Detached Eddy Simulation of Atmospheric Flow About a Surface Mounted Cube at High Reynolds Number

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1 Sue Ellen Haupt 1 haupts2@asme.og Fank J. Zajaczkowski fxz101@psu.edu L. Joel Peltie 2 ljpeltie@bechtel.com Applied Reseach Laboatoy, The Pennsylvania State Univesity, P.O. Box 30, State College, PA Detached Eddy Simulation of Atmospheic Flow About a Suface Mounted Cube at High Reynolds Numbe Modeling high Reynolds numbe (Re) flow is impotant fo undestanding wind loading on stuctues, tanspot and dispesion of aibone contaminants, and tubulence pattens in uban aeas. This study epots a high fidelity computational fluid dynamics simulation of flow about a suface mounted cube fo a Reynolds numbe sufficiently high to epesent atmospheic flow conditions. Results fom detached eddy simulations (DES) and zonal DES that compae well with field expeiment data ae pesented. A study of educing gid esolution indicates that futhe gid efinement would not make a significant diffeence in the flow field, adding confidence in the accuacy of the esults. We additionally conside what featues ae captued by coase gids. The conclusion is that these methods can poduce high fidelity simulations of high Reynolds numbe atmospheic flow conditions with a modest gid esolution. DOI: / Intoduction Flow about a suface mounted blunt body has been a classic testbed fo computational fluid dynamics CFD 1 9. It demonstates sepaation, votex shedding, and stationay votical stuctues, all of which ae difficult to model well. Thee has been ecent inteest in pushing such CFD computations to highe Reynold s numbes Re that moe closely match atmospheic flows fo studies involving wind loading on stuctues, dispesion of contaminant aound buildings, and chaacteizing flow in an uban envionment 7. To that end, this study stives to caefully model flow at atmospheic Re using high fidelity, but eadily achievable, gid esolution and state-of-the-at techniques and then to systematically elax the gid and modeling assumptions to chaacteize the fidelity necessay to epoduce cetain featues of the high Re flow. This infomation is valuable since moden atmospheic simulations often equie modeling multiple buildings in close poximity in uban aeas. It is useful to detemine which featues equie a vey fine gid esolution and which will be captued with a coase gid. The case of a suface mounted squae cylinde at lowe Re has been widely studied. Seveal expeimental studies, in paticula, ae impotant fo veifying numeical simulation esults. One physical modeling study widely used fo the validation of numeical esults is the expeimental chaacteization of thee dimensional flow aound suface mounted pismatic obstacles pefomed by Matinuzzi and Topea 10. They investigated flow aound obstacles in both wate and ai channels. Static pessue measuements, lase light sheet, oil film, and cystal violet visualization techniques wee used to ecod esults. Compaison CFD studies showed the ability of Reynolds aveaged Navie Stokes RANS models to match the majo featues Although those studies wee impotant steps towad simulating the details of flow featues at high Re, they ae insufficient fo ealistic atmospheic 1 Pesent addess: National Cente fo Atmospheic Reseach/Reseach Applications Laboatoy, Boulde, CO. 2 Pesent addess: Bechtel Copoation, Fedeick, MD. Contibuted by the Fluids Engineeing Division of ASME fo publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscipt eceived Decembe 22, 2006; final manuscipt eceived July 10, 2010; published online Mach 15, Assoc. Edito: Rajat Mittal. conditions because those expeiments wee pefomed fo fully developed channel flow at lowe Reynolds numbes Re= and Richads et al investigated full scale, high Reynolds numbe Re= flow aound a6mcube at the Silsoe Reseach Institute, poducing pessue data fo steamwise and cosssteam centelines aound the cube. Futhe investigation poduced unsteady flow velocity data along the sides of the cube 16. These studies povided the case examined in the pesent pape and ae efeed to as the full scale and field measuement data thoughout the emainde of this pape. Peviously, Wight and Easom 19 used the Silsoe case fo a RANS simulation using a nonlinea k- tubulence model. They wee able to epoduce the pessue distibution on the windwad face of the cube but had difficulty on the top, side, and leewad faces. It was detemined that isotopic tubulence models wee inadequate in this case. Some of the pevious RANS CFD modeling esults compaing the Silsoe field expeiments to RANS simulations ae summaized by Richads et al. 20. Those computational solutions wee geneated as pat of the Computational Wind Engineeing CWE 2000 Confeence Competition. Hee, we wish to detemine whethe detached eddy simulation DES appoaches can impove on those RANS appoaches. Ou CFD methodology, including gid and model details, is explained in Sec. 2. The esults ae descibed, compaed with the full scale field data of Richads et al. 14, and evaluated fo gid independence in Sec. 3. Section 4 contains a discussion of the esults and suggestions fo futhe eseach. 2 CFD Methodology The expeiments pefomed by Richads et al ae modeled hee with CFD using both the standad DES methodology with a Spalat Allmaas SA tubulence model 21 and a ecently poposed modification known as zonal DES ZDES 22. The computational domain, shown in Fig. 1, featues a6msu- face mounted cube situated within a domain that is 100 m high. This domain height accommodates the expeimentally measued atmospheic bounday laye ABL pofile descibed in detail by Richads et al ACUSOLVE. We use the commecial flow code, ACUSO- LVE, as ou computational engine. This solve is an incompess- Jounal of Fluids Engineeing Copyight 2011 by ASME MARCH 2011, Vol. 133 /

2 and the functional elationship of T to is f v1 = c, f v2 =1, v1 1+ f v1 3 f w = g 1+c 6 1/6 w3 g c w3 ible finite element code that offes seveal tubulence modeling options 23. ACUSOLVE allows vaious implementations and the ability to customize the modeling stategy. It is based on the standad Navie Stokes equations as epoted in detail by Lyons et al. 24. The filteed equations can be witten as ũ i t + ũ ũ i j = 1 p + 2 ũ i ij x i x j ũ i x i =0 whee the oveset tilde denotes a full vaiable, ũ i, one that has both a statistical mean value, U i, and a fluctuating component, u i :ũ i =U i +u i, and whee the filteed / esolved vaiables supescipt, ũ i and p ae computed and the effects of the subfilte motions supescipt s, u i s on the esolved field ae collected in the subfilte stess, ij, ij u i u j s +u i s u j +u i s u j s + u i u j u i u j. Intoducing an eddy-diffusion closue fo the subfilte stess, followed by collecting tems, yields ũ i t Fig. 1 Computational domain + ũ ũ i j = 1 p +2 + T S ij x i whee T, the eddy diffusivity, must be modeled and S ij = 1/2 ũ i / + ũ j / x i is the stain ate tenso. Ou RANS closue is the SA one-equation tubulence model 21. The SA model elates the eddy diffusivity, T, to a computed diffusivity,, that satisfies the tanspot equation, t + U j = c b1 S c w1 f w d x k x k + c b2 4a x k x k whee d is the distance to the neaest no-slip suface. The model constants ae T = f v1 whee =, g = + c w2 6, = 2 S d S = 2 ij ij, S = S + d 2 f v2, ij = 1 2 U i U j x i 4c The SA model diagnoses the time scale of the tubulence fom the mean field voticity and chooses the chaacteistic length as the maximum distance to the wall. The model constants and functions ae tuned to the data. 2.2 DES. Fo the pesent study, we use the DES subgid model to compute the flow. DES is a hybid statistical/eddyesolving technique that hanesses the fidelity of lage eddy simulation LES in egions of massive sepaation, like the sepaated flow downsteam of the cube, while etaining much of the computational efficiency of RANS nea boundaies and away fom egions of inteest. DES disciminates the LES and RANS egions by choosing a chaacteistic model length scale, d, that is smalle than the chaacteistic gid scale, C DES, and the local RANS length scale, d, d min d,cdes 5 whee C DES is an adjustable constant and max x, y, z. When d, the DES subgid model becomes a Smagoinskytype LES. Likewise, when d, the model emains RANS. Othewise, the DES model blends the RANS and LES behavios. Stelets 25 descibed how DES can be implemented fo an abitay tubulence model and povided examples showing impoved tubulence statistics ove RANS pedictions in egions of massive sepaation. ACUSOLVE implements the one-equation Spalat Allmaas tubulence model with cuvatue coections in its RANS mode. Its DES implementation, theefoe, follows the oiginal pesciption Zonal DES. In addition to the standad DES technique, a modification known as ZDES 25 is implemented in ode to impove the ageement with the measuements. This zonal appoach adds a disciminato function,, designed to etain RANS modeling in bounday layes egadless of the local gid density. The modification is implemented to coect an obseved deficiency of DES that it is allowed to tansition fom RANS to LES in bounday layes, losing the statistical effect of tubulence stesses without developing esolved tubulence stesses to compensate. Mente et al. 13 descibed this abeation as gidinduced sepaation. Theefoe, it is necessay to foce the use of RANS in the attached egions of the flow. Specifically, we define a disciminato function,, which is used in a black/white fom, =min 1 2 d C d2 a 1 k 500 1/2, 6a 1 identifies bounday layes. The model constants, a 1 and C, ae c b1 = , c b2 = 0.622, c v1 = 7.1, = 2 3 c w1 = c b c b2, c w2 = 0.3, c w3 =2, = b a 1 = 0.31, C = b Access to the tubulent kinetic enegy, k, is equied to compute fo Eq. 6a. Howeve, k is not a vaiable diectly available fom the Spalat Allmaas model. Slimon 22 deduced k fom the stain ate and eddy diffusivity, / Vol. 133, MARCH 2011 Tansactions of the ASME

3 Table 1 Gid details BASE BASE/2 BASE/4 BASE/8 Total no. of elements 3,387, , ,709 66,666 Nea-wall spacing, m Total no. of pism layes Maximum element: suface, m Maximum element: cube sides, m Maximum element: cube top, m Maximum element: density egion, m Gowth atio No. of pocessos Fig. 2 Computational mesh fo the BASE case uns. a Top view showing the efinement egion, b side view though the cube, and c close-up of the side view indicating the pism layes nea the wall. k max T a 1 S,k 0 6c whee k 0 is a feesteam value and S 2S ij S ij 1/2. Slimon 22 also epoted that numeical expeiments showed that best esults wee obtained when f v1 = f w =1 and f v2 =0, values also adopted hee. ZDES edefines d such that d = d fo 1 7 min d,c DES fo 1 The method shaply delineates RANS and LES egions but ensues a continuous, smooth solution acoss the ZDES inteface. Thus, DES is active only fo geate than 1. In this sense, the algoithm is zonal. Othewise, the govening equations ae continuous thoughout the flow. The ZDES algoithm was descibed in detail by Slimon Gids. The base case gid BASE is a high esolution, hybid tetahedal-pism gid. The unstuctued tetahedal-pism mesh was geneated with ANSYS ICEM CFD. Pism layes wee extuded fom solid walls to povide bette modeling of nea-wall physics than tetahedons. A nea-wall spacing of m about 300 wall units was used in gid constuction, and a gid expansion ate of 1.2 was enfoced in the wall nomal diection, yielding a total of 22 pism layes. Tetahedal elements suound the pism layes. The size of the elements is limited to no lage than 0.85 m in the density egion suounding the cube. The fa field elements ae allowed to gow to a maximum of 2.35 m. This high esolution BASE gid contains elements. Figue 2 displays the gid. A top view Fig. 2 a indicates a efinement egion suounding the cube. A side view Fig. 2 b shows a cut plane though the cente of the cube, and a blow-up Fig. 2 c indicates the efinement of the pism layes. Thee pogessively coase gids wee geneated to pefom a gid study and ae one-half, one-quate, and one-eighth the linea esolution of the base case, espectively. Cae was taken to maintain consistency in gid quality acoss seveal esolutions. Ou goal is to detemine what featues become unde-epesented with gid coasening. Fo the emainde of this pape, these gids will be efeed to as BASE, BASE/2, BASE/4, and BASE/8. Table 1 compaes the details of each. Finally, an extemely fine nea-wall gid, beginning at one wall unit fom the cube, was constucted to study the effect of a vey fine esolution. We found that thee was no impovement with such fine esolution. We believe that this obsevation is due to the fact that wall functions ae employed, which smoothly tansition fom the tubulent egion above to the viscous sublaye. Since these functions act to poduce a smooth vetical velocity pofile, a fine esolution is not helpful, and those esults ae not shown explicitly hee. 2.5 Bounday Conditions and Implementation. Inflow conditions wee extacted fom the Silsoe full scale expeimental data. Pofiles of the inflow velocity and eddy viscosity ae shown in Fig. 3. The eddy viscosity was diagnosed fom the measued tubulence intensities and length scales 15. Thus, both velocity and tubulence pofiles ae matched to the full scale data. In the expeimental case, a efeence velocity at a cube height was found to be 10 m/s. The Reynolds numbe based on this efeence and the cube height is Re= An exit condition is used at the downsteam bounday that allows votical stuctues to advect out of the domain without unphysical pessue eflections. Symmety conditions ae imposed on the uppe and side boundaies. Fig. 3 Inflow conditions fom expeiment Jounal of Fluids Engineeing MARCH 2011, Vol. 133 /

4 Fig. 4 Time aveaged hoizontal steamlines nea bottom wall fo BASE DES case as viewed fom above Fig. 6 Q-citeia isosuface coloed by helicity The ACUSOLVE model with DES implemented was un in unsteady mode. Selecting a time step of 0.1 s gives a maximum Couant Fiedichs Lewy CFL numbe of 1 in the wake fo the BASE gid. The BASE model was un fo ove 8000 time steps. The fist 1400 steps ae discaded fom the analysis. To deive pessue coefficients, we select pessue pofiles along the steamwise and coss-steam lines coesponding to the same distances measued in the Silsoe full scale field expeiments. Such pofiles ae deived at 1000 step intevals and aveaged fo inclusion in the plots pesented below. 3 The DES Solutions 3.1 Qualitative Desciption. We fist descibe ou time aveaged esults fom the high esolution DES BASE case and then compae the pessue and velocity pofiles to the full scale expeimental data and the CWE 2000 Competition RANS simulations 20 fo model validation. The BASE case aveaging peiod is 7 min and omits a nonconveged spin-up peiod of 1400 time steps, equivalent to 140 s. Time aveaged steamlines fom the BASE DES case ae shown, looking down fom above on a slice nea the suface Fig. 4 and along the vetical cente plane of the cube Fig. 5. These esults display the symmety expected of a conveged time aveaged solution and captue the same obseved flow featues obtained via time aveaged LES esults at lowe Re descibed by Fezige and Peic 26. Incoming flow eaches a stagnation point nea the gound upsteam fom the cube and flows aound the sides of the cube, as seen in ou DES simulation in Fig. 4. Futhe above the gound, the flow impinges on the font face of the cube and sepaates, and some of it descends into a egion of evesed flow. Figue 5 shows the stagnation point above the halfway point in ageement with the full scale Silsoe field measuements. Just upsteam fom the font face of the cube and along the lowe suface, thee is a sepaation zone, which is the head of a hoseshoe votex. This hoseshoe votex extends along the sides of the cube, as is evident in both Figs. 4 and 5. The top view Fig. 4 shows the hoseshoe votex in oughly the coect location. It shows up as a votex eciculation zone in Fig. 5. Of paticula note fo the pesent esults is the lack of eattachment fo the eciculation zone along the top face. While this agees with lowe Fig. 5 Time aveaged steamlines along a vetical slice though the centeline fo BASE DES case Re LES esults 11, it does not match the full scale esults, which do eattach. A single step of the tansient solution is shown in Fig. 6. This figue plots the Q-citeion as a way to visualize cuvatue in the flow. The Q-citeion is defined by 27 as U i = 1 2 U i + U i U i U i = S ij + ij Q = ij ij S ij S ij Hee, U i / is the gadient of the ith velocity component in the j-coodinate diection, whee i and j ange fom 1 to 3. S ij is the stain tenso and ij denotes voticity. Q is the computed value of the Q-citeion, which is meant to help identify tubulent featues. The hoseshoe votex is the dominant featue in Fig. 6, beginning upsteam of the cube and extending aound the cube. The tubulent featues fom in the sepaation egions and extend into the wake. 3.2 Impact of Gid Resolution. We investigate gid dependence by unning the DES simulation on each of the fou gids descibed in Sec. 2 and detailed in Table 1. In addition, we wish to assess which featues ae lost as the gid coasens. Ou ationale is based on the fact that fo vaious moden applications, such as tanspot and dispesion o wind loading in uban aeas, one must compute flow aound multiple buildings in an aea, pecluding high esolution aound each of the stuctues. Thus, it is useful to assess which featues ae maintained in the coasening and which may be lost. The following discussion details the changes in featues, and in paticula, the coefficient of pessue, between the diffeing esolutions as well as with the Silsoe full scale field data. Figue 7 compaes the coefficient of pessue Cp between the coasened gids to the BASE case, both ove the top and cosssteam of the cube Fig. 7 a and along steam of the cube Fig. 7 b. Ove the top of the cube, none of the esolutions of DES sufficiently captue the pessue dop. In geneal, the BASE/2 povides simila esults to the BASE case. In fact, ove the top of the cube Fig. 7 a, the pessue dop seen using the BASE/2 gid actually agees bette with the full scale field data than the BASE gid simulations, although it is too low on the sides. Along steam, howeve, the BASE/2 gid poduces pessue pofiles quite close to those of the BASE gid although neithe pofile dops as deep in the lee of the cube as the full scale field measuements. We suspect that stochastic aveaging issues impact these esults. One must be caeful in intepeting these pofiles they ae not steady state values but athe epesent an aveage ove selected times in an unsteady simulation. The BASE/4 esults show a sudden dop in accuacy in both plots. Values acoss the top face lose the pessue dop in the votex as the gid esolution is elaxed, but the pofile maintains the same basic shape as the highe esolution DES uns. Along the sides, howeve, the solution exhibits the apid dip nea the windwad face chaacteistic of RANS esults shown below. Likewise, the BASE/8 esults fail to captue the pessue dops on both / Vol. 133, MARCH 2011 Tansactions of the ASME

5 Fig. 7 Coefficient of pessue pofiles at diffeent gid esolutions the side and top faces. Oveall accuacy declines eveywhee, and even the windwad face is no longe well matched Fig. 7 b. Theefoe, we conclude that the gid spacing of BASE/2 is sufficient to geneate high fidelity Cp pofiles. Fo a good match of Cp to the field test data, the coase BASE/4 and BASE/8 ae not adequate since they do not show the expected pessue dops obseved in the cente of the votices. We also compaed the velocities at the points monitoed in the full scale field test data. The esults confim ou conclusions above and ae not shown hee. Once again, the BASE/2 solution comes close to matching the velocity values of the BASE case. The coase BASE/4 and BASE/8 cases, howeve, in the egions closest to the cube whee the flow is iegula and detached vay significantly fom the fine esolutions. Fo these egions, the fine esolution of the BASE/2 gid is necessay to get close matches to the field test data. The poximity of the BASE/2 solution to the BASE solution povides confidence that the gid esolution is adequate to povide a high fidelity solution. The DES solution alone, howeve, does not show a sufficient pessue dop in the cente of the cube. Thus, ZDES esults ae included in the esults discussed below. 3.3 Compaison to Full Scale Silsoe Field Data and Pio RANS Simulations. Figue 8 compaes pessue coefficient Cp esults fo the high esolution BASE case DES and ZDES uns to the full scale expeimental field data taken at Silsoe and to the CWE 2000 Competition RANS esults epoted in Richads et al. 20. The RANS esults include a standad k- tubulence model 28,29 and two k- modifications, MMK and enomalized goup RNG theoy based on the models developed by Tsuchiya et al. 4 and Yakhot and Oszag 30 espectively. Figue 8 a shows Cp pofiles along a steamwise vetical centeline that moves up the windwad face of the cube, along the top face, and down the leewad face. Geneally, the compaison indicates that all models match the windwad face easonably well. Standad k- pedicts pessues that ae too low on the font of the top face and pematue eattachment. The RNG modification impoves the pofile but undepedicts the pessue dop in the votex along the entie top face, while MMK fails to captue the low pessue ove the top. Ou DES simulation, although pefoming bette than MMK, also exhibits a elatively flat pofile, esulting fom an ovesized and slow eciculation zone. The ZDES implementation, howeve, shows impoved ageement with the expeimental data, paticulaly along the top face. It captues the eattachment much bette than standad DES o k- models. Figue 8 b displays vetical tansvese Cp plots that move up the cente of one side of the cube, acoss the top in the cosssteam diection, and down the othe side, as indicated in the inset. The field expeimental data exhibit minimum pessue in the cen- Jounal of Fluids Engineeing MARCH 2011, Vol. 133 /

6 Fig. 8 Coefficient of pessue pofiles compaing DES and ZDES to full scale and RANS. a Along the centeline of the cube, b along the tansvese line of the cube, and c along the hoizontal mid-height line of the cube. te of the cube. The RANS solutions, as expected fom the steamwise plots, undepedict the pessue dop acoss the top face. Additionally, the Cp values moving up the side faces incease fo all of the RANS cases, while they decease fo the field study data. Ou DES simulation povides compaable and deceasing Cp values along each face. The magnitude of these pessues is close to expeimental values despite being steadie than the expeimental values. On the top face cente of the plot, ZDES shows significant impovement ove the othe simulation methods, epoducing the expeiment s dop in pessue towad the cente of the face. The low pessue zone is too small, howeve, and on the sides of the cube, ZDES pedicts too sevee of a pessue dop. It also shows an anomalous ise in pessue at the top edge simila to the RNG and RANS simulations, but moe ponounced hee. Fig. 9 Velocities at selected positions/heights compaing DES to full scale and RANS. Locations 1, 2, and 3 ae 600 mm away fom the centes of the windwad, side, and leewad faces, espectively, and include measuements at heights of 1 m, 3 m, and 6 m. Locations 5, 6, and 7 ae positioned 9 m away fom the same faces and include measuements at the same heights. Location 4 is 600 mm above the top face of the cube with measuements at the cente of the face, 2 m upsteam, and 2 m downsteam of the cente. a, b, and c indicate u/uef, v/uef, and w/uef, espectively. Figue 8 c is a set of Cp plots along a mid-height hoizontal line that moves along the windwad face, back one side, and halfway along the leewad face see inset. Hee, all simulations do a easonable job at pedicting along the windwad and leewad faces. On the side face, the RNG model pefoms the best. DES esults continue to poduce a steady and flat pofile. The ZDES cuve once again shows disageement along the side. An explanation fo this disageement will be poposed late by consideing the velocities along the side of the cube. Figue 9 displays measued velocity values fom seven points aound the cube at thee heights each and compaes ou BASE / Vol. 133, MARCH 2011 Tansactions of the ASME

7 Table 2 Reattachment and stagnation lengths Fom cube cente Full scale RNG MMK K-E DES ZDES Wake u=0 at x=0.01 h Top face u=0 at x=0.01 h None None 0.18 Font face stagnation Upsteam stagnation DES and ZDES esults to the full scale data and the thee RANS esults. At the windwad locations 1 and 5, all of the models match the Silsoe field test data favoably. In the wake 3 and 7, both DES and ZDES pefom well at 1mand3m.At6m,the DES u-velocity is too slow, while ZDES matches the Silsoe expeimental data quite well. On the top of the cube point 4, DES pedicts evesed velocities at the cente and downsteam positions, suppoting the obsevation that it was not able to poduce a eattachment ove the cube top. Futhe, the velocity magnitudes ae elatively small, which is consistent with a lage eciculation zone. The ZDES poduces velocities ove the cube that compae favoably with the field measuements. Recall, howeve, that the Cp pofiles poduced by the ZDES model did not match the measuements and showed moe spatial vaiability than obseved. Thus, it is not supising that additional disageement is found in the velocity measuements nea the side of the cube at location 2. At heights of 1 m and 3 m, ZDES pedicts evesed flow, while the Silsoe study obseved fowad flow. This indicates that the Silsoe and ZDES measuements wee taken on opposite sides of the side votex coe and could suggest that the time aveaged Silsoe side votex is naowe than that pedicted by ZDES o that it has eattached by midface. In the fa side wake egion 6, all of the models pefom well. In this qualitative compaison, howeve, the ZDES poduces bette ageement with the measuements than the RANS uns epoted peviously 20. Table 2 shows a quantitative assessment of the eattachment and stagnation lengths fo the Silsoe full scale field expeiment data and each model. BASE ZDES pedicts eattachment most accuately both in the wake and on the top of the cube. On the font face of the cube, the CFD models all pedict stagnation too high on the cube but agee well with each othe. The stagnation point upsteam of the hoseshoe votex is best pedicted by ou BASE ZDES. Geneally, BASE ZDES pefoms the best fo pedicting stagnation and eattachment fo thee of the fou measuements. Richads et al. 20 compaed models with the aveage magnitude of coefficient of pessue diffeences. Table 3 epoduces this compaison and includes ou DES and ZDES esults. The best esults in each ow ae indicated in boldface and undelined. We see that fo fou of the six citeia, ZDES pefoms at least as well as any othe model, with DES being the best at pedicting the vetical tansvese line. This analysis again suppots the conjectue that the DES-type models impove on RANS fo modeling details of detached wake flow. 4 Discussion The Silsoe field expeiments povide an oppotunity to evaluate best pactices fo modeling flow about buildings at Re appopiate fo the atmospheic bounday laye. Oveall, the DES esults, paticulaly the zonal vesion ZDES, match the Silsoe full scale field measuement data as well as o bette than the RANS solutions, with the added benefit of pedicting tubulence. The ageement of the eattachments was quite good fo the ZDES model, although the BASE DES did not eattach on the top face of the cube. The pimay obseved discepancy in Cp obsevations when compaed with expeimental data is the disageement ove the top face of the cube. While the tuned RNG k- model impoves the RANS ageement significantly, all of the CFD esults undepedict the pessue dop in the votex ove the bulk of this face. The closest to matching the expeimental data is the ZDES simulation, but it comes at the expense of ovepedicting the low pessue anomaly on the sides of the cube. ZDES also best captues eattachment ove the top of the cube. Details of the pessue field ae expected to be sensitive to the exact location of the side votices. A diffeence between the CFD and the expeiment is the ability to contol the diection of the mean wind. In the CFD, the wind diection is pescibed so that the oncoming wind is exactly pependicula to the upsteam face of the cube. This condition was also sought in the expeiment; howeve, local meteoological conditions cannot be contolled. Instead, the expeimental esults ely on conditional sampling of the expeimental data to extact instances when the oncoming wind had the pope oientation. These instances become membes of a conditional ensemble whose mean is pesented. In fact, it has been noted that the chaacteistics of eattachment ae modified when the expeimental cube is pitched slightly into the wind 28. One expects some effect of the fluctuating wind field to be aliased into the mean simply because of limited contol of the conditional ensemble. These slight vaiations in the effective mean wind diection and the associated changes in the mean side votex positions may account fo much of the diffeences between the CFD esult and the expeimental data, paticulaly on the sidewalls. Thee ae seveal othe possible easons fo discepancies between the BASE case and full scale expeimental esults. Richads et al. 20 noted that modeling the atmospheic bounday laye with both full scale velocity and tubulence pofiles ceates a nonhomogeneous bounday laye with the k- tubulence model. Fo the pesent study, both pofiles ae based on full scale data and the Table 3 Aveage magnitude of coefficient diffeences K-E RNG MMK DES ZDES Vetical cente line Vetical tansvese line Hoizontal mid-height line u/u ef v/u ef w/u ef Jounal of Fluids Engineeing MARCH 2011, Vol. 133 /

8 Spalat Allmaas tubulence model is used. Futhe, the eddy viscosity inlet pofile used hee is based on tubulence measuements taken at only fou diffeent heights and is linealy intepolated Fig. 2. As a esult, the cuent inlet bounday laye is not homogeneous and evolves fo a shot distance downsteam. The outflow bounday laye in ou solutions has a simila velocity pofile but a much lowe eddy viscosity pofile. In summay, the esults of DES and ZDES simulations of flow aound a suface mounted cube have been validated with expeimental data. It is shown that ZDES pefoms at least as well as the best RANS solutions, and on most metics, bette. Futhe, thee is pomise that futue studies of the vaiability in wind diection will impove DES ageement with full scale expeimental esults. In addition, a study of model pefomance as a function of gid esolution demonstates that the BASE/2 mesh has vey simila esults as the BASE case, establishing an appopiate esolution fo the high fidelity DES-type modeling of atmospheic flow aound a blunt body. Acknowledgment Robet P. Wilson pefomed much of the modeling effot fo this pape, funded by the ARL Undegaduate Honos Pogam. The authos would like to thank ACUSIM Softwae Inc. fo thei suppot. Refeences 1 Casto, I. P., and Robins, A. G., 1979, Flow Aound a Suface Mounted Cube in Unifom and Tubulent Steams, J. Fluid Mech., 79, pp Muakam, S., 1997, Cuent Status and Futue Tends in Computational Wind Engineeing, J. Wind. Eng. Ind. Aeodyn., 67 68, pp Fezige, J. H., and Peic, M., 1999, Computational Methods fo Fluid Dynamics, 2nd ed., Spinge, Gemany, pp Tsuchiya, M., Muakami, S., Mochida, A., Kondo, K. and Ishida, Y., 1997, Development of a New k- Model fo Flow and Pessue Fields Aound Bluff Body, J. Wind. Eng. Ind. 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