus and s the characterstc dmenson of the grd flter, whch s assocated to element ele ele volumes n -D FEM formulatons ( = vol ). The dynamc coeffcent s updated along the tme ntegraton process takng nto account the nstantaneous condton of the flow feld (see a Braun and Awruch, 9 for addtonal nformaton). Aerodynamc forces are developed over the surface of structures mmersed n a flud stream. These forces are usually obtaned by ntegraton of pressures and shear stresses developed on the flud-structure nterface owng to the flow acton. The components of the aerodynamc forces n the along-flow and cross-flow drectons are referred to as drag and lft, respectvely. In the present work, the aerodynamc force and moment coeffcents are evaluated usng the formulae presented below: NNI NNI NNI ( Fx) ( Fy) ( Fz) C = ; C = ; C = V HW V HL V WL = = = Fx Fy Fz ρ ρ ρ NNI NNI NNI ( Fy x Fx y) ( Fz y Fy z) ( Fx z Fz x) = = = C Mz = ; C Mx = ; C My = () ρv HLW ρv HL ρv H W wth: =X -X ; =Y-Y ; =Z -Z () ( ) ( ) ( ) x g y g z g where X, Y and Z are Cartesan global coordnates of a nodal pont on the flud-structure nterface, X g, Y g and Z g are Cartesan global coordnates of a reference pont of the body, such as the gravty center, V s the flow reference speed, NNI s the number of flud nodal ponts on the body surface and L, W and H are characterstc dmensons related to length, wdth and heght of the mmersed body, respectvely. The aerodynamc forces F x, F y and F z at a nodal pont are obtaned by numercal ntegraton of Eq. (6) over the body surface. The explct two-step Taylor-Galerkn scheme s employed n ths work for the tme dscretzaton of the flow governng equatons. The fnal form of the numercal model s obtaned applyng the Bubnov-Galerkn s weghted resdual scheme nto the FEM context on the dscrete forms of the flow governng equatons. Eght-node hexahedral elements are used for spatal approxmatons employng the one-pont quadrature technque for the evaluaton of ()

4 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl element matrces. A complete descrpton of the numercal algorthm utlzed n ths work may be found n a Braun and Awruch (9) and b Braun and Awruch (9).. PARALLELIZATION METHODOLOGY The problem assocated to parallelzaton on dstrbuted memory may be summarzed to procedures related to work parttonng among the logcal processors nvolved. For fnte element models, the work parttonng procedure s based on the fnte element mesh, where parttons may be obtaned n terms of elements or nodal ponts. Parallel systems wth dstrbuted memory are usually characterzed by powerfull processors nterconected by logcal networks wth relatvely low frequences, where communcatons among processors are mnmzed by usng redundancy of work (Masuero, 9). Implementaton of numercal codes for parallel systems wth dstrbuted memory may be performed usng data transfer procedures wth or wthout redundancy. Redundancy s obtaned when the data assocated to each logcal processor of the parallel system are superposed, leadng to loss of effcency. For processes runnng on dstrbuted memory archtecture wth powerfull processors and relatvely low network devces, communcatons are usually mnmzed and redundacy s consequently ncreased. Snce fnte element models are usually mplemented employng element level quanttes, work parttonng based on nodes leads to redundancy, whch s related to elements presentng nodes assocated to dfferent logcal processors. A smple example s shown n Fg. a, where a mesh wth nodes and 5 elements s equally dvded nto two logcal processors (blue and yellow dots). Blue and yellow rectangles ndcate elements belongng to the respectve logcal processors utlzed here and grey rectangles ndcate common elements, whch are also referred to as ghost elements. Blue and yellow external lnes are showng the nodes needed by each logcal processor. By usng ths parttonng model, the logcal processors are responsble for elements, respectvely, where the frst logcal processor s related to the blue nodes ( to ) and the latter s related to the yellow nodes ( to ). Therefore, the parttonng effcency of the present example can be estmated consderng that each processor s responsble for elements, whch leads to the followng relaton between the number of elements observed n the entre mesh and the total number of elements assocated to the logcal processors: 5/ = 75%. Data referred to sx nodal ponts are requred by each logcal processor n ths case. (a) (b) Fgure. Parttonng models consderng two logcal processors and a fnte element mesh wth nodes and 5 elements: (a) nodal orderng follows horzontal lnes; (b) nodal orderng follows vertcal lnes. An alternatve to the parttonng scheme presented above s shown n Fg. b, where each logcal processor s assocated to 9 elements. The parttonng effcency corresponds now to the followng expresson: 5/8 = 8.%. Network communcatons are performed consderng the eght nodes assocated to the ghost elements. Nodal parttonng procedures may be also nterpreted as an operaton appled over the system of governng equatons, where the number of nodal varables belongng to the ghost elements s related to the bandwdth of the referred system. Consequently, the most effcent partton scheme s that where the bandwdth corresponds to the smaller value. Accordng to the work presented by Masuero (9), the parttonng procedure can be carred out employng two alternatves related to the bandwdth mnmzaton of the system of governng equatons: (a) nodal parttonng based on a sngle nodal reorderng performed wth a bandwdth mnmzaton algorthm; (b) nodal parttonng based on recursve nodal reorderng performed wth a bandwdth mnmzaton algorthm. In the frst approach, the fnte element mesh s prevously submtted to a sngle nodal reorderng, whch s obtaned consderng a bandwdth mnmzaton algorthm and nodal parttonng proportonal to the number of logcal processors utlzed n the parallel analyss. Ths methodology s very useful for problems characterzed by a reduced number of logcal processors and fnte element meshes presentng a predomnant coordnate drecton. Moreover, clusters consttuted by machnes wth multcore processor technology are also recommended, snce communcatons through the network nterface are only performed consderng one logcal processor per machne. The remanng logcal processors establsh communcaton through the local memory. The second approach s smlar to the RCB (Recursve Coordnate Bsecton) scheme presented by Fox et al. (99), where successve bsecton operatons based on geometrcal characterstcs of the fnte element mesh are adopted. However, the bsecton procedure s performed here consderng the bandwdth of the system of governng equatons n order to dentfy the bsecton drecton. The algorthm may be descrbed as follows: (a) a nodal reorderng s frst

5 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl performed over the orgnal fnte element mesh, whch s dvded nto groups of nodal ponts; (b) the same procedure descrbed n the frst step s performed over the ndvdual groups obtaned formerly; (c) the second step s repeated untl the number of groups obtaned be n accordance wth the number of logcal processors to be utlzed n the parallel analyss. An example s llustrated n Fgs. a and b, where the present method s appled consderng a smple fnte element mesh and two logcal processors. Ths methodology s recommended for stuatons where the number of logcal processors avalable s hgh. In ths case, the predomnant coordnate drecton of the fnte element mesh cannot be dentfed anymore after successve subdvsons of the orgnal mesh. (a) (b) Fgure. Nodal parttonng based on recursve nodal reorderng for two logcal processors: (a) frst step; (b) second step. Parallel processng on dstrbuted memory archtecture s carred out usng the network nterface for communcatons among the logcal processors. Ths aspect may lead to mportant losses for the parallelzaton effcency, where the relaton between the tme requred for data transferrng and the tme requred for data processng plays an mportant role. When the number of logcal processors adopted n a parallel analyss s relatvely hgh, communcaton orders must be establshed to avod losses of tme assocated to communcaton queues. Masuero (9) presented a communcaton scheme for a general stuaton where n logcal processors have to communcate wth the remanng logcal processors (or some of them), whch may be descrbed as follows: ) The logcal processors consdered n the parallel analyss are set n a rng arrangement; ) A matrx contanng communcaton steps for each logcal processor s obtaned consderng the followng expresson: j+ k + nt + l k = nt k INC = k( ) wth: (5) + l = mod where lne represents the communcaton step for a specfc logcal processor denoted by column j, nt s the nteger + result obtaned from the operaton and mod s the rest of that result. ) The present procedure begns by addng the values observed n the frst row of the matrx of communcaton steps to the number of ther respectve logcal processors, whch are dentfed from ther column postons. The communcaton s establshed wth that logcal processor whose number s obtaned from the prevous operaton. ) If exchange of data s not expected wth the logcal processor ndcated n the matrx of communcaton steps, the present logcal processor goes to the next communcaton step (next row n the matrx of communcaton steps). For a specfc communcaton step, each logcal processor may be executng a dfferent communcaton step (a dfferent row n the matrx of communcaton steps). 5) If a recprocal communcaton s not observed, the present logcal processor wats for the next recprocal communcaton. 6) If a recprocal communcaton s observed, communcaton s performed and every logcal processor goes to the next communcaton step. 7) The steps to 6 are repeated untl all logcal processors have completed ther n- communcaton steps. An example showng an arrangement wth 8 logcal processors communcatng each other s llustrated n Fg.. Contnuous lnes ndcate recprocal communcatons between logcal processors and dashed lnes stands for a logcal processor ntatng communcaton wthout recprocty, whch s dentfed by a dashed square. Logcal processors wth

6 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl all communcatons completed are represented by hexagons fulflled wth grey colour. Consderng that the number of mnmum communcaton steps for an deal arrangement wth n logcal processor s n-, the number of penalty communcatons s defned as the number of communcaton steps exceedng that mnmum value. In ths case, 8 communcaton steps and penalty step are observed. It s mportant to notce that communcatons are not generally performed among all logcal processors. Fgure. Communcaton steps consderng an arrangement wth 8 logcal processors communcatng each other. The cluster utlzed n ths work was mplemented usng personal computers wth Intel Core Quad 7 Mhz processors and 8 Gb RAM. Each ndvdual machne s connected to a Ggabt Ethernet / Mbps swtch. The opertonal system s Wndows XP Professonal. The present numercal code was wrtten utlzng the FORTRAN9 language and the Compaq Vsual Fortran Compler verson 6.6c wth the MPICH lbrary verson..5. The parallelzaton model adopted here s that where no master machne s employed, whch s also referred as to hostless program. Consequently, all logcal processors are runnng the same code and data are transferred among the logcal processors nvolved n the parallel analyss. In addton, each logcal processor can access all data on ther local hard dsc. The work charge for each logcal processor s defned consderng nodal parttonng and the number of logcal processors utlzed, where nodal reorderng based on bandwdth mnmzaton s also employed. Snce the same computatonal characterstcs are adopted by all nodes present n the cluster, the work s unformly dstrbuted. Further detals about parallelzaton procedures and the numercal algorthm utlzed n ths work may be found n Braun (7) and Masuero (9).. NUMERICAL SIMULATIONS Three smple models are adopted n ths work n order to nvestgate the wnd acton over trees. Although porosty should be consdered n the tree canopes owng to the folage, the present study neglects ths aspect. Consequently, the results obtaned here may be useful for tree speces wth dense folage or under extreme wnter condtons, where the tree canopes are usually covered wth snow. Fgure shows the fnte element meshes and some geometrcal propertes utlzed n the present smulatons. The physcal constants representng the flud and tme steps employed n the tme dscretzaton are shown n Table, leadng to a Reynolds number (Re = ρvd/µ) = 5 for all cases analyzed here. Velocty boundary condtons are mposed on the front wall of the computatonal domans n order to reproduce an atmospherc boundary layer flow on

7 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl the ncdent wnd, whch s consdered accordng to a velocty profle gven by the power law equaton for smooth flows, where velocty fluctuatons are dsregarded (see Eq. 7). In addton, non-slp condtons are mposed on the tree surfaces and on the ground. Symmetry boundary condtons are appled on the sde walls and constant pressure s consdered on the back walls. Model A Model B Model C Fgure. Fnte element meshes and geometrcal confguratons utlzed n the numercal smulatons. Table. Physcal constants and addtonal parameters adopted n the present smulatons. Parameter Model A B C Specfc mass (ρ) [Kg/m ] Dynamc vscosty (µ) [N.s/m ] 6.7x - x - x - Characterstc dmenson (D) [m]... Characterstc wnd speed (V) [m/s] Model heght (h) [m] Reference Heght (H) [m] Reference wnd speed (U H ) [m/s]... Exponent p (see Eq. 7)... Tme step ( t) [s] 5x -5.5x -5 x -5 Tme hstores of some of the aerodynamc coeffcents measured durng the present smulatons are shown n Fg. 5. Comparsons are then performed n Table, where tme-average drag values calculated from the results presented n Fg. 5 are lsted together wth expermental and numercal predctons obtaned by other authors. The results obtaned wth the numercal model proposed n ths work agree reasonably wth those obtaned by the remanng references. It s mportant to notce that the present results are observed n the range of values presented by Mayhead (97), who carred out extensve expermental analyses over several tree models. CFx CFy Model A Model A CFx CFy Model B Model B CFx Model C CFy Model C

8 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl CMy Model A CMy Model B CMy Model C Fgure 5. Aerodynamc coeffcent records obtaned durng the numercal smulatons. Table. Drag coeffcents for tree models. Source Drag coeffcent Present work Model A. Present work Model B. Present work Model C.55 Mayhead (97) varous models.7.56 Kozum () varous models.7. Gardner et al () smlar to Model B.9 Yoshda et al. (6) smlar to Model A. In order to evaluate the flow characterstcs near the model regon, tme-average velocty profles along the center lne of the computatonal doman are shown n Fg. 6. Results obtaned here are presented n the longtudnal drecton, whch s parallel to the wnd stream. Every profle poston s referred to the tree poston by usng the relatve coordnate x/h, where h s the model heght (see Table ). In addton, tme-average pressure felds obtaned wth the present numercal model are also shown n Fg. 7, whch are represented on the symmetry plane of the computatonal doman..5 x/h = -.5 x/h = x/h =.5.5 x/h = v/v x/h = v/v x/h = v/v x/h = v/v x/h = v/v.5.5 v/v.5.5 v/v.5.5 v/v Fgure 6. Velocty profles obtaned at dfferent postons along the center lne of the computatonal doman.

9 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl Fgure 7. Tme-average pressure felds obtaned on the symmetry plane of the computatonal doman. The wnd envronmental condtons around the tree models may be evaluated from Fg. 8, where nstantaneous streamlnes obtaned at t = s are shown. It s observed that the present formulaton was able to reproduce most of the crculaton patterns typcally developed n the surroundngs of bluff bodes mmersed n wnd streams wth atmospherc boundary layer characterstcs. Aerodynamc phenomena such as recrculaton zones behnd and n front of the bodes and separaton/attachment zones were reproduced n accordance wth expermental observatons (see Smu and Scanlan, 996). Fgure 8. Instantaneous streamlnes obtaned at t = s. The computatonal performance of the parallelzaton scheme adopted n ths work may be verfed usng some parameters such as Speed-up (Sp) and Effcency (Ep), whch s evaluated as functon of the number of logcal processors (p) and number of fnte elements. In Fg. 9, the Speed-up and Effcency curves obtaned n ths study are presented. Speed-up (Sp) Ideal speed-up Model A Model B Model C Number of logcal processors (p) Effcency (Ep) Model A Model B Model C Number of logcal processors (p) Effcency (Ep) A 6 Logcal processors: 8 A.E+5 6.E+5 9.E+5 Number of fnte elements Fgure 9. Computatonal performance obtaned by the parallelzaton scheme utlzed n ths work. Speed-up: Sp = T /T p, T executon tme correspondng to the sequental algorthm; T P executon tme correspondng to the parallel algorthm wth p logcal processors; Effcency: Ep = Sp/p. A A

10 Proceedngs of COBEM Copyrght by ABCM st Brazlan Congress of Mechancal Engneerng October -8,, Natal, RN, Brazl 5. CONCLUSIONS In the present work, numercal smulatons to nvestgate the wnd acton over tree models were carred out usng a numercal model to analyze wnd engneerng problems. A parallelzaton methodology was also ntroduced n order to mprove the algorthm performance for applcatons characterzed by dense fnte element meshes. The results obtaned here demonstrate that the present model can be appled to tree aerodynamcs, although some addtonal features must be mplemented n the numercal code to take nto account mportant aspects assocated to porosty of the tree canopy. Moreover, the parallelzaton methodology utlzed n ths work reduced sgnfcantly the executon tme requred by the sequental algorthm. Nevertheless, Speed-up (Sp) and Effcency (Ep) evaluatons performed here ndcate that some modfcatons are necessary to mprove the computatonal performance when a large number of logcal processors are employed n the parallel analyss. 6. ACKNOWLEDGEMENTS The authors wsh to thank CNPq (Brazlan councl of research) for the fnancal support. 7. REFERENCES Braun, A.L., 7, Smulação Numérca na Engenhara do Vento Inclundo Efetos de Interação Fludo-Estrutura, Tese de Doutorado PPGEC/UFRGS, Porto Alegre, Brasl. Braun, A.L. and Awruch, A.M., 5, Aerodynamc and aeroelastc analyss of bundled cables by numercal smulaton, Journal of Sound and Vbraton, Vol. 8, pp a Braun, A.L. and Awruch, A.M., 9. Aerodynamc and aeroelastc analyses on the CAARC standard tall buldng model usng numercal smulaton, Computers and Structures, Vol. 87, pp b Braun, A.L. and Awruch, A.M., 9. A parttoned model for flud-structure nteracton problems usng hexahedral fnte elements wth one-pont quadrature, Internatonal Journal for Numercal Methods n Engneerng, Vol. 79, pp Endalew, A.M., Hertog, M., Delele, M.A., Baetens, K., Persoons, T., Baelmans, M., Ramon, H., Ncolaï, B.M. and Verboven, P., 9. CFD modellng and wnd tunnel valdaton of arflow through plant canopes usng D canopy archtecture, Internatonal Journal of Heat and Flud Flow, Vol., pp Fox, G.C., Wllams, R.D. and Messna, P.C., 99, Parallel Computng Works, Morgan Kaufmann Publshers, San Francsco, USA. Gardner, B., Peltola, H. and Kellomäk, S.,, Comparson of two models for predctng the crtcal wnd speeds requred to damage conferous trees, Ecologcal Modellng, Vol. 9, pp. -. Germano, M., Pomell, U., Mon, P. and Cabot, W.H., 99, A dynamc subgrd-scale eddy vscosty model, Physcs of Fluds, Vol. A, No. 7, pp Kawahara, M. and Hrano, H., 98, A fnte element method for hgh Reynolds number vscous flud flow usng two step explct scheme, Internatonal Journal for Numercal Methods n Fluds, Vol., pp Kozum, A., Motoyama, J. and Sawata, K.,, Evaluaton of drag coeffcents of poplar-tree crowns by a feld test method, Journal of Wood Scence, Vol. 56, pp Lang, L., Xaofeng, L., Borong, L. and Yngxn, Z., 6. Improved k-ε two-equaton turbulence model for canopy flow, Atmospherc Envronment, Vol., pp Llly, D.K., 99, A proposed modfcaton of the Germano subgrd-scale closure method, Physcs of Fluds, Vol. A, No., pp Masuero, J.R., 9, Computação Paralela na Análse de Problemas de Engenhara Utlzando o Método dos Elementos Fntos, Tese de Doutorado PPGEC/UFRGS, Porto Alegre, Brasl. Mayhead, G.J., 97, Some drag coeffcents for Brtsh forest trees derved from wnd tunnel studes, Agrcultural Meteorology, Vol., pp. -. Mochda, A. and Lun, I.Y.F., 8. Predcton of wnd envronment and thermal comfort at pedestran level n urban area, Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 96, pp Mochda, A. and Tabata, Y., Iwata, T. and Yoshno, H., 8. Examnng tree canopy models for CFD predcton of wnd envronment at pedestran level, Journal of Wnd Engneerng and Industral Aerodynamcs, Vol. 96, pp Smu, E. and Scanlan, R., 996, Wnd Effects on Structures, Wley, New York, USA. Smagornsky, J., 96, General crculaton experments wth the prmtve equatons, I, the basc experment, Monthly Weather Revew, Vol. 9, pp Yoshda, S., Ooka, R., Mochda, A., Murakam, S. and Tomnaga, Y., 6, Development of the three dmensonal plant canopy model for numercal smulaton of outdoor thermal envronmental, In: proceedng of the ICUC6, Sweeden. 8. RESPONSIBILITY NOTICE The authors are the only responsble for the prnted materal ncluded n ths paper.