Field Validation of Algebraic Equations for Stack and Wind Driven Air Infiltration Calculations

Transcription

1 LBNL 4361 Field Validati f Algebraic Equatis fr Stack ad Wid Drive Air Ifiltrati Calculatis Published i ASHRAE HVAC&R Research Jural, Vl. 4, N., April Iai S. Walker* ad David J. Wils** * Eergy Perfrmace f Buildigs Grup Eergy ad Evirmet Divisi Lawrece Berkeley Natial Labratry Berkeley, CA, USA ** Departmet f Mechaical Egieerig Uiversity f Alberta Edmt, AB, Caada ABSTRACT Explicit algebraic equatis fr calculati f wid ad stack drive vetilati were develped by parametrically matchig exact slutis t the flw equatis fr buildig evelpes. These separate wid ad stack effect flw calculati prcedures were icrprated i a simple atural vetilati mdel, AIM-, with empirical fuctis fr superpsiti f wid ad stack effect ad fr estimatig wid shelter. The majr imprvemets ver previus simplified vetilati calculatis are: a pwer law pressureflw relatiship is used t develp the flw equatis frm first priciples, the furace r fireplace flue is icluded as a separate leakage site ad the mdel differetiates betwee huses with basemets (r slab--grade) ad crawlspaces. Over 3400 hurs f measured vetilati rates frm the test huses at the Alberta Hme Heatig Research Facility were used t validate the predictis f vetilati rates ad t cmpare the AIM- predictis t thse f ther vetilati mdels. The AIM- mdel had bias ad scatter errrs f less tha 15% fr wid-dmiated vetilati, ad less tha 7% fr buyacy ("stack-effect") dmiated cases. KEYWORDS Vetilati, ifiltrati, mdelig, pwer-law, wid shelter, furace flue. 1

2 INTRODUCTION This paper is iteded t derive the techical basis fr the relatiships used i the AIM- air ifiltrati mdel, ad t describe the validati prcedure used t evaluate its predictive skill. Sme f the algebraic equatis used i AIM- were preseted i Walker ad Wils (1990a). A simplified versi f AIM- has als bee used fr calculatig attic vetilati rates by Walker, Frest ad Wils (1995). Hwever, derivati r physical explaati f the relatiships were give. AIM- cmbies ideas frm previus vetilati mdels (particularly the LBL mdel f Sherma ad Grimsrud (1980)) with ew ccepts (rigially develped by Walker (1989)) that accut fr pwer law evelpe leakage, separate flue/fireplace leaks ad the differeces betwee huses with basemets (r slab--grade) ad crawlspaces. Additial refiemets regardig wid shelter calculatis ad adjustig widspeeds frm the measuremet site t the buildig have als bee added.. Althugh AIM- has t bee published i cmplete frm the algrithms have bee used sice they were listed by Walker ad Wils (1990a). AIM- is used i the HOT000/AUDIT000 series f eergy aalysis prgrams prduced by Natural Resurces Caada (CHBA (1994)). AIM- has bee used by ther researchers i studies t mdel ifiltrati rates i residetial buildigs. The predictis f AIM- were evaluated by cmparig t measured data by Palmiter ad Bd (1994) ad Palmiter, Bd ad Sherma (1991), ad i the develpmet f a simple methd fr cmbiig atural ad mechaical vetilati by Palmiter ad Bd (1991). I ather study by Hamli ad Pushka (1994), the AIM- algrithms were used t predict ifiltrati rates fr a idr air quality mdel. I the preset study, ver 3400 hurs f measured vetilati rates i tw huses were used t test AIM-. This is part f the data base f vetilati measuremets frm six huses f the Alberta Hme Heatig Research Facility that iclude huses with ther magitudes ad distributis f leakage. The large set f measured data prvided a wide rage f weather cditis ad huse leakage distributis, i rder t exercise all parts f the mdel. Large quatities f measured data were required fr validati because f the substatial hurly variati f atural vetilati rates. The measured data were t used t tue cefficiets i the AIM- mdel equatis. Istead, the measuremets were used t determie typical errrs that might ccur i calculatig vetilati rates based parameters that are easily determied fr mst huses. I.e., rather tha specifyig the size ad lcati f every leak (which is t pssible i mst practical situatis) the parameters used i the mdel are the evelpe leakage characteristics (usually determied usig a fa pressurizati test, e.g., ASTM (1995) r CGSB (1986)) ad simple estimates f the evelpe leakage distributi. The evaluati als icluded cmparis f the measuremets with ther simple vetilati mdels. The ther mdels icluded fr cmparis are: the LBL (USA) mdel Sherma ad Grimsrud (1980), the VFE (Caada) the variable extesis f the LBL mdel by Yuill (1985) ad by Reard (1989), the NRC (Caada) mdel f Shaw (1985), ad the BRE (U.K.) mdel f Warre ad Webb (1980). MODEL DEVELOPMENT The develpmet f the AIM- mdel bega with derivig a exact umerical sluti t the -liear cmbied wid pressure ad buyacy-drive mass flw balace it ad ut f the buildig. This exact sluti is preseted i the Appedix. The algebraic 1

3 relatiships used i AIM- were the develped by trial ad errr as clsed frm apprximatis t this exact sluti. Fr AIM- wid ad stack effect flws are determied separately, the superpsed as a sum f effective pressures, with a crrecti term that accuts fr the iteracti f wid ad stack iduced pressure. This wid ad stack effect iteracti term is the ly empirical cstat determied by cmparig the AIM- equatis t measured data. The AIM- mdel imprves estimates f air ifiltrati rates by icrpratig a pwer law pressure-flw relatiship, Q = C P, it the mdel frm first priciples, by treatig the furace r fireplace flue as a separate leakage site with its w wid shelter, ad by lcatig the flue utlet abve the huse (depedig the actual flue height), rather tha grupig the flue leakage with the ther buildig leaks as i ther mdels. The fllwig simplifyig assumptis were used i the develpmet f the exact vetilati calculatis: The buildig is a sigle, well mixed ze, wall leaks are evely distributed ver fur walls, evely distributed with height, the flue is filled with air at idr rm temperature, ad the flw thrugh all buildig leaks are characterised by the same pwer law expet f pressure,. I rder t simplify the calculati f wid factr, the fllwig assumptis were made abut the pressure cefficiets i crawl spaces ad attics: The pressure cefficiet the exterir flr f the buildig i a crawl space ca be apprximated by averagig the pressure cefficiets the fur exteral surfaces f the crawl space; the pressures crawl space surfaces were the same as the walls abve them each side f the buildig; ad the pressure cefficiet fr the ceilig (i.e. fr the attic) was assumed t be the average f the expsed attic rf ad sffit surfaces. Determiig Algebraic Apprximatis t Exact Numerical Slutis A key part f AIM- was the develpmet f the algebraic apprximatis t the exact umerical slutis f the flw equatis. The chice f algebraic fuctis was made by lkig at plts f the depedece f the wid ad stack factrs (f s ad f w ) the leakage lcati ad pressure expet parameters. A list f cadidate algebraic fuctis that had the same shape ad asympttic limits was the made. The algebraic fuctis fr each parameter were the chse sequetially, with the mst sigificat parameters selected first. Less sigificat parameters were the cmbied i such a way that they did t mdify the existig fuctis. The fuctis fr the mst sigificat parameters were chse t capture mst f the variability (e.g., the depedece wall leakage) ad the additi r multiplicati f ther fuctis are fr secdary effects (e.g., the separate furace flue leakage). Thus a cmpsite fucti was built up that has several primary fuctis embedded withi it. The algebraic equatis i this mdel were develped based several guidig pricipals: The fuctis had t retai dimesial csistecy. The fuctis had t be as simple as pssible (e.g., hyperblic tagets) s that they culd be used i egieerig desig (spreadsheet) calculatis. The fuctis had be rbust (i.e. t blw up fr ay pssible iput parameter, e.g., limits f impermeable walls cmbied with leaky ceiligs) ad smth s as t t give uusual values fr specific cases. The cstats ad expets were chse t be itegers, prper fractis r the leakage parameters themselves.

4 Pwer Law Flw Relatiship Fa pressurizati tests f huses perfrmed by the authrs ad thers, icludig Beach (1979), Sulatisky (1984) ad Warre ad Webb (1980), as well as theretical csideratis frm Walker, Wils ad Sherma (1996), have shw that the rifice flw assumpti used i the may ifiltrati mdels is urealistic, ad that it is better t use a pwer law pressureflw relatiship: Q = C P (1) The parameters C ad are usually fud frm fa pressurizati tests f the buildig. Fr a typical residetial buildig ~ 0.67, abut midway i its rage frm = 0.50 fr rifice flw t = 1.0 fr fully develped lamiar flw. Leakage Distributi Pieerig wrk by Sherma ad Grimsrud (1980) itrduced the idea f usig a set f quatitative parameters t describe the leakage distributi f a buildig evelpe, ad t determie the idepedet stack-drive ad wid-drive flw rates i terms f stack ad wid factrs, f s ad f w. Sherma ad Grimsrud characterised the leakage distributi i terms f R, the fracti f the 4 Pa fa pressurizati leakage area (A 4 ) i the flr plus the ceilig, ad X, the differece i leakage betwee the flr ad ceilig as fractis f the ttal leakage. They defied the "flr" leakage as thse leakage sites that are lcated at (r ear) the level f the buildig flr that rests the basemet walls, slab--grade r crawlspace. The "ceilig" leakage are the leakage sites that are at (r ear) the ceilig level f the upper strey f the buildig. I AIM-, the furace/fireplace flue is treated separately frm the ther leaks. ad additial parameters are itrduced t accut fr this separate leak: the flue leakage fracti, Y, ad a flue height parameter, Z f. The leakage distributi is specified i terms f the rati parameters R, X ad Y, that are calculated frm the leakage cefficiets C flue, C c, C f, ad C w, i Equati (1) rather tha frm the A 4 leakage areas. Explicit slutis require the assumpti that the expet i Equati (1) is the same fr all leakage sites. I this case, the ttal leakage cefficiet, C, is simply the algebraic sum C = C + C + C + C () c f w flue Leakage distributi parameters are defied usig the frmat suggested by Sherma (1980), but usig C istead f leakage area A 4, ad with the additi f a separate flue fracti, Y. C Cf R = C ceilig - flr sum (3) Cc Cf X = C ceilig - flr differece (4) Cflue Y = C flue fracti (5) c + I additi t the distributed leakage f the buildig evelpe expressed i terms f R, X ad Y, the rmalized height Z f f the flue is give by 3

5 Hf Zf = (6) H Stack Effect Ifiltrati The flw iduced by stack effect, Q s, is give by Q s s s = Cf P (7) where P s is the drivig pressure fr buyacy-drive stack-effect flw. Ti - Tut Ps = ρ gh ut (8) Ti The stack factr, f s, was determied usig the umerical sluti f the exact flw equatis t calculate the stack drive vetilati rate flwrate, Q s i Equati (7) ver a wide rage f R, X, Y, Z f ad flw expet,. The explicit algebraic apprximati fr stack factr was develped (as discussed earlier) t give the same geeral depedece f f s these parameters as the umerical sluti f the liear flw balace equatis. The resultig apprximati fr f s is give by Equati (9). The fuctial frm f this apprximati was selected t prduce the crrect limits fr f s whe all leakage is ccetrated i the walls (R = 0), r i the flr ad ceilig (R = 1), fr the ceilig-flr differece rati limits f X = +1.0, -1.0 ad at the X = 0 midpit. 1 + R 1 1 = - M +1 5 f 4 s where (X + ( +1)Y ) M = - R with a limitig value f M = 1.0 fr +1 + F (X + ( +1)Y ) - R (X + ( +1)Y ) fr - R > 1 The additive flue fucti, F, is give by F = Y(Z where f -1) (Xc X ) R 1- (Zf +1) 1- (9) 1 (10) (11) (1) (1- R - Y) Xc = R + - Y(Zf -1) (13) +1 The flue factr F i Equati (9) is always additive because the flue utlet is the highest leakage site ad will always act t icrease the vetilati flws. With very strg flue exfiltrati, eve the ceilig ca becme a ifiltrati site, thrugh which attic air is draw it the buildig. The variable X c is the critical value f the 4

6 ceilig-flr leakage differece X at which the eutral level (zer idr t utdr pressure differece) is lcated at the ceilig i the exact umerical sluti. Fr X > X c the eutral level will be abve the ceilig, ad air will flw i thrugh the ceilig. Fr X < X c rm air will exfiltrate thrugh the ceilig. (These flw directis assume T i > T ut, ad will be reversed if T ut > T i.) The rle f the flue i reducig ceilig exfiltrati is evidet frm the ctributi f the Y factr i Equati (13). The stack factr f s frm Equati (9) is shw i Figure 1a fr typical values f = 0.67, Z f = 1.5 ad Y = 0., ad fr flue, Y=0. Figure 1a shws that treatig the flue as a separate leakage site with a stack height abve the ceilig has a sigificat effect the stack factr f s. I additi, Figure 1a shws the reducti i f s as leakage becmes ccetrated at sigle lcatis, i.e. whe X = R. Whe R = 0 the X = 0 ad ly a sigle pit ca be determied. I Figure 1a, the value f f s fr R = 0 is give by a crss fr the flue case ad by a star fr Y = 0.. Because the AIM- relatiships fr calculatig f s are apprximatis, they d t match the exact umerical sluti perfectly. Differeces betwee the stack factr estimated by Equati (9) ad the exact umerical sluti are abut ±0.005 fr a huse with Y = 0 ( flue) t ±0.01 fr Y=0.. With f s typically abut 0.3, these differeces represet errrs f abut ±1.5% i f s. The maximum differece betwee exact ad apprximate stack factrs ca be as high as 0.03, abut 10% i f s ad i Q s. Wid Effect Ifiltrati Fr AIM- we prpse tw differet mdels, e fr huses with basemets r slab grade cstructi, ad ather fr huses with crawl spaces. The differece betwee the tw is the pressure cefficiet applied t the flr level leaks. Fr basemet r slab grade cstructi the flr level leaks are split it fur equal parts belw each wall, each assumed t have the same pressure cefficiet as the walls abve them. Fr crawlspaces the pressure cefficiets the fur walls were averaged ad used as the pressure cefficiet i the crawlspace actig the flr level leakage betwee the huse ad the crawlspace. Fr bth cases the wid pressure cefficiets measured by Akis et al. (1979) wid tuel simulatis were used fr the walls f the buildig. The attic pressure cefficiet i AIM- is assumed t be a eave-legth weighted average f the pressure cefficiets the eave ad ed wall vets, ad the rf surface vets. The eave vets are assumed t have the same pressure as the adjacet wall. The attic rf vets were assumed t have a size equal t the sum f the eave vets. These algebraically averaged wid pressure cefficiets imply a liear relatiship betwee pressure ad flw, which is clearly t true if 1 i Equati (1). The errrs caused by algebraically averagig pressure cefficiets were determied by applyig the exact -liear flw balacig equatis t fid the actual pressure cefficiets the flr ad ceilig required t balace the flw i ad ut f attics r crawlspaces. The algebraic average pressure cefficiet fr the fur walls f a square buildig with the wid rmal t the upwid wall (the mst extreme case) was -0.5, usig pressure cefficiets frm Akis et al. (1979). The exact equatis shwed that the actual pressure cefficiet required t balace the flws was -0.3, with =0.67. This result shwed that a simple algebraic average f wall pressure cefficiets was sufficietly accurate t defie crawl space r attic pressures. 5

7 Wid Shelter Effect Wid Pressures The wid iduced ifiltrati rate Q w is give by Q = Cf P (14) w w w where P w is give by ( S U) ρut w Pw = (15) Lcal shieldig by earby buildigs, trees ad bstructis is difficult t estimate by ispectig the buildig site, ad ucertaity i estimatig the lcal shelter cefficiet S w is fte the majr surce f errr i estimatig wid drive ifiltrati flw rates. Previus vetilati studies have icluded shelter ly i brad classes, with sharp chages frm class t class. Fr example, Sherma ad Grimsrud (1980) used a lk-up table with five descriptive classes f shelter such as "Light lcal shieldig with few bstructis". T allw fr chages i wid shelter with wid directi, AIM- uses the shelter iterplati fucti suggested by Walker ad Wils (1991) t determie the shelter fr the buildig, S w. This fucti takes estimates f wid shelter fr wids perpedicular t each side f the buildig ad calculates wid shelter fr ay itermediate agle. S w is cmbied i AIM- with a differet cefficiet (S wflue ) fr the tp f the flue stack t give a imprved estimate f the ttal shieldig. These wid shelter factrs are cmbied liearly: S = S (1 Y) S (1.5Y) (16) w w + wflue where the factr 1.5 is a empirical adjustmet fud by cmparig the AIM- mdel predictis t the exact umerical sluti where each leakage site has its w pressure cefficiet ad shelter. S wflue = 1.0 fr a usheltered flue, which prtrudes abve surrudig bstacles, ad S wflue = S w fr a flue tp which has the same wid shelter as the buildig walls. With flue, Y = 0 ad S w = S w. Table 1 gives the AIM- wid shelter factr estimates fr wids perpedicular t the sides f the buildig. This table uses the same shieldig class descripti suggested by Sherma ad Grimsrud (1980), with the additi f a ew class f "cmplete shieldig". Hwever, it is imprtat t te that althugh the terrai classes are the same, the shelter values i Table 1 are t the same as Sherma ad Grimsrud s geeralized shieldig cefficiet. Adjustig Widspeed fr Lcal Terrai The pressure cefficiets used t fid f w were take frm wid tuel tests. Fr mst wid tuel tests the wid pressure cefficiet, Cp, was calculated usig a referece wid speed at eaves height, H. Mst meterlgical data is measured at greater heights ad must be cverted t the eave height t accut fr the chage i widspeed with height i the atmspheric budary layer. Walker ad Wils (1990b) shwed hw meterlgical widspeeds measured remtely frm the buildig site ca be cverted t a eaves height widspeed at the buildig assumig a pwer law budary layer wid velcity prfile. Wieriga (1980) recmmeded usig the wid speed at the tp f the cstat shear stress surface layer whe cvertig wid speeds frm e lcati t ather. Wieriga estimated this height t be abut 80m plus the area-averaged height δz, f the rughess elemets betwee the tw lcatis. 6

8 Usig this referece height, the relatiship fr cvertig airprt widspeeds t lcal cditis is p p met 80 + δz H U = Umet H met 80 (17) + δz p ad p met deped widspeed, grud rughess, slar islati ad atmspheric stability. Irwi (1979) gives values f p frm 0.1 t 0.47 fr a wide rage f cditis. Fr typical urba husig p ~ 0.3, ad fr meterlgical statis lcated at airprts r ther expsed sites p ~ Huses with Basemets r Slab--Grade Cstructi The wid factr, f w, was fud by usig the exact flw balace equatis t determie Q w umerically. f w was the determied by rearragig Equati (14) ad substitutig this value f Q w ad the apprpriate value f P w. The apprximatig fucti fr f w was geerated usig the methds discussed earlier, by calculatig f w ver a wide rage f leakage parameters ad fidig fuctial frms that wuld reprduce the same characteristic depedece the leakage lcati ad pressure expet. The exact umerical sluti fr f w, ad its apprximatig fucti deped the set f wid pressure cefficiets used. I AIM-, the wid pressure cefficiets frm Akis et al. (1979) ad the flue cap pressure cefficiet frm Haysm ad Swit (1987) were used. Usig these pressure cefficiets, f w was fud t be apprximated by 3 ( -Y) X + R Y f = 0.19( - ) 4 w 1- - (J - YJ ) (18) 4 where X + R + Y J = (19) The fuctial frm fr f w was chse t prduce the crrect behaviur fr the limitig values f all leakage ccetrated i either walls, flr r ceilig, ad fr X = 0 where the flr ad ceilig leakage are equal. The flue height, Z f, des t appear i Equati (18) because flue height is ly felt very weakly thrugh the chage i widspeed at the flue/fireplace utlet. The wid factr calculated usig Equati (18) is shw i Figure 1b fr = /3, Y = 0., ad fr flue (Y=0). This figure shws that there is little effect wid factr f w f csiderig the flue leakage as a hle i the ceilig (equivalet t Y=0), vetig it the attic, r as a separate leakage site with its w flue cap pressure cefficiet abve the rf (Y=0.). I the same way as fr the stack factr, whe R = 0 the X = 0 ad ly a sigle pit ca be determied. I Figure 1b, the value f f w fr R = 0 is give by a crss fr the flue case ad by a star fr Y = 0.. It will be shw later that the majr advatage f the separate flue leakage site fr wid effect is t allw it t have differet wid shelter tha the rest f the buildig. As with the stack factr, fr the wid effect there are differeces betwee the exact umerical sluti ad the apprximatig equatis. A typical differece i wid factrs is abut ±0.005, r with f w typically 0., a errr f ±.5%. The maximum errr i f w is abut ±0.0 r abut ±10%. 7

9 Huses With Crawl Spaces Fr a huse with a crawl space, the pressure iside the crawl space was apprximated i AIM- by the average f the fur walls which chaged the depedece f f w X ad R. Usig this assumpti chaged bth the exact umerical sluti (see Appedix) ad the required apprximatig fucti. Therefre a differet wid factr was required fr huses with crawl spaces, f wc. The algebraic apprximati fr f wc was develped usig the same methds as f s ad f w ad is give by: * * * f = 0.19( ) X R Y (0) wc where R * = 1 R + 0. (1) Y Y * = 1 4 () X * 3 4 X X s 1 = (3) R ad 1 R X s = 1.5Y (4) 5 The critical value f the flr-ceilig differece fracti, X crit, abve which f wc des t chage with X is give by = 1 Y (5) X crit I the AIM- apprximati, if X > X crit the X is set equal t X crit. Fr the case where all the leaks are i the walls (R = 0) the wid factr fr huses with crawl spaces shuld be the same as huses withut crawl spaces. Usig Equati (1) fr this case is f wc = 0.76, which is 3% less tha fr a huse with crawl space. The small differece represets the errr caused by usig apprximatig fuctis fr f w ad f wc. Three ther wid tuel data sets, ASHRAE (1989), Liddamet (1986) ad Wire (1984), fr wall ad rf pressure cefficiets were als used t fid umerical slutis fr f w. These ther sets f pressure cefficiets prduce wid factrs that are fuctially the same, but with a differece i the magitude f the leadig cefficiet 0.19 i Equatis (16) ad (18). The tw extreme results are frm Wire's ad ASHRAE's data sets, ad these prduce values f f w that are respectively 10-0% larger ad 10-0% smaller cmpared t the values f f w fud usig the data set frm Akis et al. The exact umerical flw balace equatis were used t estimate the variability f Q s with wid directi. These exact calculatis f the vetilati rate fr each wid directi usig pressure cefficiets frm Akis et al. itrduced a variability i f w f abut ±10% with wid directi. The AIM- mdel eglects these wid directi effects. Cmbiig Wid ad Stack Effect Flws 8

10 The superpsiti techique used i AIM- adds the stack ad wid drive flws -liearly, as if their pressure differeces added, ad itrduces a extra term t accut fr the iteracti f the wid ad stack effects i prducig the iteral pressure that acts t balace the flws i ad ut f the buildig. The AIM- mdel uses a simple first-rder eutral pressure level shift that prduces the superpsiti ( Q Q ) 1 Q = Q s Qw B1 s w (6) where Q is the ttal flw due t cmbied wid ad stack effects [m 3 /s], ad B 1 is the stack ad wid effect iteracti cefficiet, assumed cstat. A study f superpsiti effects i air ifiltrati mdels was perfrmed by Walker ad Wils (1993) t shw that simple pressure additi superpsiti with B 1 = 0 ca prduce as little bias as the superpsiti techique used here. Hwever further parametric studies have shw that the iteracti term with B 1 0 is ecessary whe applied ver a wider rage f leakage distributis. The cstat B 1 was determied empirically usig direct measuremets f air ifiltrati. Aalysis f data frm the six test huses i several differet leakage cfiguratis fr perids where Q s ad Q w were apprximately equal suggested that a reasable estimate fr B 1 is As discussed further i Walker ad Wils (1993), this aalysis methd ivlved least squares fittig t data at lw temperature differeces t determie the relatiship betwee widspeed ad measured vetilati rate ad similarly, usig lw widspeed data t determie a empirical relatiship betwee the temperature differece ad the measured vetilati rate. These empirical relatiships were the used t calculate Q s ad Q w fr ay wid speed r temperature differece. Equati 6 was the used t estimate the ttal vetilati rate ad cmpare it t the measured vetilati rate fr differet values f B 1. The value f B 1 used here prved t be the mst apprpriate ver a wide rage f leakage distributis. Hwever, differet values f B 1 wuld give better results fr sme specific leakage distributis, s this value f B 1 is t uiversal, it just represets the best cmprmise fr the widest rage f cditis. Frtuately, the agreemet betwee measured ad predicted vetilati rates was t very sesitive t the value f B 1 because it is a secd rder effect (cmpared t the sesitivity t f s ad f w, fr example). Give the scatter i measured data, selecti f ther values fr B 1 did t make much differece t the cmparis f measured ad predicted values. Because B 1 is egative it reduces the ttal ifiltrati rate frm the level predicted by a simple sum f pressures superpsiti. It is imprtat t keep i mid that the iteracti cefficiet B 1 is the ly cstat that was determied by fits t measured ifiltrati data. Mdel evaluati, described i the fllwig secti used data sets chse t be dmiated by wid r stack effects, s that iteracti term i Equati (4) ivlvig the empirical cefficiet B 1 was egligible. I this way, the mdel culd be tested agaist idepedet ifiltrati measuremets that played part i its develpmet. Cmparis f AIM- With Other Vetilati Mdels The ther mdels icluded fr cmparis t AIM- ad measured data were: the LBL (USA) mdel Sherma ad Grimsrud (1980), the VFE (Caada) the variable extesis f the LBL mdel by Yuill (1985) ad by Reard (1989), the NRC (Caada) mdel f Shaw (1985), ad the BRE (U.K.) mdel f Warre ad Webb (1980). 9

11 The tw mdels that mst clsely resemble AIM- use variable leakage distributi. They are Sherma's rifice flw mdel frm Sherma ad Grimsrud (1980) (fte referred t as the LBL mdel), ad a variable flw expet mdel, adapted by Reard (1989) frm Yuill's (1985) extesi f Sherma's mdel that used a pwer law fr evelpe leakage. The sigificat differeces betwee AIM- ad Sherma's ad Yuill's mdels are: AIM- des t assume a zer pressure cefficiet fr the attic r flr level leaks. AIM- differetiates betwee huses with crawl spaces ad thse with basemets r slab--grade cstructi. I AIM- the furace flue is icrprated as a separate leakage site, at a rmalized height Z f abve the flr. AIM- uses a pwer law pressure-flw relatiship. AIM- icludes a wid-stack pressure iteracti term which accuts empirically fr the buildig iteral pressure. The tw ther vetilati mdels icluded i this paper fr cmparis d t allw fr variable leakage distributi. A mdel develped i the U.K. by Warre ad Webb (1980) gives three differet stack ad wid factrs based the buildig cfigurati: detached, semi-detached ad terraced (rw huses). The mdel develped by Shaw (1985) calculates stack ad wid flw rates usig cefficiets fitted t measured data at a sigle test huse. Evaluati f Mdels with Measured Air Ifiltrati AIM- ad the ther mdels were evaluated by cmparig predictis t air ifiltrati measuremets i tw huses at the Alberta Hme Heatig Research Facility. Ctiuus hurly ifiltrati measuremets were carried ut i the test huses usig a cstat ccetrati SF 6 tracer gas ijecti system i each huse described i detail by Wils ad Dale (1985) ad Wils ad Walker (199). The test huses were sigle strey wd frame cstructi with full pured ccrete basemets. ad were umbered 4 ad 5 at the test facility. A imprtat aspect f the test facility is that the huses were situated i rural terrai. Because the huses were i a East - West rw they were usheltered fr wids frm Nrth ad Suth ad prvide strg shelter fr each ther fr East ad West wids. Evelpe leakage characteristics were measured i the tw huses usig a fa pressurizati test ver the rage frm 1 Pa t 75 Pa, frm which C, ad the 4 Pa leakage area A 4 were determied, see Table. T remve the effect f buildig size the predictis the vetilati rates were cverted frm m 3 /s t Air Chages per Hur (ACH) by dividig by the buildig vlume (apprximately 0 m 3 fr the test huses used i this study). The leakage distributi was estimated by visual ispecti at the test facility. Fr huse 4 with the flue blcked it was estimated that R=0.5, X=0, Y=0. Fr huse 4 with a 7.5 cm diameter rifice i a 15 cm diameter flue it was estimated that R=0.3, X=0, Y=0.4. Fr huse 5 with a 15 cm diameter flue R=0.1, X=0, Y=0.6. Later, the variability i R ad X prduced by havig differet peple make these estimates will be discussed. The mdels were cmpared by testig their ability t predict wid ad stack dmiated vetilati rates separately. The effects f differet superpsiti methds fr cmbiig wid ad stack effect were discussed elsewhere by Walker ad Wils (1993). The ability f the mdels t predict average hurly vetilati rates fr give ambiet weather cditis is shw by their bias ad scatter cmpared t the measured data. 10

12 The measured data was srted it bis cverig 5 C idr t utdr temperature differece fr stack dmiated vetilati ad 1 m/s wid speed rages fr wid dmiated vetilati. The criteria fr wid dmiated vetilati were U > 1.5 m/s ad T < 10 C. Fr stack dmiated vetilati the criteria were U < 1.5 m/s ad T > 10 C. T be able t srt fr high ad lw wid speeds ad temperature differeces, ad still prvide eugh data fr biig, a large umber f hurs f vetilati mitrig were required. Fr this study 01 hurs were measured i huse 4 ad 154 i huse 5. Large quatities f data were required due t the substatial hurly variati i vetilati rates. The average weather cditis fr each bi were used as the iput values t the mdels ad the mdel predictis fr a give bi are cmpared t the average measured vetilati rate i the bi. Bias idicates the average errr that wuld be btaied ver a lg time perid if each bi f widspeed r temperature differece were equally likely t ccur. Scatter is the variati betwee the predicted ad measured averages frm bi t bi, ad is a idicatr f hw well the mdels fllw treds i the data if the bias is remved. The bias ca be thught f as the errr i prprtiality cstats, ad the scatter as the errr i the fuctial frm f the mdels. The predictis f AIM- ad the ther fur mdels, are cmpared t measured data i Table 3 fr usheltered cditis (Nrth ad Suth wids) fr huse 5 with a 15 cm diameter flue, ad fr huse 4 with the flue blcked. These results shw that AIM- has the best verall perfrmace fr huses with ad withut furace flues. Fr huses with a flue AIM- is clearly superir because the furace flue is treated as a separate leakage site with its w wid pressure ad wid shelter cefficiets. Fr the VFE ad LBL mdels the furace flue leakage is assumed t be i the ceilig. The ther tw mdels d t separate the leakage by lcati the buildig evelpe s that the flue leakage is simply icluded i the ttal leakage fr the buildig, ad t ccetrated at a sigle lcati. The same data used t calculate bias ad scatter i Table 3 are shw i Figures a ad b with bied data where the mea is shw by a square symbl ad e stadard deviati by errr bars. Figure 4a cmpares the widspeed depedece f the mdels fr huse 5 with a pe 15 cm diameter flue where the huse is heavily sheltered (East ad West wids). All the mdels except AIM- sigificatly uderpredict the wid effect ifiltrati rate Q w because they cat have a usheltered flue utlet with a sheltered buildig. The same data pits that were bied fr Figure 4a are shw idividually i Figure 3. This shws the amut f variati preset i the measured data ad the eed fr data biig fr mdel cmpariss. The measured variati was maily due t the wid speed ad directi variability durig the e hur averagig perid fr the measured data where e stadard deviati fr a sigle bi (a rage f widspeeds f 1 m/s) is abut 0.04 ACH. The ucertaity f the ifiltrati measuremets themselves was abut ±5% r ±0.004 ACH (frm Wils ad Dale (1985)). Table 4 presets a summary f the bias ad scatter fr each mdel fr wid dmiated sheltered buildigs, alg with mdel predictis fr a huse withut a flue. The mdels f Shaw ad Warre ad Webb verpredict i part because they are icapable f accutig fr the variati i leakage distributi. Figure 4b illustrates the temperature differece depedece f the mdels fr huse 4 with a 7.5 cm diameter restricti rifice i the flue, ad Table 5 presets a summary f the bias ad scatter fr stack dmiated vetilati. AIM- gave the best verall agreemet because it allwed the flue leakage t be abve the ceilig height fr stack effect. Table 5 als icludes the mdel errrs fr stack dmiated vetilati i huse 5 with flue. As 11

13 with wid dmiated vetilati the assumptis abut leakage distributi, ad mdel cefficiets frm limited data sets itrduced large errrs it the mdel predictis f Shaw ad Warre ad Webb. I mst cases the LBL mdel had the greatest scatter. This was because its assumpti f rifice flw fr the buildig evelpe prduces a icrrect variati i vetilati rate with widspeed ad temperature differece. Sesitivity t Leakage Distributi Oe f the mst difficult iput parameters t estimate is the distributi f leakage betwee the flr, walls ad ceilig. T estimate the magitude f variati likely t ccur i vetilati rates predicted usig differet leakage distributis, a ifrmal survey f the staff wrkig at Alberta Hme Heatig Research Facility was cducted. The survey resulted i eight differet estimates f leakage distributi fr huse 4. The estimated leakage distributis cvered a rage f 10% t 45% fr flrs, 35% t 60% fr walls ad 0% t 40% fr the ceilig. These were sigificat chages i leakage distributi ad idicated the ucertaity with which these values may be estimated, eve by peple familiar with the structure i questi. This rage f leakage distributi parameters resulted i predicted vetilati rates frm 0.91 t ACH, r abut ±7% f the average. Hwever, due t the liear ature f vetilati flws this relatively small ucertaity ccurs ly if the leakage distributi is varied ver a reasable rage. Puttig all f the leakage i a sigle lcati ca cause large chages i calculated vetilati rate. e.g. puttig all f the leakage i the ceilig wuld result i zer vetilati because all f the leakage wuld experiece the same pressure differece. Errrs due t leakage distributi estimates were reduced fr huses with furace ad fireplace flues because a sigificat prprti f the leakage has a specific, well kw, size ad lcati. This aalysis shwed that estimates f leakage distributi are t critical uless extreme values are used. Cclusis A simple algebraic mdel, AIM-, has bee develped t calculate vetilati rates frm weather cditis ad buildig leakage parameters. The explicit relatiships i AIM- were develped t reprduce the results f umerical slutis f the exact flw balace equatis. Over 3400 hurs f measured vetilati rates were used t validate the AIM- predictis. By cmparig the perfrmace f AIM- t bth measured data ad ther simple vetilati mdels the fllwig cclusis ca be made. The pwer law flw relatiship ad the separate treatmet f the furace flue were sigificat imprvemets, reducig errrs by up t a factr f five. Icludig the furace flue (r fireplace) as a separate leakage site allws AIM- t accut fr the effect f the flue atural vetilati rates better tha the ther simple mdels tested i the paper. This is because the furace flue is lcated at a differet height fr stack effect ad has its w wid pressure cefficiet ad wid shelter factr. Usig a pwer law pressure-flw relatiship esures that AIM- has the apprpriate fuctial frm fr the depedece f vetilati rate the wid ad stack pressures. Typical differeces betwee measured vetilati rates ad AIM- mdel predictis were abut ±10% APPENDIX: EXACT NUMERICAL SOLUTION TO FLOW EQUATIONS 1

14 AIM- ad this umerical sluti use the same methd f separatig leak lcati ad geeratig stack ad wid effect pressures. The umerical vetilati mdel explicitly states the flw thrugh each leak lcati as a fucti f the amut f leakage at that lcati ad the effective wid ad stack pressures actig at that lcati. The effective pressure acrss the leak icludes the chage i iterir pressure f the buildig required t balace the flws i ad ut thrugh the evelpe. The chage i iterir pressure is cmm t the flws fr all the leaks ad is determied umerically s that the iflw thrugh the evelpe is equal t the utflw. Oce this iteral pressure is kw, the the flws thrugh all the leaks ad the ttal vetilati flw are als kw. Cmbiig this ttal flw with the ttal evelpe leakage ad the wid ad stack effect pressures allws the calculati f wid ad stack factrs (f w ad f s ) determied frm a exact umerical sluti. Stack Effect The fllwig example calculati shws hw the exact equatis were develped. I this case, T i > T ut ad the eutral pressure plae lies belw the ceilig. The same apprach was used fr ther cases, but t give here fr brevity. The height f each leak was give i -dimesialized frm (Z). It was -dimesialized by dividig by the height f the ceilig abve grade. At the eutral pressure plae: Z = Z. Ceilig leaks have utflw. Q ceilig s = C P (1 Z ) (A1) c Flr leaks have iflw. Qflr = Cf Ps (Z ) (A) The furace/fireplace flue(s) have utflw. Qflue = Cflue Ps ( Zf - Z) (A3) The walls have iflw belw the eutral level ad utflw abve it. Als, the flw geerated by the pressure differece prfile must be itegrated ver the wall due t the liearity f flw with pressure. Fr this itegrati, a elemet f the wall was determied by its fracti f the ttal wall height ad is give by: CwdZ dcw = (A4) H This fractial wall height wasexpressed i dimesial height dz dz = (A5) H Assumig that the leaks are evely distributed with height ver the wall, the the icremetal flw dq w t be itegrated becmes dq = C ( P ( Z Z) ) dz (A6) wall w s Belw the eutral level the ifiltrati flw is 13

15 Z ( Z Z) Q = C P dz (A7) walli w Perfrmig the itegrati gives + 1 Z Qwalli = Cw Ps + 1 s 0 Similarly, fr flw ut abve the eutral level + 1 ( 1 Z ) Qwallut = Cw Ps + 1 (A8) (A9) Equatis (A1), (A), (A3), (A8) ad (A9) ca be writte i terms f R, X ad Y, ad all the iflw terms gruped tgether t give ( R X) ( 1 R Y) +1 Q stacki = C Ps Z + Z (A10) + 1 Similarly fr the utflws (R + X) (1- R - Y) +1 Q = C Ps (1- Z ) + (1- Z ) + Y(Zf Z ) +1 Settig the iflws ad utflws equal gives a sigle equati, with a sigle ukw Z stackut (A11) R Z X = + (1- Z (1- R - Y) ( - (1- Z ) ) + ( Z - (1- Z ) ) +1 Z ) - Y(Z The wid iduced flw at each leakage site was the determied by the flw cefficiet fr each site ad the pressure differece calculated usig Equati (A14). Settig the iflw ad utflw t be equal resulted i a sigle equati that is slved fr the iterir pressure 14 f Z ) (A1) Z was fud usig a Newt-Raphs techique. The et ifiltrati rate was fud by averagig the iflw ad utflw tgether ad substitutig Equati (A1) fr X. After csiderable algebraic maipulati, the stack factr was give by f s Z = 1+ R - Y + Y(Z +1 Z + (1- Z ) (1- Z ) f Z ) Z (A13) The eutral level determied frm the sluti t Equati (A1) was substituted i Equati (A13) t btai a umerical value f the stack factr. Wid Effect Fr wid effect, the pressure acrss each leak was determied by the pressure cefficiet the exterir surface, Cp i, ad the iterir pressure cefficiet, Cp i, that acts t balace the iflws ad utflws. Fr leak i 1 Pi = ρutu ( Cpi Cpi ) (A14)

16 cefficiet. The Cp's were take frm measured wid tuel data. The ceilig ad flr Cp's were discussed i the mai text. The flue pressure cefficiet f -0.5 was take frm measured data by Haysm ad Swit (1987) ad was crrected fr the icreased widspeed at the flue tp cmpared t the referece widspeed at eaves height. Usig the expet, p frm the budary layer wid prfile p flue = -0.5Z f Cp (A15) A value f p = 0.17 was used here. Assumig we have a slab grade r basemet huse the flw fr the walls ad flrs is give by Equati (A16). Q wall, i = C 1- R X + Ai 1 - Y ρ A i ut U ( Cp - Cp ) wall,i i (A16) The prcedure fr a crawlspace is the same except that the flr level leaks were expressed separately. The flw fr the ceilig was give by Q ceilig ( Cpceilig Cpi R + X 1 = C ρutu ) (A17) ad the flw thrugh the flue(s) was Q flue p ( 0.5Zf Cpi 1 = CY ρutu ) (A18) Cp i is the fud by grupig the iflws ad utflws tgether (by lkig at the sig f the pressure differece acrss each leak) ad equatig them. The resultig equati was the slved usig a Newt-Raphs umerical techique. The resultig flws were the used t determie the wid factr, f w. NOMENCLATURE A 4 effective leakage area fr 4.0 Pa pressure differece, m A i area f wall i, m B 1 wid ad stack effect pressure iteracti cefficiet C flw cefficiet, m 3 /spa C c leakage flw cefficiet, C, f ceilig, m 3 /spa at H [m] C f leakage flw cefficiet, C, f flr level leaks, m 3 /spa C flue leakage flw cefficiet, C, f flue ad fireplaces, m 3 /spa at H f C w leakage f walls, m 3 /spa Cp wid pressure cefficiet Cp ceilig wid pressure cefficiet fr ceilig leaks Cp flue wid pressure cefficiet fr flue/fireplace tp Cp i wid pressure cefficiet fr leak i Cp i wid pressure cefficiet fr iside buildig Cp wall,i wid pressure cefficiet fr wall if s stack factr wid factr f w 15

17 f wc wid factr fr a huse with a crawlspace F flue fucti g gravitatial accelerati, m/s H ceilig height f tp strey abve flr (same as eaves height), m H f height f flue utlet abve flr, m H met height at which U met is measured, m J wid factr parameter M stack factr parameter pressure flw expet p met pwer law expet f the wid speed prfile at the meterlgical stati p pwer law expet f the wid speed prfile at the buildig site Q flw rate, m 3 /s Q ceilig ceilig flw, m 3 /s Q flr flr flw, m 3 /sq flue flue/fireplace flw, m 3 /s Q s stack effect flw, m 3 /s Q stacki stack effect iflw, m 3 /s Q stackut stack effect utflw, m 3 /s Q w wid effect flw, m 3 /s Q wall wall flw, m 3 /s Q wall,i wall flw thrugh wall i, m 3 /s Q walli iflw thrugh wall, m 3 /s Q wallut utflw thrugh wall, m 3 /sr cmbied fracti f leakage i the flr plus ceilig R * crawlspace wid factr parameter fr R S w ttal wid shelter factr S w wid shelter factr fr buildig walls S wflue wid shelter factr fr flues ad fireplaces T i idr temperature, K T ut utdr temperature, K U wid speed at eaves height at the buildig site, m/s U met wid speed at the meterlgical site, m/s X differece i leakage fracti betwee the flr ad ceilig X c critical value f X fr which eutral level is at ceilig fr stack effect X crit critical value f X fr which eutral level is at ceilig fr wid effect X s shifted value f X fr crawlspace wid factr X * crawlspace wid factr parameter fr X Y flue leakage fracti Y * crawlspace wid factr parameter fr Y Z rmalized height abve flr Z f rmalized flue height Z rmalized eutral pressure plae height δz area averaged height f terrai rughess elemets P buildig evelpe pressure differece, Pa P i pressure acrss leak i, Pa P s stack effect referece pressure, Pa P w referece wid pressure, Pa T idr-utdr temperature differece, K 16

18 ρut utdr air desity, Kg/m 3 REFERENCES Akis, R.E., J.A. Peterka ad J.E. Cermak Averaged Pressure Cefficiets fr Rectagular Buildigs. Wid Egieerig Vl. 1, Prc. 5th It. Wid Egieerig Cferece. pp ASHRAE ASHRAE Hadbk - Fudametals. Air Flw Arud Buildigs (Chapter 14). Atlata: ASHRAE. ASTM ASTM Stadard E Determiig Air Leakage by Fa Pressurizati. Aual bk f ASTM Stadards. Vl , pp Philadelphia. America Sciety fr Testig ad Materials. Beach, R.K Relative Airtightess f New Husig i the Ottawa Area. Buildig Research Nte N Ottawa: Natial Research Cucil Caada. CGSB CGSB Stadard M86. Determiati f Airtightess f Buildig Evelpes by the Fa Depressurizati Methd. Ottawa. Caada. Caadia Geeral Stadards Bard. CHBA HOT000 Techical Maual. Ottawa. Caada. Caadia Hme Builders Assciati. Hamli, T. ad W. Pushka Predicted ad Measured Air Chage Rates i Huses with Predictis f Occupat IAQ Cmfrt. Prc. 15th AIVC Cferece, Buxt, UK, pp Haysm, J.C. ad M.C. Swit The Ifluece f Termiati Cfigurati the Flw Perfrmace f Flues. Caada Mrtgage ad Husig Crprati Research Reprt. Ottawa: Caada Mrtgage ad Husig Crprati. Irwi, J.S A Theretical Variati f the Wid Prfile Pwer Law Expet as a Fucti f Surface Rughess ad Stability. Atmspheric Evirmet (13): pp

19 Liddamet, M.W Air Ifiltrati Calculati Techiques - A Applicatis Guide. Air Ifiltrati ad Vetilati Cetre, Brackell, U.K. Palmiter, L. ad T. Bd Mdeled ad Measured Ifiltrati II - A Detailed Case Study f Three Hmes. Electric Pwer Research Istitute Reprt TR Pal Alt, Califria: Electric Pwer Research Istitute. Palmiter, L. ad T. Bd Iteracti f Mechaical Systems ad Natural Ifiltrati, Prc. 1th AIVC Cferece, Ottawa, Caada, pp Palmiter, L., T. Bd ad M. Sherma Mdeled ad Measured Ifiltrati - A Detailed Case Study f Fur Electrically Heated Hmes. Electric Pwer Research Istitute Reprt CU 737. Pal Alt, Califria: Electric Pwer Research Istitute. Reard, J.T Air Ifiltrati Mdellig Study. Reprt #CR fr Eergy Mies ad Resurces Caada. Ottawa: Natial Research Cucil Caada. Shaw, C.Y Methds fr Estimatig Air Chage Rates ad Sizig Mechaical Vetilati Systems fr Huses. Buildig Research Nte 37. Ottawa: Natial Research Cucil Caada. Sherma, M.H. ad D.T. Grimsrud Measuremet f Ifiltrati Usig Fa Pressurizati ad Weather Data. Reprt #LBL Lawrece Berkeley Labratry, Berkeley, Califria. Sulatisky, M Airtightess Tests 00 New Huses Acrss Caada: Summary f Results. Buildigs Eergy Techlgy Trasfer Prgram, Publicati N Ottawa, Caada: Eergy Mies ad Resurces Caada. Walker, I.S Sigle Ze Air Ifiltrati Mdellig. M.Sc. Thesis, Departmet f Mechaical Egieerig, Uiversity f Alberta, Edmt, Caada. Walker, I.S. ad D.J. Wils. 1990a. Icludig furace flue leakage i a simple air ifiltrati mdel. Air Ifiltrati Review, Vl.11, N.4, September 1990, AIVC, Cvetry, U.K. Walker, I.S. ad D.J. Wils. 1990b. The Alberta Ifiltrati Mdel: AIM-. Techical reprt N. 71. Edmt: Uiversity f Alberta, Dept. f Mechaical Egieerig. Walker, I.S. ad D.J. Wils Evaluatig Mdels fr Superpsiti f Wid ad Stack Effect i Air Ifiltrati. Buildig ad Evirmet, Vl. 8, N., pp , 1993, Oxfrd, U.K., Pergam Press. 18

20 Walker, I.S. ad D.J. Wils Simple Methds fr Imprvig Estimates f Natural Vetilati Rates. Prc. 15th AIVC Cferece, Buxt, UK. September Walker, I.S., T.W. Frest ad D.J. Wils A Simple Mdel fr Calculatig Attic Vetilati Rates, Prc. 16th AIVC Cferece, Palm Sprigs, USA. September Walker, I.S., D.J. Wils ad M.H. Sherma Des the Pwer Law Rule fr Lw Pressure Buildig Evelpe Leakage? Prc. 17th AIVC Cferece. Gtebrg. Swede. September Warre, P.R., ad B.C. Webb The Relatiship Betwee Tracer Gas ad Pressurizati Techiques i Dwelligs, Prc. First Air Ifiltrati Ceter Cferece. pp , Widsr, U.K., Wieriga, J., Represetativeess f wid bservatis at airprts. Bulleti Am. Met. Sc., N. 61, pp Wils, D.J. ad I.S. Walker Feasibility f Passive Vetilati by Cstat Area Vets t Maitai Idr Air Quality. Prc. Idr Air Quality '9. ASHRAE/ACGIH/AIHA Cf., Sa Fracisc, Octber 199. Wils, D.J., ad J.D. Dale Measuremet f Wid Shelter Effects Air Ifiltrati. Prceedigs f Cferece Thermal Perfrmace f the Exterir Evelpes f Buildigs, Clearwater Beach, Flrida, Dec Wils, D.J. ad I.S. Walker Wid Shelter Effects fr a Rw f Huses. Prc. 1th AIVC Cf., Ottawa, Caada. Wire, B.G Wid Pressure Distributis ad Vetilati Lsses fr a Sigle- Family Huse as Iflueced by Surrudig Buildigs - A Wid Tuel Study, Prc. Air Ifiltrati Cetre Wid Pressure Wrkshp, pp , Brussels, Belgium, Yuill, G.K Ivestigati f Surces f Errr ad Their Effects the Accuracy f the Miimum Natural Ifiltrati Prcedure. Reprt fr Saskatchewa Research Cucil. Saskat, Caada : Saskatchewa Research Cucil. 19

21 Table 1. Estimates f Shelter Cefficiet Shelter Cefficiet, S w Descripti 1.00 N bstructis r lcal shieldig 0.90 Light lcal shieldig with few bstructis withi tw buildig heights 0.70 Lcal shieldig with may large bstructis withi tw buildig heights 0.50 Heavily shielded, may large bstructis withi e buildig height 0.30 Cmplete shieldig with large buildigs immediately adjacet Huse Number Flue Cfigurati Table. Huse Leakage Characteristics Flw cefficiet, C [m 3 /spa ] Flw expet, Leakage area at 4 Pa, A 4 [cm ] 4 clsed pe with 7.5 cm diameter rifice 5 pe with 15 cm diameter flue

22 Table 3. Differeces Betwee Mdel Predictis ad Measured Data fr Bied Averages Wid Dmiated Vetilati fr Usheltered Buildigs at AHHRF Huse 4: flue (85 hurs) Huse 5: 15 cm flue (79 hurs) Mdel Bias Scatter Bias Scatter AIM- 10% (0.008 ACH) LBL (Sherma) 34% (0.018 ACH) VFE (Yuill/Reard) 5% (0.0 ACH) Shaw 45% (0.038 ACH) Warre ad Webb 4% (0.005 ACH) 3% (0.00 ACH) 18% (0.016 ACH) 4% (0.003 ACH) % (0.00 ACH) 5% (0.003 ACH) -8% (-0.0 ACH) -0% ( ACH) -% ( ACH) -1% ( ACH) -19% ( ACH) 4% (0.011 ACH) 6% (0.016 ACH) 3% (0.009 ACH) 8% (0.017 ACH) % (0.009 ACH) Table 4. Mdel Errrs fr Bied Averages f Wid Dmiated Vetilati fr a Sheltered Buildig at AHHRF Huse 4: flue (464 Hurs) Huse 5: 15 cm flue (461 Hurs) Mdel Bias scatter Bias Scatter AIM- % (0.003 ACH) LBL (Sherma) 11% (0.00 ACH) VFE (Yuill/Reard) -7% ( ACH) Shaw 65% (0.030 ACH) Warre ad Webb 43% (0.07 ACH) 14% (0.006 ACH) 14% (0.008 ACH) 7% (0.004 ACH) 13% (0.007 ACH) 4% (0.011 ACH) -1% ( ACH) -60% ( ACH) -66% (-0.15 ACH) -9% (-0.1 ACH) -35% (-0.11 ACH) 4% (0.011 ACH) 8% (0.078 ACH) 3% (0.063 ACH) 30% (0.084 ACH) 6% (0.014 ACH) 1

23 Table 5. Mdel Errrs fr Bied Averages f Stack Dmiated Vetilati Huse 4: 7.5 cm flue rifice (10 Hurs) Huse 5: N flue (74 Hurs) Mdel Bias Scatter Bias Scatter AIM- -3% ( ACH) % (0.00 ACH) 1% (0.001 ACH) 7% (0.005 ACH) LBL (Sherma) -14% ( ACH) 7% (0.008 ACH) 4% (0.015 ACH) 1% (0.009 ACH) VFE (Yuill/Reard) -6% (-0.03 ACH) % (0.00 ACH) 4% (0.00 ACH) 7% (0.005 ACH) Shaw 4.6% (0.051 ACH) % (0.00 ACH) 45% (0.03 ACH) 7% (0.005 ACH) Warre ad Webb -44% ( ACH) 5% (0.006 ACH) -% ( ACH) 9% (0.007 ACH)