REAL TIME AIRFLOW SIMULATION IN BUILDINGS Wangda Zuo, and Qngyan (Yan) Chen School of Mechancal Engneerng, Purdue Unversty, West Lafayette, USA ABSTRACT Real tme flow smulaton s crucal n emergency management n buldngs, such as fre or accdental release of chemcal/bologcal agents. Proper measures can be taken to mnmze casualtes wth correct and tmely predcton of the spread of the fre or contamnants. Although the tradtonal CFD smulaton n buldngs s accurate, t s too tme consumng. Multzone flow modelng s fast, but ts accuracy s poor. Therefore, t s very necessary to develop a new method that s faster than the tradtonal CFD, but more accurate than the multzone modelng. Recently, the modfed sem-lagrangan method based on Naver-Stokes equaton has been used for flow smulaton. Ths method s uncondtonally stable and can use a larger tme step than tradtonal CFD. The method has been successfully used n computer game ndustry and n computer graphc scence. However, the results are only vrtually real and are not rgorously valdated. Ths nvestgaton used the method to systematcally study three basc flows n buldngs and compared the numercal results wth the correspondng expermental data or drect numercal smulaton data from the lterature. The results conclude that t s possble to conduct flow smulatons faster than real tme by usng the method, although some dscrepances exst between the numercal results and the data. KEYWORDS CFD, Real Tme, Sem-Lagrangan method, Fast Flud Dynamcs INTRODUCTION Fre or accdental release of chemcal/bologcal agents n buldngs happens occasonally. In such emergent stuatons, quck predcton of the smoke or contamnant transport s crucal for proposng measures to mnmze casualtes. The predcton should be not only accurate and nformatve, but also faster than the real tme. Unfortunately, current modelng technologes cannot meet such requrements. Ether ther computng speed s too slow or ther accuracy s too poor. For example, Computatonal Flud Dynamcs (CFD) by large eddy smulaton (LES) of arflow and contamnant transport n a buldng demands an mpractcally large computer capacty (tens of Gb memory) and long computng tme (weeks). Although CFD smulatons usng unsteady Reynolds averaged Naver-Stokes equatons (URANS) are much faster than the LES, t stll takes a desktop several hours to a few days to compute the arflow and contamnant transport n the buldng. On the other hand, by assumng the flow n a room s unform, multzone flow network models need lttle computng tme (a few seconds) (Wang 007). However, the homogenous assumpton of arflow n each room does not provde nformatve results for emergency management. Therefore, t s necessary to develop a method that s faster than the CFD, but more accurate and nformatve than the multzone modelng. Weather forecast requres quck and accurate calculaton of ar moton and temperature of the atmosphere. By treatng the lnear terms responsble for gravtatonal oscllatons n an mplct manner, Robert et al. (197) proposed a sem-lagrangan scheme. Ths scheme can ncrease the tme step sze Correspondng Author: Tel: + 1 765 496 756, Fax: + 1 765 496 7534 E-mal address: yanchen@purdue.edu
by about sx tmes at lttle addtonal cost and wthout degradng the accuracy of the soluton. Applyng the sem-lagrangan approach, Stanforth and Cote (1991) calculated flow for weather forecast and Stam (1999) and Harrs (003) smulated flud moton n computer games and acheved plausble results on real tme. To dstngush the dfferences from tradtonal CFD, the method usng sem-lagrangan approach s named as Fast Flud Dynamcs or FFD. We have attempted to use the FFD predctng ndoor arflows (Zuo and Chen 007). By comparng the computed results wth correspondng data on ndoor arflow from the lterature, our results show that that FFD could predct such flows wth reasonable accuracy and the smulatons were faster than real tme. However, our early work was for sothermal flow wth unform grds so that very fne grds were used for some cases. Ths nvestgaton extended the smulatons to non-sothermal arflows for ndoor envronment and developed our code further wth non-unform grd meshes. The results are reported n ths paper. SCHEME OF FAST FLUID DYNAMICS Before reportng the results, ths secton presents the basc equatons and numercal technques used by FFD. The FFD solves Naver-Stokes equatons for ncompressble flud: カU = 0, (1) カx U = U U + υ U + + P f, () t x x x where U and U are flud velocty components n x and x drectons, respectvely; υ s knematc molecular vscosty; P s pressure; and f s forces, such as buoyancy force. Applyng the Euler approach to the scalar varables (such as contamnant concentraton and ar temperature), the state equaton of the contamnant concentraton or ar temperature s: C = U C + k C + S, (3) t x x where C s contamnant concentraton or ar temperature; k dffusvty; and S source. In each tme step, the FFD solves the Naver-Stokes equatons (1) and () n four stages: (0) (1) () (3) (4) add force dffuse advect proect U U U U U. (4) At the frst stage, the FFD smply adds the force term n equaton () as: (1) (0) U = U + t f, (5) where t s the tme step. The second stage s to solve the dffuson term n equaton () through a frst order mplct scheme: () (1) () U U U = υ. (6) t x By applyng the mplct scheme, the smulaton s always stable even when the Courant number s much large than 1. The thrd stage s to solve the advecton term n equaton (): U (3) (3) () U = U x t, (7)
wth a sem-lagrangan approach (Courant et al. 195): ( ) (3) () () U ( x ) = U x t U, (8) where U (3) (3) (3) (x ) s U at locaton x = (x 1, x, x 3 ). However, the U does not satsfy the contnuty equaton (1). Hence, the last stage s to correct U (3) by a pressure-correcton proecton scheme (Chorn 1967). The proecton operaton ensures the conservaton of mass and t solves a Posson equaton for pressure: The veloctes are then corrected by P U = x x (4) (3) (3). (9) U = U P x, (10) where U (4) s the velocty satsfyng the contnuty equaton (1). A smlar approach can be appled for scalar varable state equaton (3) for comtanmant concentraton or ar temerpature except the proecton stage. RESULT ANALYSES Ths nvestgaton studed three typcal ndoor arflows: (1) a fully developed flow n a plane channel; () a natural convecton flow n a tall cavty; and (3) a forced convecton flow n a ventlated room. The flows represent the most basc elements of flows found n buldngs. Fully Developed Flow n a Plane Channel Flow through a corrdor n a buldng s smlar to that n a plane channel. Therefore, ths study selected a fully developed flow n a plane channel as a test case for the FFD. Based on wall shear velocty, U τ, and the channel half-wdth, H, the flow Reynolds number studed s Re τ = 180. Km et al. (1987) dd drect numercal smulaton (DNS) for ths flow and ther data were used as reference. The FFD smulaton was carred out wth 64 3 non-unform grds. Fgure 1 compares the normalzed mean streamwse veloctes obtaned by the FFD wth the DNS data. The FFD can capture the man shape of the velocty profle, although t under-predcts the velocty at the near wall regon and overpredcts t at the center of the channel. Ths dsagreement s possbly due to the wall treatment. The FFD used a smple no-slp wall boundary condton. Ths boundary treatment s proper for the lamnar flow. However, the channel flow at Re τ = 180 s turbulent (Km et al. 1987). Therefore, n order to mprove the accuracy, more advanced models for the wall are necessary. Our prevous work (Zuo and Chen 007) found that the velocty profle predcted by the FFD dd not satsfy the mass conservaton. Ths nvestgaton successfully solved ths problem by fxng the pressure at a gven pont n the doman. Natural Convecton Flow n a Tall Cavty The arflow due to natural convecton n a tall cavty s lke that n a room wth a heater n the wnter. Ths study used a case wth expermental data from Betts and Bokhar (1995). The cavty was 0.076 m wde and.18 m tall as shown n Fgure. The rght wall was heated at T = 34.7 o C and the left wall cooled at T 1 = 15.1 o C. The correspondng Raylegh number was 0.86 10 6. The FFD smulaton was carred out on 10 0 non-unform grd cells (Fgure 3) wth a tme step equal to 0.05 s.
Fgure 1. The comparson of mean streamwse velocty of the plane channel flow at Re τ = 180, predcted by the FFD and DNS (Km et al. 1987) Fgure. The sketch of natural convecton n a tall cavty Fgure 3. The mesh used n the case of the natural convecton n a tall cavty Fgure 4 compares the predcted temperature and vertcal velocty by the FFD wth the correspondng expermental data. Although the temperature profles predcted by the FFD are steeper at the near wall regon and flatter at the center of the cavty, the agreement wth the expermental data s acceptable consderng the smple flow model used. The computed vertcal veloctes agree wth the expermental data better at the center of the cavty than at the near wall regons. Ths s probably due to the overpredcted heat transfer from the walls by the FFD, whch generated a larger buoyancy force and, consequently, a larger velocty near the walls.
(a) Ar temperature (b) Vertcal ar velocty Fgure 4. Comparson of the averaged ar temperature and vertcal ar velocty predcted by the FFD wth the expermental data (Betts and Bokhar 1995). Forced Convecton Flow n a Room The forced convecton case used s based on Restvo s experment (1979). Fgure 4 shows the sketch of the experment, where H was 3 m. The nlet heght, h n, was 0.168 m (0.056 H) and nlet velocty, U n, was 0.455 m/s. The outlet heght, h out, was 0.48 m (0.16 H). Based on the nlet heght and nlet velocty, the Reynolds number was 5000. Multple boundary condtons, such as nflow, outflow and walls, were appled on the flow doman. The FFD used 36 36 non-unform grd cells and a tme step of 0.5 s (Fgure 6). Fgure 5. The sketch of a forced convecton flow n a room Fgure 6. The mesh used n the case of forced convecton flow n a room Fgure 7 compares the FFD results n two vertcal and two horzontal lnes across the room wth the expermental data. The expermental data llustrates that the flow was complex because there was a secondary recrculaton n the upper-rght corner and another n the lower-left corner. The FFD can properly predct the velocty at the center of the room (x = H and H), but t dd not work perfectly at the near wall regons (y = 0.08H and 0.97H). Two possble reasons may cause that problem. Frst, the grd resoluton of the near wall regon s coarse. Second, flow near the wall s very complex and current no-slp wall boundary condton s not proper. As dscussed n channel flow secton, to correctly capture the flow at the near wall regon, one has to apply approprate wall treatment.
Fgure 7. Comparson of horzontal ar veloctes by the FFD and the expermental data (Restvo 1979). The data are extracted at two vertcal and horzontal sectons across the room. DISCUSSION Ths nvestgaton evaluated also the computng speed of the FFD method. The evaluaton defned a speed enhancement as N = t physcal / t cpu, where t cpu s the elapsed CPU tme used by the FFD and t physcal the physcal tme of flow moton. Thus, real tme smulaton means N = 1. When N > 1, the FFD smulaton s faster than real tme. For the three cases, the FFD smulatons were faster than the real tme on a HP workstaton wth an Intel Xeon (TM) CPU at 3.60 GHz. Table 1 lsts the performance of the FFD smulatons. The FFD ran much faster than real tme n all the three cases. However, the N strongly depends on number of grds and tme step sze. For example, the forced convecton case used fner grd (6.5 tmes), but even larger tme step (10 tmes) than the natural convecton case. Furthermore, the FFD dd not solve temperature equaton for the sothermal flow n the forced convecton. Therefore, the FFD for the forced convecton obtaned more speed enhancement than the natural convecton. Obvously, a coarse grd sze and large tme steps can
accelerate the smulaton but accordngly degrade the accuracy. Therefore, one has to fnd a trade-off between the computatonal performance and accuracy. Table 1 Performance of the FFD smulatons Case Grds t (s) N Channel flow 64 3 0.1 6.1 Natural convecton 10 0 0.05 5.4 Forced convecton 36 36 0.5 98.6 CONCLUSIONS Ths paper ntroduced a scheme of fast flud dynamcs (FFD) method. The FFD has been used to compute arflow and temperature dstrbutons for a fully developed plane channel flow, a natural convecton flow n a tall cavty, and a forced convecton flow n a ventlated room. The three flows represent the basc flow features n buldngs. The correspondng expermental or DNS data from the lterature for the three flows were used to compare the FFD results. The results show that the FFD can predct the arflows wth acceptable accuracy at a speed 6 to 100 tmes faster than real tme. NOMENCLATURE C Contamnant concentraton or ar temperature K Contamnant or thermal dffusvty f Force P Pressure S Source t Tme step U, U Velocty components n x and x drectons, respectvely x, x Spatal coordnates υ Dynamcs molecular vscosty ACKNOWLEDGEMENTS Ths proect was funded by U.S. Federal Avaton Admnstraton (FAA) Offce of Aerospace Medcne through the Ar Transportaton Center of Excellence for Arlner Cabn Envronment Research under Cooperatve Agreement 04-C-ACE-PU. Although the FAA has sponsored ths proect, t nether endorses nor reects the fndngs of ths research. The presentaton of ths nformaton s n the nterest of nvokng techncal communty comment on the results and conclusons of research. REFERENCES 1. P. L. Betts and I. H. Bokhar (1995) "New experments on turbulent natural convecton of ar n a tall cavty", Proc. of IMechE Conference Transactons, 4th UK Natonal Conference on Heat Transfer.. A. J. Chorn (1967) "A numercal method for solvng ncompressble vscous flow problems", Journal of Computatonal Physcs, Vol., 1-6. 3. R. Courant, E. Isaacson and M. Rees (195) "On the soluton of nonlnear hyperbolc dfferental equatons by fnte dfferences", Communcaton on Pure and Appled Mathematcs Vol. 5, 43 55. 4. J. Km, P. Mon and R. Moser (1987) "Turbulence statstcs n fully-developed channel flow at low Reynolds-number", Journal of Flud Mechancs, Vol. 177, 133-166. 5. A. Robert, C. Turnbull and J. Henderso (197) "Implct tme ntegraton scheme for baroclnc models of atmosphere", Monthly Weather Revew, Vol. 100, 39-335.
6. J. Stam (1999) "Stable fluds", Proc. of SIGGRAPH 99. 7. L. Wang (007) "Couplng of multzone and CFD programs for buldng arflow and contamnant transport smulatons", Ph.D. Thess, Purdue Unversty. 8. W. Zuo and Q. Chen (007) "Valdaton of fast flud dynamcs for room arflow", Proc. of Internatonal Symposum on Heatng, Ventlatng and Ar Condtonng, Beng, Chna.