UrbaWnd, a Computatonal Flud Dynamcs tool to predct wnd resource n urban area Karm FAHSSIS a, Gullaume DUPONT a, Perre LEYRONNAS a a Meteodyn, Nantes, France Presentng Author: Karm.fahsss@meteodyn.com, Tel: +33 240 71 05 05 Correspondng Author: Gullaume.dupont@meteodyn.com, Tel: +1 267 475 4278 Abstract: Computatonal Flud Dynamcs (CFD) s already a necessary tool for modelng the wnd over complex rural terrans. In order to maxmze energetc yeld and optmze the costs, before nstallng the wnd energy systems, a good knowledge of wnd characterstcs on ste s requred. Meteodyn has developed UrbaWnd, whch s an automatc CFD software for computng the wnd n urban envronment for small wnd turbnes. Compared to rural open spaces, the geometry n urban areas s more complex and unforeseeable. The effects created by the buldngs, such as vortexes at the feet of the towers, Ventur effect or Wse effect, make the modelng of urban flows more dffcult. The model used n UrbaWnd allows to take these effects nto account by solvng the equatons of Flud Mechancs wth a specfc model that can represent the turbulence and the wakes around buldngs as well as the porosty of the trees and the effects of the ground roughness (asphalt, water or grass). In order to valdate UrbaWnd s results, dfferent study cases proposed by the Archtectural Insttute of Japan have been set up. The three selected cases have an ascendng complexty, from the smple block to the complete rebuldng of a quarter of the Japanese cty of Ngata. The results valdate UrbaWnd as well for theoretcal cases as for real cases by offerng a mnor error margn on the wnd speed predcton. Keywords: Wnd modelng, CFD, urban wnd energy 1.1 INTRODUCTION In order to valdate UrbaWnd s results, dfferent study cases based on practcal uses proposed by the Archtectural Insttute of Japan [1] have been set up. The three selected cases have an ascendng complexty, from the smple block to the complete rebuldng of a quarter of the Japanese cty of Ngata. These publshed cases allowed to compare the computatons results of UrbaWnd wth the measurements of the AIJ. Therefore, the stes have been recreated n a fle format that can be used by UrbaWnd and the condtons taken for the CFD computatons are as smlar as possble to the experments condtons. The values obtaned by the computatons are then compared wth the measured values. At frst a graphcal comparson s done by placng the ponts n a graph wth the computed values n ordnate and the measured values n abscse (regresson lne). Statstcal ndcators of the results accuracy are proposed as followed: 1
The error, calculated by the formula: The determnaton coeffcent R², whch corresponds to the square of the Pearson product-moment correlaton coeffcent : Ths last value s the square of the covarance of the reduced centered varables. Its value s between 0 and 1. The value 0 means a total ndependence between both varables. In these equatons as well as n the whole document, y corresponds to the computed values and x to the measured values, both normalzed. In every case, results are consdered for all ponts n a frst tme and only for consstent ponts n a second tme. For the consstent ponts, we exclude all the very low speed ponts, whch lead to the bggest error and for whch a great accuracy s not requred when consderng the nstallaton of wnd turbnes. The dfference between the results obtaned for both all ponts and consstent ponts s summarzed n a table n the concluson. 1.2 DESCRIPTION OF THE CFD CODE URBAWIND 1.2.1 The Equatons UrbaWnd solves the equatons of Flud Mechancs,.e. the averaged equatons of mass and momentum conservatons (Naver-Stokes equatons). When the flow s steady and the flud ncompressble, those equatons become: u x u u x 0 P x x u x u x u' ' u F 0 (1) (2) The turbulent fluxes are parameterzed by usng the so-called turbulent vscosty. The turbulent vscosty µ s consdered as the product of a length scale by a speed scale whch are both characterstc lengths of the turbulent fluctuatons. The speed scale s gven as the square root of the turbulent knetc energy multpled by the densty. The turbulent knetc energy s solved usng the transport equaton by ncludng the producton and dsspaton terms of the turbulence where the turbulent length scale L T vares lnearly wth the dstance at the nearest wall (ground and buldngs). Boundary condtons are automatcally generated. The vertcal profle of the mean wnd speed at the computaton doman nlet s gven by the logarthmc law n the surface layer, and by the Ekman functon [2]. A Blasus -type ground law s mplemented to model frctons (velocty components and turbulent knetc energy) at the surfaces (ground and buldngs). 2
The effect of porous obstacles s modeled by ntroducng a snk term n the cells lyng nsde the obstacle: F V. Cd. U. U (3) 1.2.2 Mesh generaton Ths meshng s generated by followng the computed wnd drecton. The sze of the computaton doman s automatcally generated so that the mnmum dstance between a buldng and a boundary condton s equal to 6 tmes the heght of the hghest buldng of the smulaton. The generated meshng s Cartesan and unstructured (usng of overlapped meshng), wth automatc refnement near the ground, obstacles and of course at result ponts locatons. For ths study, the vertcal mesh dmenson around the blocks n the two frst cases (smple block and group of blocks) has been taken equal to 20 cm. The mesh dmenson for the case of Cty of Ngata was 50cm n the horzontal and vertcal drectons for the refned cells around the buldngs. 1.2.3 MIGAL-UNS Solver 1.2.3.1 DESCRIPTION The MIGAL-UNS solver has been regularly used for some years now, and has already been fully valdated on number of academc cases [3]. MIGAL s an teratve lnear equatons solver whch updates smultaneously the wnd speed components as well as the pressure on the whole computatonal doman, so-called coupled resoluton. Ths method demands more storage capacty, but t has the advantage to dramatcally ncreasng the convergence process. The dscretzed equatons lnear system, s transformed va an ncomplete LU decomposton ILU(0) [4]. A precondtoner of type GMRES s used n order to ncrease the terms n the man dagonal so that the solvng robustness s mproved. Moreover, MIGAL uses a mult-grd procedure whch conssts n solvng successvely the equatons on dfferent grd levels (from the fner one to the coarser one). Ths method accelerates the convergence of the low frequency errors, whch are known to be the lmtng factor n the convergence process. For the type of problem solved here, dfferent tests have shown a better convergence for the V cycles method than for the W cycles method. The number of grd levels s automatcally computed by MIGAL. 1.2.3.2 REFINEMENT STRATEGY: ALGORITHM OF AGGLOMERATION For the mult-grd computaton, MIGAL-UNS uses an agglomeraton method whch ons together and agglomerates control volumes near the fne grd. Ths process s executed recursvely untl havng generated a whole sequence of coarse meshes. Once the grd herarchy s defned, one stll has to determne how the equatons are created on the coarse meshes and how ther solutons wll be used n order to decrease the errors of long wavelengths on the fnest grds. 3
MIGAL employs a Galerkn s proecton method for generatng the equatons on the coarse grd. Ths technque, so-called "Addtve Correcton Mult-grd" conssts n generatng the equaton of the coarse mesh as the sum of the equatons of each correspondng fne cell. Once the soluton s obtaned on the coarse grd, t s ntroduced by correctng the values calculated prevously on the fne grd wth the calculated error. 1.3 THEORETICAL CASES: SIMPLE BLOCK AND GROUP OF BLOCKS 1.3.1 Descrpton The frst study has been done on a square tower of 20 m hgh wth a base of 10 m by 10 m. A wnd wth a drecton of 270 s appled and the computatons are done on the result ponts spread n two plans: a vertcal plan located on x=0, whch cut a tower on ts mddle. The second studed ste s bult up of 8 blocks of 20 m of edge and an empty space n the center. The computatons are done wth a wnd comng from the West (blue arrow) and the result ponts are located around the central empty space at two meters hgh, lke shown n the fgure 1. 1.3.2 Results 1.3.2.1 SIMPLE BLOCK Fgure 1 : Results ponts, z=2m The speed-up coeffcents of the computaton have been compared to the coeffcents obtaned by the expermental measurements. In the followng fgure 2, the computed values functons of the measured values for consstent ponts have been represented. Table 1: Comparson Computatons vs. Measurements for the smple block Frst case Smple Block Error R 2 For all ponts 5.5% 0.92 For the consstent ponts 4.9% 0.93 4
Computed speed-up factor Computed speed-up factor 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Measured speed-up factor Err = 4,9% R² = 0,93 1.3.2.2 GROUP OF BLOCKS Fgure 2: Frst case, horzontal at z=1,25m, consstent ponts The speed-up factors of the computaton have been compared wth the speed-up factors obtaned by the expermental measures. In the followng fgure 3, the computed values functons of the measured values for consstent ponts have been represented. Table 2: Comparson Computatons vs. Measurements for the group of blocks Frst case Group of Blocks Error R 2 For all ponts 8.5% 0.70 For the consstent ponts 5.8% 0.71 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Err= 5,8% R² =0,71 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Measured speed-up factor 1.3.3 Dscusson Fgure 3: Second case, group of blocks, consstent ponts The error (5.5% n average for all ponts and 4.9% when selectng only the consstent ponts) and the determnaton coeffcent allow to confrm the accuracy of UrbaWnd s results for ths frst case. We can observe that the results provded by the software UrbaWnd are very good 5
for most of the ponts. Only a few ponts are far from the lnear regresson curve. These dfferences have several explanatons. At frst most of the ponts correspond to low wnd speeds. The dfferences of values are thus proportonally bgger than for hgher wnd speeds. Furthermore, by vsualzng these ponts, we can notce that these ponts are n general near the walls n areas where bg speed dfference can exst between ponts that are very near. Ths explans that the computaton results can be dfferent wthout necessarly castng doubt on the general aspect of the smulaton. A 2D map of the mean acceleraton around the structure has been represented n the fgure 4. The worst ponts are ndcated n red n the fgure. Fgure 4: Second case, vsualzaton We can notce that the less consstent ponts are the ponts located n the areas where the mean acceleraton s near zero. As all the CFD models, t s n the area near the onng dstance that the results are the most dffcult to reproduce. Thus, for both theoretcal cases, the underestmaton of these low values does not cast doubt on the relevance of the computaton. Moreover one can observe a value of the error whch s equal to 4.9% for the frst case and 5.8% for the second case when selectng only the consstent ponts, whch valdates partly the results provded by UrbaWnd n both cases. 1.4 PRACTICAL CASE: QUARTER OF NIIGATA (JAPAN) 1.4.1 Descrpton The last study has been done n the quarter of the Japanese cty of Ngata. The wnd s comng n the drecton of 225 (blue arrow) and results ponts are placed n several random locatons as ndcated n the fgure 5, at two meters hgh. 6
Computed speed-up factor 1.4.2 Results Fgure 5: Thrd case, result ponts, z=2m The speed-up factors of the computaton have been compared to the speed-up factors obtaned by the expermental measurements. In the followng fgure 6, the computed values functons of the measured values for consstent ponts have been represented. Table 3: Comparson Computatons vs. Measurements for the cty of Ngata Thrd case Cty of Ngata Error R 2 For all ponts 5.9% 0.75 For the consstent ponts 5.4% 0.79 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Err= 5,4% R² = 0,79 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Measured speed-up factor Fgure 6: Thrd case, quarter of Ngata, consstent ponts 7
1.4.3 Dscusson Lke n the prevous cases, the ponts where the computed value of the speed-up factor s far from the measured value are represented n the software UrbaWnd. Fgure 7: Thrd case, quarter of Ngata, vsualzaton The stuaton s smlar to the cases 1 and 2. Indeed, one can observe n the fgure 7 that the worst ponts correspond ether to low-speed areas, or to areas where a small change of locaton can lead to an mportant speed varaton. Moreover, the error and the determnaton coeffcent allow agan to valdate the results of UrbaWnd. Indeed 90% of the ponts have an error value lower than 12% and the mean error s lower than 5.9% for all ponts and 5.4% when selectng only the consstent ponts. 1.5 CONCLUSION Fnally, the table 1 shows that the results provded by UrbaWnd are much closed to the results of the expermental measurements of the Archtectural Insttute of Japan. Indeed the typcal error of the computatons when consderng all ponts s at most 8.5% and even decrease to 5.5% n the frst case. Table 4: Summary table of the comparson Computatons vs. Measurements Error for all Error for the ponts consstent ponts R² Frst case Smple Block 5.5% 4.9% 0.93 Second case Group of Blocks 8.5% 5.8% 0.71 Thrd case Cty of Ngata 5.9% 5.4% 0.79 To conclude, ths study allows valdatng the software UrbaWnd as well for theoretcal cases (frst and second cases) as for real cases (quarter of Ngata) by offerng a mnor error margn. 8
Abbrevatons: u : Components of the mean wnd vector n a Cartesan frame u' : Components of the turbulent fluctuatons P : Mean pressure value : Ar dynamc vscosty : Ar densty C d : Volume coeffcent of frctons, whch s proportonal to the porous obstacle densty V : Volume of the consdered cell. References: [1] Archtectural Insttute of Japan, 2008, Gudebook for Practcal Applcatons of CFD to Pedestran Wnd Envronment around Buldngs. (http://www.a.or.p/pn/publsh/cfdgude/ndex_e.htm) [2] Garratt J.R., 1992, The atmospherc boundary layer, Cambrdge Atmospherc and space scences seres. [3] Ferry M., 2000, The MIGAL solver, Proc. Of the Phoencs Users Int. Conf., Luxembourg, 2000 [4] Ferry M., 2002, New features of the MIGAL solver, Proc. Of the Phoencs Users Int. Conf., Moscow, Sept. 2002 9