Probabilistic model PROMO for evaluation of air change rate distribution

Transcription

1 Probabilistic moel PROMO for evaluatio of air chage rate istributio Krystya Pietryk a Carl-Eric Hagetoft Sweish Testig a Research Istitute, Departmet of Eergy Techology, Builig Physics, Borås, SE-505, Swee Chalmers Uiversity of Techology, Departmet of Builig Techology, Builig Physics, Gotheburg, SE-496, Swee ABSTRACT: The probabilistic moel (PROMO) applie to the problem of air ifiltratio i low-rise builigs is presete. The PROMO moel allows the estimatio of the effect of variatios of climatic coitios o air exchage i a builig. I PROMO, experimetal ata are use i orer to evaluate the parameters a types of the istributios of temperature, wi spee, a wi irectio. Those istributios are employe to evaluate the istributios of air chage rate cause by air ifiltratio a ca be use to estimate probability of iaequate vetilatio. FORM (First-Orer Reliability Metho) techique is use for probabilistic approximatios. For valiatio of the PROMO moel, the probability esity fuctios of the air chage rate for the test house situate ear Gotheburg are estimate from the results of full-scale measuremets of pressure iffereces across the evelope a compare to those calculate by PROMO from the climatic parameters measure at the site. The agreemet of the results obtaie i these two ways is very goo. KEYWORDS: air ifiltratio, air chage rate, probabilistic moel, reliability, FORM INTRODUCTION The mai subect of the paper is a stuy of climate-iuce air ifiltratio i low-rise builigs. The probabilistic moel PROMO, allowig the estimatio of probability esity fuctios of air chage rate has bee evelope a valiate with the help of experimetal ata. It ca be use to evaluate the cotributio of air ifiltratio to vetilatio a eergy balace a the ifluece of that cotributio o the reliability of air exchage or reliability of eergy performace of a builig. I the cotext of air exchage, air ifiltratio costitutes a complemet to the esig of vetilatio. This complemet is ofte isregare, or cosiere i a very simplifie maer. The teecy of relyig to larger egree o atural vetilatio calls for better moellig techiques for air ifiltratio. A attempt to create such a moellig techique is presete. A moellig approach propose seems very well suite to halig the atural rivig forces goverig the rate of air ifiltratio. It also gives a possibility to quatify the probability of isufficiet or excessive air exchage (Pietryk, 000). Physical relatioships for air ifiltratio a vetilatio i builigs, which form the backgrou to the probabilistic moellig ca be fou i the AIVC publicatios (for ex. i Liamet, 986), or i (Etherige & Saberg, 996). FORM techique is use for the probabilistic approximatios of air chage rate (Pietryk & Hagetoft, b, Pietryk 000) a reliability aalysis (Pietryk, 000, c). The escriptio of FORM ca be fou i (Halar, 000, Ditlevse, 996) a also i (Pietryk & Hagetoft, a). PROBABILISTIC MODEL PROMO The probabilistic moel PROMO has bee create uer the followig assumptios: a lowrise builig with sigle vetilatio a temperature oe, the steay-state coitios of air

2 flow, the leakage area uiformly istribute over a builig compoet except for the big opeigs. The etaile escriptio of the moel ca be fou i (Pietryk & Hagetoft, b). Iput ata to the ifiltratio moel The iput ata to the ifiltratio moel cosist of raom variables (italic bol text) a etermiistic parameters. The probability esity fuctios of raom variables are estimate from the series of hourly experimetal ata. The family of istributios, typical for certai climatic parameters ca be chose.. Evirometal ata (escriptio of the site a climatic ata): wi spee a wi irectio from the earest meteorological statio (the set of measuremets or parameters of the statistical istributios) for each wi irectio sector : surface roughess, the evaluatio of the shelterig effect of the earest surrouig, exteral temperature (the set of measuremets or parameters of the statistical istributio), correlatio coefficiet betwee wi spee a exteral temperature. Parameters of a builig: geometry of the builig (the area of builig compoets A, the volume of the house V, etc.), the leakage characteristics of the house estimate for each builig compoet a/or for the whole builig, the locatio of eutral pressure layer, the orietatio of the builig agaist ifferet wi irectios, the pressure coefficiets Cp ext a Cp it for ifferet facaes a wi irectio sectors accoutig for the shelterig effect of the surrouigs 3. Serviceability ata: assume iteral temperature urig heatig seaso, itetioal opeigs Ifiltratio moel The ifiltratio moel give by Equatio is base o the superpositio of wi a stack effect (Etherige,996). Temperature ifferece across evelope, a wi spee v evaluate for each irectio sector are treate as raom variables..5 4 ACH sδt + s ΔT + s 3 ΔT + w,v + w,v + = w v (),3 3 where s, s, s 3 are etermiistic coefficiets epeet o the parameters of the flow balace for the stack effect, w,, w,, w,3 are etermiistic coefficiets epeet o the flow balace for various wi irectios. s 3600 = A a V ρ = s 3600 = A b V ρ = 3600 s = a b V ρ = =.5 3

3 w w 3600, = A a C p,, V = 3600 w, = A b C p,, V = 3600 = a C p,, b V = =,3 C p,, The coefficiets a a b escribe leakage characteristics of the builig compoet. They ca be evaluate from the results of blower oor tests carrie out o the staar compoets or they ca be assume accorig to esig values of the leakage area. Parameter gives the locatio of the compoet relate to the eutral pressure layer. The probabilistic istributios of the air chage rate are approximate usig FORM. The air chage rate follows ifferet probability istributios epeig o the cotributio a the quatity of the stack a wi forces as well as leakage istributio over the evelope. CASE STUDY Descriptio of the test house The obect of the stuy is a two-story timber-frame oe family etache house with a cocrete basemet situate ear Gotheburg. There is a ope passage betwee the basemet a the livig area. The house is surroue by a forest with trees of ifferet heights excluig the souther sie of a builig expose to a ope area. The house was costructe i 979 with the itetio of usig it for experimetal stuies i builig physics with focus o vetilatio a eergy savig. The garage with oors facig south is locate i the extee south part of the cellar as show i Figure. Figure. Obect of the stuy

4 Measuremet program The followig parameters have bee measure, as is show i Figure : leakage characteristics of the house usig blower oor tests, mea value of pressure ifferece across the 6 builig compoets with Valiye pressure trasucers, wi spee a wi irectio with the aemometer locate o a small hill about 5 m from the house, iteral a exteral temperatures. The measuremet program was carrie out for 8 moths. As a result, hourly mea ata have bee obtaie. Figure. Measuremet program for valiatio of probabilistic moel of air ifiltratio The results of the pressure rop measuremets have bee use to calculate the air exchage through the evelope. A opeig uer the garage oor has bee treate separately i the calculatio moel (see Pietryk & Hagetoft, b, Pietryk, 000). Case stuy with the help of PROMO moel The moellig flow for the PROMO moel together with the results obtaie is show i Figure 3. For each wi irectio sector the moellig proceure has bee performe. Evetually, two cases have bee istiguishe. The first oe cosierig those wi irectio sectors to which the opeig uer the garage oor has bee expose a the seco oe cocerig all remaiig wi irectio sectors. The probability esity fuctios of the air chage rate for these cases approximate usig the first orer reliability metho FORM (Pietryk & Hagetoft, a) are presete i Figure 3. For the case oe (the opeig expose to wi) a log-ormal probability esity fuctio has give the best fit accorig to Kolmogorov-Smirov test with sigificace level of For the other case, a ormal probability esity fuctio has bee fitte.

5 Figure 3. Moellig flow a the results obtaie from probabilistic approximatios usig FORM Valiatio of the PROMO moel The probabilistic moel of air ifiltratio has bee valiate o the basis of full-scale pressure ifferece measuremets carrie out o the test house. The valiatio moel is escribe i (Pietryk & Hagetoft, b). The results of air chage rate calculatios have bee show i Figure 4 i the form of histograms a probability esity fuctios fitte to those results. They preset the same cases as approximate with the help of the PROMO moel. The mea value, the staar eviatio, the skewess a the peakeess of valiatio results agree with the momets calculate for the probabilistic approximatios. Evetually, the recommee types of istributios are similar (see Figures 3 a 4). Figure 4. The results of valiatio of the PROMO moel i the form of histograms a probability esity fuctios of ACH estimate for the case - left (wi irectios: S, SE) a the case - right (other wi irectios). APPLICATION OF PROMO RESULTS The probability esity fuctios of air chage rate ca be use to evaluate the reliability of atural vetilatio for a builig but also to evaluate the reliability of the eergy performace of the builig evelope. I the cotext of eergy balace, air ifiltratio costitutes oe of may possible processes of heat exchage betwee the iterior a the exterior of a builig. Air ifiltratio ca also be cosiere from the poit of view of its ifluece o the properties

6 (thermal a structural) of builig compoets. Some parameters of the builigs, usually treate as etermiistic, are i reality epeet o climate-iuce airflow through the structure a those shoul be treate as raom variables. For some builig techologies, especially those ivolvig lightweight timber frame with mieral wool fillig, a loose mieral wool layers for roof isulatio oe ca speak about the epeece of the thermal properties of builig compoets o air ifiltratio. It is very clear for the, so calle, yamic wall (Aerli & Johasso, 983), specially esige to save eergy. The iteractio betwee thermal trasmittace a airflow through the compoets shoul be cosiere while calculatig heat loss through a builig evelope. The thermal trasmittace becomes the most iterestig parameter that ca vary with the climatic parameters a shoul be treate as a raom variable. Probabilistic escriptio of air filtratio through the wall is a importat iput to probabilistic moel of thermal trasmittace (Pietryk & Hagetoft, 004). Evetually, reliability of eergy performace for builig evelope compoets expose to various evirometal a climatic coitios ca be aalyse. Differet esig optios cocerig also the effect of air ifiltratio o variatios of thermal trasmittace of the evelope ca be calculate i the form of probability esity fuctios of heat loss characterisig eergy performace of the evelope. Aitioally, ifferet vetilatio strategies ca be cosiere i terms of reliability (Pietryk, c). CONCLUSIONS The probabilistic moel PROMO for the approximatio of probability esity fuctio of air chage rate for a aturally vetilate house o the basis of the probabilistic escriptio of climatic ata is evelope a valiate with the help of the results of full-scale pressure ifferece measuremets. The probability esity fuctios of air chage rate ca be use to evaluate the reliability of atural vetilatio for a builig but also to evaluate the reliability of the eergy performace of builig evelope. ACKNOWLEDGMENT Fiacial support of the Sweish Coucil for Builig Research is gratefully ackowlege. REFERENCES Aerli G, Johasso B. (983). Dyamic isulatio. A theoretical aalysis of thermal isulatio through which a gas or flui flows, The Sweish Coucil for Builig Research, Stockholm, Ditlevse O., Mase H.O. (996). Structural reliability methos, Egla, Joh Wiley & Sos Etherige D., Saberg M. (996). Builig Vetilatio: Theory a Measuremets, Joh Wiley & Sos Halar A., Mahaeva S. (000). Probability, Reliability a Statistical Methos i Egieerig Desig, Joh Wiley & Sos. Liamet, M.W. (986). Air Ifiltratio Calculatio Techiques - A Applicatios Guie, AIVC, Great Britai Pietryk K. (000). Probabilistic moellig of air ifiltratio a heat loss i low-rise builigs. Ph.D. thesis, ISSN X, School of Architecture, Chalmers Uiversity of Techology, Gotheburg, Swee. Pietryk K., Hagetoft C-E. (a). Reliability aalysis i builig physics esig. Accepte for publicatio i Builig a Eviromet Pietryk K., Hagetoft C.-E. (b). Probabilistic aalysis of air ifiltratio. Accepte for publicatio i Builig a Eviromet Pietryk K., Hagetoft C.-E. (004). Probabilistic moellig of yamic U-value. Performace of Exterior Evelopes of Whole Builigs IX, Floria, USA Pietryk K. (c). Probability-base esig i vetilatio. Submitte for publicatio to The Iteratioal Joural of Vetilatio.