THE USE OF CFD TOOLS FOR INDOOR ENVIRONMENTAL DESIGN

Transcription

1 Chen, Q. and Zha, Z. 24. "The use of CFD tools for ndoor envronmental desgn" Advanced Buldng Smulaton, Edted by A. Malkaw and G. Augenbroe, Spon Press, New York, pp THE USE OF CFD TOOLS FOR INDOOR ENVIRONMENTAL DESIGN Qngyan (Yan) Chen * Professor of Mechancal Engneerng Ray W. Herrck Laboratores School of Mechancal Engneerng Purdue Unversty 585 Purdue Mall, West Lafayette, IN , USA Emal: yanchen@purdue.edu Zhqang (John) Zha Assstant Professor of Archtectural Engneerng Department of Cvl, Envronmental & Archtectural Engneerng Unversty of Colorado 428 UCB, Engneerng Center, Room ECOT-44, Boulder, CO USA Emal: John.Zha@Colorado.edu ABSTRACT Ths paper presents a short revew of the applcatons of CFD to ndoor envronment desgn and studes, and brefly ntroduces the most popular CFD models used. The paper concludes that, although CFD s a powerful tool for ndoor envronment desgn and studes, a standard procedure must be followed so that the CFD program and user can be valdated and the CFD results can be trusted. The procedure ncludes the use of smple cases that have basc flow features nterested and expermental data avalable for valdaton. The smulaton of ndoor envronment also requres creatve thnkng and the handlng of complex boundary condtons. It s also necessary to play wth the numercal grd resoluton and dstrbuton n order to get a grd-ndependent soluton wth reasonable computng effort. Ths nvestgaton also dscusses ssues related to heat transfer. It s only through these ncremental exercses that the user and the CFD program can produce results that can be trusted and used for ndoor envronment desgn and studes. Keywords: Computatonal Flud Dynamcs (CFD), Ar dstrbuton, Indoor envronment, Expermental valdaton NOMENCLATURE A o Effectve area of a dffuser m Mass flow rate (kg/s) C Smagornsky model coeffcent p ar pressure (Pa) C SGS Smagornsky model constant S stran rate tensor (/s) C ε coeffcent n k-ε model t tme (s) averaged ar velocty components n the C ε2 coeffcent n k-ε model U, U x and x drectons (m/s) C μ coeffcent n k-ε model U o face velocty at a dffuser k knetc energy (J/kg) u, u ar velocty components n the x and x drectons (m/s)

2 P averaged ar pressure (Pa) x, x coordnates n and drectons (m) Greek Symbols Δ flter wdth (m) ρ ar densty (kg/m 3 ) δ Kronecker delta σ k Prandlt number for k dsspaton rate of knetc energy ε σ (W/kg) ε Prandlt number for ε ν ar knematc vscosty (m 2 /s) τ subgrd-scale Reynolds stresses (m 2 /s 2 ) ν SGS subgrd-scale eddy vscosty (m 2 /s) φ scalar varables ν t turbulent ar knematc vscosty (m 2 /s) Φ averaged scalar varables Superscrpts - grd flterng or Reynolds averagng fluctuatng component of a varable INTRODUCTION Snce human bengs spend more than 9% of ther tme ndoors n developed countres, desgn of ndoor envronment s crucal to the comfort and welfare of the buldng occupants. However, ths s not an easy task. Woods (989) reported that about 8, to,2, commercal buldngs n the Unted States contanng 3 to 7 mllon workers have had problems related to the ndoor envronment. If the problems can be fxed through technologes, Fsk (2) estmated that for the U.S., the potental annual savngs and productvty could be $5 to $4 bllon from reduced sck buldng syndrome symptoms, and $2 to $2 bllon from drect mprovements n worker performance that are unrelated to health. In addton, buldng safety s a maor concern of buldng occupants. Smoke and fre has clamed hundreds of lves every year n the Unted States. After the anthrax scare followng the September, 2 attacks n the Unted States, how to protect buldngs from terrorst attacks by releasng chemcal/bologcal warfare agents becomes another maor ssue of buldng safety concerns. In the past few years, Computatonal Flud Dynamcs (CFD) has ganed popularty as an effcent and useful tool n the desgn and study of ndoor envronment and buldng safety, after havng been developed for over a quarter of a century. The applcatons of CFD n ndoor envronment and buldng safety are very wde, such as some of the recent examples for natural ventlaton desgn (Carrho-da-Graca et al. 22), predcton of smoke and fre n buldngs (Lo et al. 22 and Yeoh et al. 23), partculate dsperson n ndoor envronment (Qunn et al. 2), buldng element desgn (Manz 23), and even for space ndoor envronment analyss (Eckhardt and Zor 22). Some other applcatons are more complcated and may deal wth sold materals, and may ntegrate other buldng smulaton models. Recent examples are the study of buldng materal emssons for ndoor ar qualty assessment (Murakam et al. 23, Huang and Haghghat 22, and Topp et al. 2) and for more accurate buldng energy and thermal comfort smulatons (Zha and Chen 23, Bartak et al. 22, and Beausolel-Morrson 22). Often, the outdoor 2

3 envronment has a sgnfcant mpact on the ndoor envronment, such as n buldngs wth natural ventlaton. To solve problems related to natural ventlaton requres the study of both the ndoor and outdoor envronment together, such as smulatons of outdoor arflow and pollutant dsperson (Sahm et al. 22 and Swaddwudhpong and Khan 22) and combned ndoor and arflow studes (Jang and Chen 22). CFD s no longer a patent for users wth Ph.D. degrees. Tsou (2) has developed onlne CFD as a teachng tool for buldng performance studes, ncludng ssues such as structural stablty, acoustc qualty, natural lghtng, thermal comfort, and ventlaton and ndoor ar qualty. Compared wth expermental studes of ndoor envronment and buldng safety, CFD s less expensve and can obtan results much faster, due to the development n computng power and capacty as well as turbulence modelng. CFD can be appled to test flow and heat transfer condtons where expermental testng could prove very dffcult, such as n space vehcles (Eckhardt and Zor 22). Even f expermental measurements could be conducted, such an experment would normally requre hundreds of thousands dollars and many months of workers tme (Yuan et al. 999). However, CFD results cannot be always trusted, due to the assumptons used n turbulence modelng and approxmatons used n a smulaton to smplfy a complex real problem of ndoor envronment and buldng safety. Although a CFD smulaton can always gve a result for such a smulaton, t may not necessarly gve the correct result. A tradtonal approach to examne whether a CFD result s correct s by comparng the CFD result wth correspondng expermental data. The queston now s whether one can use a robust and valdated CFD program, such as a wellknown commercal CFD program, to solve a problem related to ndoor envronment and buldng safety wthout valdaton. Ths forms the man obectve of the paper. COMPUTATIONAL FLUID DYNAMICS APPROACHES Indoor envronment conssts of four maor components: thermal envronment, ndoor ar qualty, acoustcs, and lghtng envronment. Buldng thermal envronment and ndoor ar qualty nclude the followng parameters: ar temperature, ar velocty, relatve humdty, envronmental temperature, and contamnant and partculate concentratons, etc. The parameters concernng buldng safety are ar temperature, smoke (contamnant and partculate) concentratons, flame temperature, etc. Obvously, normal CFD programs based on Naver-Stokes equatons and heat and mass transfer cannot be used to solve acoustc and lghtng components of an ndoor envronment. However, the CFD programs can be used to deal wth problems assocated wth thermal envronment, ndoor ar qualty, and buldng safety, snce the parameters are solved by the programs. Hereafter, the paper wll use ndoor envronment to narrowly refer to thermal envronment, ndoor ar qualty, and buldng safety. Almost all the flows n ndoor envronment are turbulent. Dependng on how CFD solves the turbulent flows, t can be dvded nto drect numercal smulaton, large eddy smulaton (LES), and the Reynolds averaged Naver-Stokes equatons wth turbulence models (hereafter denotes as RANS modelng). Drect numercal smulaton computes turbulent flow by solvng the hghly relable Naver- Stokes equaton wthout approxmatons. Drect numercal smulaton requres a very fne grd resoluton to capture the smallest eddes n the turbulent flow at very small tme steps, even for a steady-state flow. Drect numercal smulaton would requre a fast computer that currently does not exst and would take years of computng tme for predctng ndoor envronment. Large eddy smulaton (Deardorff 97) separates turbulent moton nto large eddes and small eddes. Ths method computes the large eddes n a three-dmensonal and tme dependent way whle t estmates the small eddes wth a subgrd-scale model. When the grd sze s suffcently 3

4 small, the mpact of the subgrd-scale models on the flow moton s neglgble. Furthermore, the subgrd-scale models tend to be unversal because turbulent flow at a very small scale seems to be sotropc. Therefore, the subgrd-scale models of LES generally contan only one or no emprcal coeffcent. Snce the flow nformaton obtaned from subgrd scales may not be as mportant as that from large scales, LES can be a general and accurate tool to study engneerng flows (Pomell 999 and Leseur and Metas 996). LES has been successfully appled to study arflow n and around buldngs (Emmerch and McGrattan 998, Thomas and Wllams 999, Murakam et al. 999, Jang and Chen 22, Kato et al. 23). Although LES requres a much smaller computer capacty and s much faster than drect numercal smulaton, LES for predctng ndoor envronment demands a large computer capacty ( byte memory) and a long computng tme (days to weeks). The Reynolds averaged Naver-Stokes equatons wth turbulence models solve the statstcally averaged Naver-Stokes equatons by usng turbulence transport models to smplfy the calculaton of the turbulence effect. The use of turbulence models leads to some errors, but can sgnfcantly reduce the requrement n computer memory and speed. The RANS modelng provdes detaled nformaton on ndoor envronment. The method has been successfully appled to the buldng ndoor arflow and thermal comfort and ndoor ar qualty analyss, as revewed by Ladende and Nearon (997) and Nelsen (998). The RANS modelng can be easly used to study ndoor envronment. It would take only a few hours of computng tme n a modern PC, should the RANS modelng be used to study a reasonable sze of ndoor envronment. In order to better llustrate the LES and RANS modelng, the followng sectons wll dscuss the fundamentals of the two CFD approaches. For smplcty, ths paper only dscusses how the two CFD approaches solve Naver-Stokes equatons and the contnuty equaton. Namely, the flow n ndoor envronment s consdered to be sothermal and no gaseous and partculate contamnants and chemcal reactons, are taken nto account. In fact, temperature (energy), varous contamnants, and varous chemcal reactons are solved n a smlar manner. Large eddy smulaton By flterng the Naver-Stokes and contnuty equatons n the LES approach, one would obtan the governng equatons for the large-eddy motons as u t u + = p (u u ) = ρ 2 u + ν τ () (2) where the bar represents grd flterng. The subgrd-scale Reynolds stresses, τ, n Eq. (), τ = u u u u (3) are unknown and must be modeled wth a subgrd-scale model. Numerous subgrd-scale models have been developed n the past thrty years. The smplest and probably the most wdely used s the Smagornsky subgrd-scale model (Smagornsky 963) snce the poneerng work by Deardorff (97). The model assumes that the subgrd-scale Reynolds stress, τ, s proportonal to the stran rate tensor, 4

5 S u u = ( + ) (4) 2 SGS τ = 2ν S (5) where the subgrd-scale eddy vscosty, ν SGS, s defned as SGS = ( CSGSΔ) (2S S ) = CΔ (2S S) ν (6) The Smagornsky constant, C SGS, ranges from. to.2 determned by flow types, and the model coeffcent, C, s the square of C SGS. The model s an adaptaton of the mxng length model of RANS modelng to the subgrd-scale model of LES. RANS modelng Reynolds (895) ntroduced the Reynolds-averaged approach n 895. He decomposed the nstantaneous velocty and pressure and other varables nto a statstcally averaged value (denoted wth captal letters) and a turbulent fluctuaton supermposed thereon (denoted wth superscrpt). Takng velocty, pressure, and a scale varable as examples: u = U + u p = P + p φ = Φ + φ (7) The statstcal average operaton on the nstantaneous, averaged, and fluctuant varables have followed the Reynolds average rules. Takng velocty as an example, the Reynolds average rules can be summarzed as: u = U = U u u U = u + u = U + U u u = U U + u u (8) = Note that the bars n Eq. (8) stand for statstcal average and are dfferent from those used for LES. In LES, those bars represent grd flterng. By applyng the Reynolds averagng method to the Naver-Stokes and contnuty equaton, they become: U t U + U u = U = P = ρ + U ν u u (9) () where u u s the Reynolds stress that s unknown and must be modeled. In the last century, numerous turbulence models have been developed to represent u u. Dependng on how the Reynolds stress s modeled, RANS turbulence modelng can be further dvded nto Reynolds stress models and eddy vscosty models. For smplcty, ths paper dscusses only eddy-vscosty 5

6 turbulence models that adopt the Boussnesq approxmaton (877) to relate Reynolds stress to the rate of mean stream through an eddy vscosty ν t. 2 U U u = δ ν + u k t () 3 where δ s the Kronecker delta (when, δ =; and when =, δ =), and k s the turbulence u u knetc energy ( k = ). Among hundreds of eddy vscosty models, the standard k-ε model 2 (Launder and Spaldng 974) s most popular. The standard k-ε model solves eddy vscosty through ν t 2 k = C μ (2) ε where C μ =.9 s an emprcal constant. The k and ε can be determned by solvng two addtonal transport equatons: where, k ν t k U = ν + + P ε σ k (3) U ε ν t ε ε = + [ C P C ε] x x ν + ε ε x σ ε k (4) P U U 2 = ν t + (5) 2 and σ =. k, σ =. 3 ε, Cε =. 44, and C ε 2 =. 92 are emprcal constants. The two-equaton k-ε model s most popular but not the smplest one. The smplest ones are zero-equaton turbulence models, such as the constant vscosty model and the one proposed by Chen and Xu (998). The constant vscosty model and zero-equaton models do not solve turbulence quanttes by transport equatons. Be t LES or RANS modelng, the above-mentoned equatons cannot be solved analytcally because they are hghly non-lnear and nter-related. However, they can be solved numercally on a computer by dscretzng them properly wth an approprate algorthm. Many textbooks have been devoted to ths topc. Due to lmted space avalable, ths paper does not dscuss ths ssue here. Fnally, boundary condtons must be specfed n order to make the equatons solvable for a specfc problem of ndoor envronment. If one has used a CFD program wth the above-mentoned equatons and specfed boundary condtons for a flow problem, can one trust the results obtaned? The followng secton wll use an example to llustrate how one could obtan CFD results for an ndoor envronment problem and how one could evaluate the correctness of the results. SIMULATION AND ANALYSIS 6

7 The followng example s a study of ndoor ar and contamnant dstrbuton n a room wth dsplacement ventlaton, as shown n Fg.. The room was 5.6 m long, 3.65 m wde, and 2.43 m hgh. Cold ar was suppled through a dffuser n the lower part of a room, and warm ar was exhausted at the celng level. The two-person offce contaned many heated and unheated obects, such as occupants, lghtng, computers, and furnture. For ths case, Yuan et al. (999) measured the ar temperature, ar velocty, and contamnant concentraton by usng SF 6 as a tracer-gas. The tracer-gas was used to smulate contamnant emssons from the two occupants, such as CO 2. The temperature of the nlet arflow from the dffuser was 7. º C and the ventlaton rate was 83 m 3 /h. The total heat sources n the room were 636 W. Fg. The schematc of a room wth mxed convecton flow General problems n usng CFD programs Ths s a proect the author assgned to tran hs graduate students n ganng experence and confdence n usng a well-valdated commercal CFD program. The graduate students maored n mechancal engneerng and had suffcent knowledge of flud dynamcs, heat transfer, and numercal methods. Wthout excepton, no student could obtan correct results n the frst nstance when they attempted to drectly solve such a problem. Ther CFD results were compared wth the expermental data from Yuan et al. (999). The problems can be summarzed as follows: Dffculty n selectng a sutable turbulence model Incorrect settng of boundary condtons for the ar-supply dffuser Inapproprate selecton of grd resoluton Falure to estmate correctly convectve porton of the heat from the heat sources, such as the occupants, computers, and lghtng Improper use of numerc technques, such as relaxaton factors and nternal teraton numbers For such a problem as shown n Fg., both the LES and RANS approaches were sutable. Through the RANS approach, many commercal CFD programs offer numerous turbulence models for CFD users. It s a very challengng ob for a begnner to decde whch model to use. Although 7

8 for some cases, more sophstcated models can generate more accurate results, our experence found that the Smagornsky subgrd-scale model for LES and the standard k-ε model for RANS are more unversal, consstent and stable. Unfortunately, they do not always produce accurate results and can perform poorer than other models n some cases. Smulaton of a specfc problem of ndoor envronment requres creatve approaches. One typcal example s how to smulate the ar-supply dffuser, whch s a perforated panel wth an effectve area of less than %. Some commercal codes have a lbrary of dffusers that can be used to smulate an array of complex dffusers, such as Arpak from Fluent. Wthout such a lbrary, we found that only experenced CFD users may know how to smulate such a dffuser. Snce the geometry of the dsplacement ventlaton case s rectangular, many of the students would select a grd dstrbuton that fts the boundares of the obects n the room. The grd sze would be selected n such a way that no nterpolaton s needed to obtan results n places of nterest. Not everyone would refne the grd resoluton to obtan grd-ndependent results. It s hard to obtan grd-ndependent results, especally when LES s used. When a wall-functon s used for boundary layers, t s very rare that a CFD user would check f the grd resoluton near a wall s satsfactory. ASHRAE (Chen and Srebrc 22) has developed a gude on usng CFD to smulate ndoor envronment. One maor emphass s on establshng a CFD model that could smulate a specfc problem. If we take the dsplacement ventlaton case as an example, t s not an easy task to provde the thermal and flud boundary condtons. For example, t s dffcult to estmate temperature or heat fluxes for the buldng enclosure surfaces and the heated obects, such as computers, occupants, and lghtng. As a consequence, the mean ar temperature computed by dfferent users wth the same CFD program can dffer as much as 3 K. Most CFD programs, especally the commercal ones, are generalzed and desgned to solve flow and heat and mass transfer, not ust for smulatng ndoor envronment. As a result, the CFD programs provde many optons. A user can fne tune the parameters to obtan a result. The parameters that can be tuned nclude, but are not lmted to, model coeffcents, relaxaton factors, and teraton numbers. Wth dfferent tunng values, the CFD results are often not the same. Therefore, a CFD begnner, who attempted to solve flow and heat and mass transfer for the dsplacement ventlaton case, became frustrated when he/she found that hs/her CFD results were dfferent from the measured data. If no measured data were avalable for comparson, the user would have no confdence about the correctness of the CFD results. In order to correctly perform a CFD smulaton for a specfc flow problem related to ndoor envronment, we strongly recommend the use of ASHRAE procedure for verfcaton, valdaton, and reportng of ndoor envronment CFD analyses (Chen and Srebrc 22). How to conduct CFD analyses of ndoor envronment To desgn or study an ndoor envronment problem wth CFD, one needs to Confrm the abltes of the turbulence model and other auxlary models to predct all physcal phenomena n the ndoor envronment Confrm the dscretzaton method, grd resoluton, and numercal algorthm for the flow smulaton Confrm the user s ablty to use the CFD code to perform ndoor envronment analyses The confrmatons are ndeed a valdaton process through whch a user can know hs/her ablty to perform a CFD smulaton and the correctness of the CFD results. If the user s asked to smulate the dsplacement ventlaton case, no expermental data s avalable for comparson, as n most 8

9 ndoor envronment desgns and studes. The valdaton would use several subsystems that represent the complete flow, heat and mass transfer features of the case. For the dsplacement ventlaton that has a mxed convecton flow, the user may start a two-dmensonal natural convecton n a cavty and a forced convecton n a cavty. Snce mxed convecton s a combnaton of natural and forced convecton, the two subsystems can represent the basc flow features of the dsplacement ventlaton. Of course, CFD valdaton s not only for flow type; the CFD valdaton should done n progressve stages. A typcal procedure for correctly smulatng the dsplacement ventlaton would be: Smulaton of a two-dmensonal natural convecton case Smulaton of a two-dmensonal forced convecton case Smulaton of a smple three-dmensonal case Smulaton of complex flow components Change n grd resoluton, especally the resoluton near walls Calculaton of convectve/radatve rato for dfferent heat sources Smulaton of the dsplacement ventlaton Ths procedure s ncremental n the complexty of the CFD smulatons. Snce t s relatvely easy to udge the correctness of the CFD results for smple cases (many of them have expermental data avalable n lterature), the user can gan confdence n the smulaton exercse. Whle such a smulaton seems to take longer tme than drect smulaton of the dsplacement ventlaton, the procedure s more effectve and can actually obtan the correct results for the dsplacement ventlaton, rather than drectly solvng the case wthout the basc exercse. Ths s because the CFD user would have a hard tme to fnd out where the smulaton has gone wrong, due to the complexty of the dsplacement ventlaton and nexperence n usesage of the CFD program. The followng sectons llustrate the smulaton procedure. Smulaton of a two-dmensonal natural convecton case The two-dmensonal natural convecton case concerns flow n a cavty of.5m wdth and 2.5m heght, as shown n Fg. 2. Cheesewrght et al. (986) conducted the expermental studes on ths case. The experment mantaned sothermal condtons (64.8 C and 2 C) on the two vertcal walls and nsulated the two horzontal walls, even though they were not deally nsulated. The Raylegh number (Ra) based on the cavty heght (h) was 5x 5. The smulaton employed both the zero-equaton model (Chen and Xu 998) and the standard k-ε model. 9

10 Fg. 2 Geometry and boundary condtons for 2-D natural convecton n a cavty Fg. 3(a) compares the computed and measured mean velocty at the md-heght of the cavty, whch shows good agreement except at the near-wall regons. The standard k-ε model wth the wall functon appears to capture the arflows near the surfaces better than the zero-equaton model. The predcted core ar temperatures wth the k-ε model, as shown n Fg. 3(b), also agree well wth Cheesewrght s measurements. The results wth the zero-equaton model are hgher than the measurements, although the computed and measured temperature gradents n the core regon are smlar. A begnner may not be able to fnd the reasons for the dscrepances. Wth the use of two models, t s possble to fnd that dfferent models do produce dfferent results U(m/s) X/L Exp -Equ. Model K-E Model Exp -Equ. Model K-E Model Y/L (T-Tc)/(Th-Tc) (a) (b) Fg. 3 The vertcal velocty profle at md-heght (a) and temperature profle (b) n the md-heght for 2-D natural convecton case Snce dsplacement ventlaton conssts of natural and forced convecton, t s necessary to smulate a forced convecton n order to assess the performance of the turbulence models. A case proposed by Nelsen et al. (974) wth expermental data s most approprate. Due to lmted space

11 avalable, ths paper does not report the smulaton results. In fact, the zero-equaton model and the k-ε model have performed smlarly for the two-dmensonal forced convecton case as they dd for the natural convecton case reported above. Smulaton of a three-dmensonal case wthout nternal obstacles The next step s to smulate a three-dmensonal flow. As the problem becomes more complcated, the expermental data often becomes less detaled and less relable n terms of qualty. Fortunately, wth the experence of the two-dmensonal flow smulaton, the three-dmensonal case selecton s not crtcal. For example, the expermental data of mxed convecton n a room as shown n Fg. 4 from Fsher (995) seems approprate for ths nvestgaton. Fg. 4 Schematc of expermental faclty (Fsher 995) Fg. 5 presents the measured and calculated ar speed contours, whch show the smlarty between the measurement and smulaton of the prmary arflow structures. The results show that the et dropped down to the floor of the room after travelng forward for a certan dstance due to the negatve buoyancy effect. Ths comparson s not as detaled quanttatvely as the twodmensonal natural convecton case. However, a CFD user would gan some confdence n hs/her results through ths three-dmensonal smulaton. (a) (b) Fg. 5 Ar speed contour n the room (a) as measured; (b) as smulated by CFD.

12 Smulaton of complex flow components A room normally conssts of several complex flow elements, such as ar-supply dffusers, rregular heat sources, and complcated geometry. Correct modelng of these flow components s essental for achevng accurate smulaton of arflow n the room. Ths paper takes an ar supply dffuser used for dsplacement ventlaton as an example for llustratng how the complex flow components should be modeled. Fg. 6 shows the flow development n front of a dsplacement dffuser. The et drops mmedately to the floor n the front of the dffuser because of the low ar supply velocty and buoyancy effect. The et then spreads over the floor and reaches the opposte wall. In front of the dffuser, the et velocty profle changes along ts traectory. Close to the dffuser, no et formula can be used snce the et s n a transton regon. Only after.9 m (3. ft) does the et form an attached et, where a et formula could be used. However, et formulae can only predct veloctes n the et regon that s less than.2 m above the floor, because the veloctes above the regon are nfluenced by the room condtons. In fact, the velocty profle above the et regon represents the backward arflow towards the dsplacement dffuser. x=.5 ft x=. ft x=.5 ft x=2. ft x=3. ft x=4. ft x Fg. 6 Development of the wall et n front of the dsplacement dffuser Chen and Moser (99) proposed a momentum method that de-couples momentum and mass boundary condtons for the dffuser n CFD smulaton. The dffuser s represented n the CFD study wth an openng that has the same gross area, mass flux, and momentum flux as a real dffuser does. Ths model enables specfcaton of the source terms n the conservaton equatons over the real dffuser area. The ar supply velocty for the momentum source term s calculated from the mass flow rate, m, and the dffuser effectve area A : U o = m /(ρ A o ) (6) Srebrc (2) demonstrated that the momentum method can produce satsfactory results, and the method s thus used for ths nvestgaton. As one can see, modelng of a complex flow element requres substantal effort and knowledge. Change n grd resoluton, especally the resoluton near walls So far we have dscussed the establshment of a CFD model for dsplacement ventlaton. Numercal procedure s equally mportant n achevng accurate results. In most cases, one would demand a grd-ndependent soluton. By usng Fsher s case (995) as an example, ths nvestgaton has used four sets of grds to smulate the ndoor arflow: a coarse grd ( = 5,6 cells), a moderate grd ( = 44,88 cells), a fne grd ( = 5,47 cells), 2

13 and a locally refned coarse grd ( = 8,72 cells) that has the same resoluton n the nearwall regons as the fne grd. Fg. 7 presents the predcted temperature gradent along the vertcal central lne of the room wth the dfferent grd resolutons. Obvously, a coarse grd dstrbuton can not produce satsfactory results. The moderate and fne grd systems produced smlar temperature profle and could be consdered as grd ndependent. It s also nterestng to know that by usng locally refned grd dstrbuton, a coarse grd system can yeld satsfactory results. 2.5 Coarse Grd Adusted Grd Moderate Grd Fne Grd 2 Z(m) T(C) Fg. 7 Predcted temperature gradent along the vertcal central lne of the room The grd dstrbuton has a sgnfcant mpact on the heat transfer. Fg. 8 shows the predcted convectve heat fluxes from enclosures wth dfferent grd systems. The convectve heat fluxes from the floor predcted wth the refned grd systems are much closer to the measurement than those wth the coarse grd. However, the dfference between the measured and smulated results at wall Level 2 s stll dstnct, even wth the fne grd. The analyss ndcates that the mpact of the hgh speed et flow on Level 2 of the north wall s the man reason for the large heat flux at the entre wall Level 2. Snce the vertcal et slot s very close to the north wall, the cold arflow from the et nlet causes the strong shear flow at the north wall, ntroducng the extra heat transfer at ths partcular area. The experment dd not measure ths heat transfer zone wthn the nner et flow. If the north wall was removed from the analyss of the wall convectve heat fluxes, the agreement between the computed results and measured data would be much better. 3

14 Surface Heat Flux (W/m Convectve Heat Flux Dstrbuton (6ACH, C, Sdewall Jet) Experment CFD-CoarseGrd CFD-ModerateGrd CFD-FneGrd CFD-LocalRefnedGrd CFD-FneGrd:w /onorthwall CFD-LocalRefnedGrd:w /onorthwall -5 Floor Level Level 2 Level 3 Celng Fg. 8 Comparson of convectve heat fluxes from enclosures wth varous grd resolutons Fg. 8 also ndcates that, nstead of usng a global refned grd that may need long computng tme, a locally refned coarse grd can effectvely predct the arflow and heat transfer for such an ndoor case. Good resoluton for the near-wall regons s much more mportant than for the nner space because the ar temperature n the core of a space s generally more unform than that n the permeter of a space. Calculaton of convectve/radatve rato for dfferent heat sources In most ndoor arflow smulatons, the buldng nteror surface temperatures are specfed as boundary condtons. Then, the heat from heat sources must be splt nto convectve and radatve parts. The convectve part s needed as boundary condtons for the CFD smulaton, whle the radatve part s lumped nto the wall surface temperatures. Ths splt can be rather dffcult, snce the surface temperature of the heat sources and/or the surface area are unknown n most cases. Wthout a correct splt, the fnal ar temperature of the room could devate a few degrees from the correct one. Therefore, the splt would requre a good knowledge of heat transfer. Ths problem wll not be dscussed n detal here, snce t s problem dependent. For the dsplacement ventlaton, the convectve/radatve rato should be 8/2 for occupants, 56/44 for computers, and 6/4 for lghtng. Smulaton of dsplacement ventlaton Wth all the above exercses, a CFD user would gan suffcent experence n ndoor envronment smulaton by CFD. The user could use CFD to study ndoor envronment, such as arflow n a room wth dsplacement ventlaton (as shown n Fg. ), wth confdence. The results wll then be somewhat trusted. Ths secton shows the CFD results computed by the co-author for the dsplacement ventlaton case (Fg. ). The expermental data from Yuan et al. (999) was avalable for ths case. The data s used as a comparson n showng f the CFD results can be trusted. Ths nvestgaton used a CFD program wth the zero-equaton turbulence model and the standard k-ε model. The computatonal grd s , whch s suffcent for obtanng the grdndependent soluton, accordng to Srebrc (2) and our experence n Fsher s case (995). Fg. 9(a) shows the calculated ar velocty and temperature dstrbutons n the mddle secton of the 4

15 room wth the zero-equaton model. The solutons wth the standard k-ε model are farly smlar. The computed results are n good agreement wth the flow pattern observed by smoke vsualzaton, as llustrated n Fg. 9(b). The large re-crculaton n the lower part of the room, whch s known as a typcal flow characterstc of dsplacement ventlaton, s well captured by the CFD smulaton. The arflow and temperature patterns n the respectve sectons across a person and a computer, as shown n Fgs. 9(c) and (d), clearly exhbt the upward thermal plumes due to the postve buoyancy from the heat sources. Fg. 9 Velocty and temperature dstrbutons for the dsplacement ventlaton case (a) calculated results n the mddle secton, (b) observed arflow pattern wth smoke vsualzaton n the mddle secton, (c) calculated results n the secton across a computer, and (d) calculated results n the secton across an occupant. The study further compared the measured and calculated velocty, ar temperature, and tracergas concentraton (SF 6 used to smulate bo-effluent from the two occupants) profles at fve locatons where detaled measurements were carred out. The locatons n the floor plan are llustrated n the lower-rght of Fgs. -2. The fgures show the computed results by RANS modelng wth the zero-equaton model and the standard k-ε model, and large-eddy smulaton wth the Smogrnsky subgrd-scale model (SSGS). Clearly, the computed results are not exactly the same as the expermental data. In fact, the two results wll never be the same due to the approxmatons used n CFD and errors n the measurng equpment and expermental rg. The agreement s better for temperature than the velocty and tracer-gas concentraton. Snce omn-drectonal anemometers were used to measure ar velocty and the ar velocty s low, the convecton caused by probes would generate a false velocty of the same magntude. Therefore, the accuracy of the measured velocty s not very hgh. For tracer-gas concentraton, the arflow pattern s not very stable and measurng SF 6 concentraton at a sngle pont would take 3 seconds. The measurement has a great uncertanty as well. On the other hand, the performance of the CFD models s also dfferent. The LES results seem slghtly better than the others. Snce LES uses at least one-order magntude computng tme than the RANS modelng, LES seems not worth n such an applcaton. The profle curves are not very smooth that may ndcate more averagng tme needed. Nevertheless, the CFD results do reproduce the most mportant features of arflow n the room, and can quanttatvely predct the ar dstrbuton. The dscrepances between the computed results and expermental data can be accepted for ndoor envronment desgn and study. We may conclude that the CFD results could be trusted for ths case even f no expermental data were avalable for valdaton. 5

16 .8.6 Plot-.8.6 Plot Experment RANS: -Eq. RANS: k-e LES: SSGS Plot V/Vn V/Vn V/Vn Plot-6.4 Plot V/Vn V/Vn Fg. The comparson of the velocty profles at fve postons n the room between the calculated and measured data for the dsplacement ventlaton case. Z=heght/total room heght (H), V=velocty/nlet velocty (V n ), H=2.43m, V n =.86m/s 6

17 Plot-.4 Plot-3.4 Plot (T-Tn)/(Tout-Tn) (T-Tn)/(Tout-Tn) Expermen.2 t RANS: - Eq. RANS: k- E (T-Tn)/(Tout-Tn) Plot-6.4 Plot (T-Tn)/(Tout-Tn).5.5 (T-Tn)/(Tout-Tn) Fg. The comparson of the temperature profles at fve postons n the room between the calculated and measured data for the dsplacement ventlaton case. Z=heght/total room heght (H), T=(T ar -T n /T out -T n ), H=2.43m, T n =7. o C, T out =26.7 o C 7

18 Plot-.4 Plot-3.4 Plot C/Cs C/Cs.2 Experment RANS: - Eq. RANS: k-e C/Cs Plot-6.2 Plot C/Cs C/Cs Fg. 2 The comparson of the tracer-gas concentraton profles at fve postons n the room between the calculated and measured data for the dsplacement ventlaton case. Z=heght/total room heght (H), H=2.43m, C s =.42 ppm CONCLUSIONS Ths paper shows that applcatons of CFD program to ndoor envronment desgn and studes need some type of valdaton of the CFD results. The valdaton s not only for the CFD program but also for the user. The valdaton process wll be ncremental, snce t s very dffcult to obtan correct results for a complex flow problem n ndoor envronment. Ths paper demonstrated the valdaton procedure by usng dsplacement ventlaton n a room as an example. The procedure suggests usng two-dmensonal cases for selectng a turbulence model and employng an approprate dffuser model for smplfyng complex flow components n the room, such as a dffuser. Ths paper also demonstrates the mportance n performng grdndependent studes and other techncal ssues. Wth the exercses, one would be able to use a CFD program to smulate arflow dstrbuton n a room wth dsplacement ventlaton, and the CFD results can be trusted. 8

19 ACKNOWLEDGEMENT Ths nvestgaton s supported by the Unted States Natonal Insttute of Occupatonal, Safety, and Health (NIOSH) through research grant No. R OH476-. REFERENCES Bartak, M., Beausolel-Morrson, I., Clarke, J.A., Denev, J., Drkal, F., Lan, M., Macdonald, I.A., Melkov, A., Popolek, Z. and Stankov, P. 22. Integratng CFD and buldng smulaton, Buldng and Envronment, 37(8), Beausolel-Morrson, I. 22. The adaptve conflaton of computatonal flud dynamcs wth whole-buldng thermal smulaton, Energy and Buldngs, 34(9), Boussnesq, J Théore de l écoulement tourbllant, Mem. Présentés par Dvers Savants Acad. Sc. Inst. Fr., 23, Carrlho da Graca, G., Chen, Q., Glcksman, L.R. and Norford, L.K. 22. Smulaton of wnddrven ventlatve coolng systems for an apartment buldng n Beng and Shangha, Energy and Buldngs, 34(), -. Cheesewrght, R., Kng, K.J. and Za, S. Expermental data for the valdaton of computer codes for the predcton of two-dmensonal buoyant cavty flows, In: Sgnfcant Questons n Buoyancy Affected Enclosure or Cavty Flows (Ed. by J. A. C. Humphrey, C. T. Adedsan and B. W. le Tourneau), ASME, 75-8, 986. Chen, Q. and Moser A. 99. Smulaton of a multple-nozzle dffuser, Proceedngs of the 2th AIVC Conference on Ar Movement and Ventlaton Control wthn Buldngs. Ottawa, Canada, Vol. 2, pp. -3. Chen, Q. and Xu, W A zero-equaton turbulence model for ndoor arflow smulaton, Energy and Buldngs, 28(2), Chen, Q. and Srebrc, J. 22. A procedure for verfcaton, valdaton, and reportng of ndoor envronment CFD analyses, Internatonal Journal of HVAC&R Research, 8(2), Deardorff, J.W. 97. A numercal study of three-dmensonal turbulent channel flow at large Reynolds numbers, Journal of Flud Mechancs, 4, Eckhardt, B. and Zor, L. 22. Computer smulaton helps keep down costs for NASA's lfeboat for the nternatonal space staton, Arcraft Engneerng and Aerospace Technology: An Internatonal Journal, 74(5), Emmerch, S.J. and McGrattan, K.B Applcaton of a large eddy smulaton model to study room arflow, ASHRAE Transactons, 4, Fsk, W.J. 2. Health and productvty gans from better ndoor envronments and ther relatonshp wth energy effcency, Annual Revew of Energy and the Envronment, 25, Fsher, D.E An expermental nvestgaton of mxed convecton heat transfer n rectangular enclosure, Ph.D. Thess, Unversty of Illnos at Urbana-Champagn, IL. Huang, H. and Haghghat F. 22. Modellng of volatle organc compounds emsson from dry buldng materals, Buldng and Envronment, 37(2), Jang, Y. and Chen, Q. 22. Effect of fluctuatng wnd drecton on cross natural ventlaton n buldng from large eddy smulaton, Buldng and Envronment, 37(4), Kato, S., Ito, K. and Murakam, S. 23. Analyss of vstaton frequency through partcle trackng method based on LES and model experment, Indoor Ar, 3(2), Ladende, F. and Nearon, M CFD applcatons n the HVAC&R ndustry, ASHRAE Journal, 39(), 44. 9

20 Launder, B.E. and Spaldng, D.B. The numercal computaton of turbulent flows, In Computer Methods n Appled Mechancs and Energy, vol. 3, pp , 974. Leseur, M. and Metas, O New trends n large eddy smulatons of turbulence, Annual Revew of Flud Mechancs, 28, Lo, S.M., Yuen, K.K., Lu W.Z., and Chen, D.H. 22. A CFD study of buoyancy effects on smoke spread n a refuge floor of a hgh-rse buldng, Journal of Fre Scences, 2(6), Manz, H. 23. Numercal smulaton of heat transfer by natural convecton n cavtes of facade elements, Energy and Buldngs, 35(3), Murakam, S., Kato, S., Ito, K. and Zhu, Q. 23. Modelng and CFD predcton for dffuson and adsorpton wthn room wth varous adsorpton sotherms, Indoor Ar, 3(6), Murakam, S., Izuka, S. and Ooka, R CFD analyss of turbulent flow past square cylnder usng dynamc LES, Journal of Fluds and Structures, 3(78), Nelson, P.V Flow n ar condtoned rooms, Ph.D. Thess, Techncal Unversty of Denmark, Copenhagen. Nelsen, P.V The selecton of turbulence models for predcton of room arflow, ASHRAE Transactons, 4(). Pomell, U Large eddy smulaton: achevements and challenges, Progress n Aerospace Scences, 35, Qunn, A.D., Wlson, M., Reynolds, A.M., Coulng, S.B. and Hoxey, R.P. 2. Modellng the dsperson of aeral pollutants from agrcultural buldngs - an evaluaton of computatonal flud dynamcs (CFD), Computers and Electroncs n Agrculture, 3(), Reynolds, O On the dynamcal theory of ncompressble vscous fluds and the determnaton of the crteron, Phlosophcal Transactons of the Royal Socety of London, Seres A, 86, p. 23. Sahm, P., Louka, P., Ketzel, M., Gulloteau, E. and Sn, J.-F. 22. Intercomparson of numercal urban dsperson models part I: street canyon and sngle buldng confguratons, Water, Ar and Sol Polluton: Focus, 2(5-6), Smagornsky, J General crculaton experments wth the prmtve equatons. I. The basc experment, Monthly Weather Revew, 9, Srebrc, J. 2. Smplfed methodology for ndoor envronment desgn, Ph.D. Thess, Department of Archtecture, Massachusetts Insttute of Technology, Cambrdge, MA. Swanddwudhpong, S. and Khan, M.S. 22. Dynamc response of wnd-excted buldng usng CFD, Journal of Sound and Vbraton, 253(4), Thomas, T.G. and Wllams, J.J.R Generatng a wnd envronment for large eddy smulaton of bluff body flows - a crtcal revew of the technque, Journal of Wnd Engneerng and Industral Aerodynamcs, 82(), Topp, C., Nelsen, P.V. and Heselberg, P. 2. Influence of local arflow on the pollutant emsson from ndoor buldng surfaces, Indoor Ar, (3), Tsou J.-Y. 2. Strategy on applyng computatonal flud dynamc for buldng performance evaluaton, Automaton n Constructon, (3), Woods, J.E Cost avodance and productvty n ownng and operatng buldngs, Occupatonal Medcne: State of the Art Revews, 4(4): Yeoh, G.H., Yuen, R.K.K., Lo, S.M. and Chen D.H.23. On numercal comparson of enclosure fre n a mult-compartment buldng, Fre Safety Journal, 38(), Yuan, X., Chen, Q., and Glcksman, L.R., Hu, Y., and Yang, X Measurements and computatons of room arflow wth dsplacement ventlaton, ASHRAE Transactons, 5(), Zha, Z. and Chen, Q. 23. Soluton characters of teratve couplng between energy smulaton and CFD programs, Energy and Buldngs, 35(5),