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Building nd Environment 54 (22) 6e25 Contents lists ville t SciVerse ScienceDirect Building nd Environment journl homepge: www.elsevier.com/locte/uildenv A resistnce-cpcitnce network model for the nlysis of the interctions etween the energy performnce of uildings nd the urn climte Bruno Bueno,, *, Leslie Norford, Grégoire Pigeon, Rex Britter Msschusetts Institute of Technology, Cmridge, MA, USA CNRM-GAME, Météo Frnce nd CNRS, Toulouse, Frnce rticle info strct Article history: Received August 2 Received in revised form 29 Jnury 22 Accepted 3 Jnury 22 Keywords: Anthropogenic het Building energy model Stte-spce Urn cnopy model Urn het islnd This pper presents n urn cnopy nd uilding energy model sed on therml network of constnt resistnces nd cpcitnces. The RC model represents the fundmentl physicl reltions tht govern the energy interctions etween uildings nd their urn environment, retining the sensitivity to the design prmeters typiclly used in uilding energy nd urn climte studies. The enefits of the RC model re its simplicity nd computtionl efficiency. It llows for etter understnding the physics of the prolem nd mkes it possile to esily evlute modelling hypotheses nd the sensitivity of different prmeters. In this study, the RC model is evluted ginst dvnced simultion tools tht re well ccepted nd evluted within their individul scientific communities. The model is then used in series of prmetric nlyses to investigte the impct of the Urn Het Islnd effect on the energy consumption of uildings in configurtions tht re prmeterized in terms of internl het gins, construction, geometry, glzing rtio, nd infiltrtion level. The RC model is lso used to investigte the dominnt mechnisms y which the indoor environment ffects outdoor ir tempertures. Prmeters such s indoor ir tempertures, exfiltrtion het, nd wste het from HVAC systems re nlysed. The conclusions otined y this study cn e pplied to wide rnge of urn configurtions. Ó 22 Elsevier Ltd. All rights reserved.. Introduction Urniztion produces higher ir tempertures in cities thn in the undeveloped rurl surroundings [,2]. This phenomenon, known s the Urn Het Islnd (UHI) effect, is usully more intense under cloudless sky nd light wind conditions nd is minly cused y the geometric nd construction differences etween the urn nd rurl surfces [3] nd the nthropogenic het relesed in the urn environment [4]. The UHI effect cn increse cooling energy consumption of uildings [5,6] ut cn lso reduce the heting energy consumption in winter. Different numericl models hve een developed in the lst two decdes to nlyse the cuses nd consequences of the UHI effect. The Cluster Therml Time Constnt (CTTC) model [7] clcultes urn ir tempertures from mesurements t rurl meteorologicl sttion, pplying simple nlyticl expressions tht tke into ccount the storge nd relese of het in the uilt re. The model represents the urn re s lumped ody chrcterized y sky view fctor nd CTTC prmeter tht mesures its therml inerti. * Corresponding uthor. Msschusetts Institute of Technology, 77 Msschusetts Ave., R.5-44, Cmridge, 239 MA, USA. Tel.: þ 857 654 99. E-mil ddress: ueno@mit.edu (B. Bueno). The new genertion of urn cnopy models is sed on the surfce energy lnce [8], which ccounts for the re-verged fluxes through the surfce of n imginry ox tht represents n urn cnyon. The literture reports different urn cnopy models, which re sed on physicl or empiricl pproches to the surfce energy lnce. The Town Energy Blnce (TEB) model [9e2] is physiclly-sed urn cnopy model tht considers two-dimensionl pproximtion of n urn cnyon formed y three generic surfces: wll, rod, nd roof. It clcultes the climte conditions, the drg force nd energy fluxes of town or neighourhood formed y identicl urn cnyons, where ll the orienttions re possile nd ll exist with the sme proility. To represent the effect of the energy performnce of uildings on the urn climte, simplified uilding energy models re implemented in urn cnopy models [3,4]. These models re le to cpture the min het trnsfer processes tht occur inside uildings nd to clculte uilding energy demnd, heting, ventiltion nd ir-conditioning (HVAC) energy consumption nd wste het emissions [5,6]. Given the inherent interreltions etween uilding energy nd urn climte studies, Coupled Scheme (CS) etween detiled uilding energy progrm, EnergyPlus [7], nd the TEB model hs een developed [8] to more profoundly integrte oth fields of study. 36-323/$ e see front mtter Ó 22 Elsevier Ltd. All rights reserved. doi:.6/j.uildenv.22..23

B. Bueno et l. / Building nd Environment 54 (22) 6e25 7 Nomenclture C CHTC COP f wste GR k l v _m s Q R t T u ex U VH ld VH ur Cpcitnce W s K Convective het trnsfer coefficient W m 2 K Coefficient of performnce of n HVAC system Frction of wste het relesed into the urn cnyon Glzing rtio Therml conductivity W m K Wter condenstion het J kg Mss flow rte kg s Het flux W/W m 2 Resistnce K W Time s Temperture C, K Exchnge velocity m s Window U-fctor W m 2 K Verticl-to-horizontl uilding re rtio, defined s exterior verticl uilding re divided y uilding pln re, VH ld ¼ VH ur =r ld Verticl-to-horizontl urn re rtio, defined s exterior verticl uilding re divided y the pln re V o w r ld rc p s of the urn site (this prmeter is n input in the TEB model) Infiltrtion/exfiltrtion irflow rte ACH Specific humidity kg kg Solr sorptivity Building density, defined s uilding pln re divided y the pln re of the urn site (this prmeter is n input in the TEB model). Volumetric het cpcity J m 3 K Window trnsmittnce Suscripts tm Atmosphere ig Internl het gins in Indoor ir HVAC Building energy demnd lt Dehumidifiction energy s Supply sol Solr rdition ur Conditions inside the urn cnyon wste Wste het from HVAC systems As complement to the sophisticted models ove mentioned, this pper presents n urn cnopy nd uilding energy model sed on therml network of constnt resistnces nd cpcitnces. The enefits of the RC model re its simplicity nd computtionl efficiency. The model represents the fundmentl physicl reltions tht govern the reciprocl energy interctions etween uildings nd the urn environment, retining the sensitivity to the design prmeters typiclly used in uilding energy nd urn climte studies. The RC model is sed on stte-spce formultion tht cn e very efficiently solved y numericl progrm, such s Mtl. This llows for fster prmetric nlyses nd mkes it possile to esily evlute modelling hypothesis nd the sensitivity of different prmeters. The RC model cn e used s reserch nd didctic tool nd hs the potentil to ecome n opertionl tool for the design nd nlysis of uildings nd urn res. In this pper, the RC model is descried nd evluted ginst the CS for summer nd winter nd for different scenrios of wste het emissions. The model is then used in series of prmetric nlyses to investigte the impct of the UHI effect on the energy consumption of uildings for different uilding configurtions. The model is lso used to investigte the dominnt mechnisms y which the indoor environment nd the energy performnce of uildings ffect outdoor ir tempertures. The conclusions of this study cn e pplied to wide rnge of uilding nd urn configurtions. 2. The urn RC model Fig. shows the therml RC network model of the indoor nd outdoor environments. The indoor environment represents single-zone uilding with n internl therml mss. The outdoor environment represents n verge-oriented urn cnyon, composed of generic fçde nd generic rod. 2.. Physics The RC model represents the following het trnsfer phenomen nd clcultions: Trnsient het conduction through uilding wlls nd roof Stedy stte het conduction through windows Solr trnsmission through windows Het storge in intermedite floor constructions Longwve rdint het exchnge mong interior surfces (wll, roof, nd mss) Sensile het lnce of the indoor ir, including the convective het fluxes from wlls, windows, roof, nd intermedite floors, the convective frction of internl het gins, the het fluxes due to infiltrtion nd ventiltion ir, nd the het fluxes from the HVAC system. Sensile het lnce of the urn cnyon ir, including the convective het fluxes from wlls, windows nd the rod, the sensile het exchnge etween the cnyon ir nd the tmosphere, the het fluxes due to exfiltrtion nd exhust ir, nd the wste het from HVAC equipment. Solr rdition sored y wlls, roof, nd rod ssuming n verge orienttion of n urn cnyon [9] Het storge in the rod soil Wll-sky, rod-sky, roof-sky, nd wll-rod longwve rdint het exchnges, tking into ccount the view fctors etween ech pir of elements. This represents the longwve trpping of urn res due to reduced sky view fctors. 2.2. Assumptions The ojective of the RC model is to cpture the fundmentl physicl reltions tht govern the indoor nd outdoor energy interctions, while keeping stte-spce formultion tht cn e efficiently solved. This implies constnt resistnces nd cpcitnces in the therml network represented in Fig.. The rte of het exchnge etween the urn cnyon ir nd the tmosphere is usully chrcterized y n exchnge velocity (u ex ), which cn e defined s: u ex ¼ Q tm rc p ðt ur T tm Þ where Q tm is the sensile het exchnge etween the urn cnyon nd the tmosphere, T ur is the urn cnyon men ir temperture, nd T tm is the ir temperture ove the urn cnopy lyer. Preliminry results otined with the RC model ()

8 B. Bueno et l. / Building nd Environment 54 (22) 6e25 Fig.. Representtion of n urn cnopy nd uilding energy model sed on therml network of constnt resistnces nd cpcitnces. A cpcitnce is ssocited with ech temperture node. Nodes re connected y resistnces. The het sources of ech node re represented y rrows. Four nodes re used to clculte the het trnsfer through the wll, the roof nd the rod. showed tht urn cnyon ir tempertures re sensitive to the vlues of the exchnge velocity. Different methods re proposed in the literture to clculte exchnge velocities. In this version of the RC model, the correltions of Louis (979) [9] re used. In this method, exchnge velocities depend on the Richrdson numer, which is mesure of the ir stility inside the cnyon nd is function of the cnyon ir temperture clculted y the RC model. Therefore, n itertion of the RC model is required to mtch the input nd clculted exchnge velocities. As consequence of the stte-spce formultion, the RC model ssumes tht the convection het trnsfer coefficients (CHTC) nd the exchnge velocities remin invrint during the simultion. In detiled uilding energy progrms nd urn cnopy models, the CHTC cn e clculted y correltions s function of the wind speed nd surfce-ir temperture difference. Exchnge velocities usully depend on geometry, roughness length for momentum nd het, wind speed, nd tmospheric stility. Even so, the RC model is le to reproduce the verge diurnl cycle of the results of more sophisticted models y using the verge exchnge velocity clculted y correltions for the simultion period. Other ssumptions of the RC model include: Constnt indoor ir temperture. Constnt infiltrtion nd ventiltion irflow rte. Constnt internl het gins. Single-zone uilding with intermedite floors represented s n internl therml mss. The trnsmitted solr rdition nd the rdint frction of internl het gins re perfectly sored y the internl therml mss nd then re relesed into the indoor environment. Aditic uilding floor. This condition is resonle if the floor is well insulted. Idel HVAC system: the energy supplied y the system equls the uilding energy demnd, nd the energy consumption is clculted from constnt efficiency. Well-mixed ir inside the urn cnyon. This is resonle ssumption for reltively homogenous urn cnopies composed of low-rise to medium-rise uildings. Building, crs, nd other het sources keep positive uoyncy level inside urn cnyons, even t night, nd enhnce the mixing of ir inside the urn cnopy. Linerized rdition formultion nd one-ounce pproximtion for indoor nd outdoor longwve rditive het exchnges. 2.3. Stte-spce formultion The RC model is derived from energy conservtion principles. For ech cpcitnce node (Fig. ), the rte of chnge of its internl energy is relted to the het fluxes reching the node. This cn e generlly expressed s: C j dt j dt ¼ X k R k Tk T j þ X Qj (2) where C j nd T j represent the cpcitnce nd temperture of the node j, R k nd T k represent the resistnce nd temperture of the nodes k tht interct with the node j, nd Q j represents the het fluxes cting on the node j. Using these reltions, stte-spce formultion cn e set up nd efficiently solved y numericl simultion tool, such s Mtl. The generl formultion cn e written s: dt j ðtþ ¼ A$T dt j ðtþþb$u j ðtþ (3) where T j (t) is vector of stte vriles tht correspond to ech of the temperture nodes ssocited with cpcitnce, u j (t) is

B. Bueno et l. / Building nd Environment 54 (22) 6e25 9 vector of inputs tht cn e known tempertures or het fluxes, nd A nd B re coefficient mtrices. 2.4. Het fluxes The trnsmitted solr rdition is otined y multiplying the solr rdition tht reches the verge-oriented wll y constnt window trnsmittnce provided y the user. In the cse of cooling sitution, wste het from the outdoor equipment is relesed into the outdoor environment (Q wste ). The wste het is clculted s function of the cooling energy demnd of the uilding (Q HVAC ) nd the energy consumed y the HVAC system to dehumidify the ir tht psses through the cooling coil (Q lt ): Q wste ¼ f ðq HVAC þ Q lt Þ (4) where the function f depends on the coefficient of performnce (COP) of the cooling system, f ¼ ð þ =COPÞ. The dehumidifiction energy (Q lt ) is otined y ssuming tht the ir enters the cooling coil t indoor conditions nd leves the cooling coil t supply temperture nd t 9% reltive humidity. Then, Q lt ¼ _m s l v ðw in w s Þ (5) where _m s is the supply mss flow rte; l v is the wter condenstion het; w s is the supply specific humidity, clculted from the supply temperture (T s ) nd 9%RH; nd w in is the specific humidity of the indoor ir, clculted from the set-point of temperture nd reltive humidity provided y the user. To otin the supply mss flow rte, the model requires the mximum sensile cooling lod of the uilding, which is clculted through the simultion. Therefore, n itertion of the RC model is required in order to clculte wste het emissions. 2.5. Boundry conditions, inputs nd outputs As oundry conditions, the RC model requires time-step vlues of ir tempertures nd wind speed t the top of the urn cnyon (ove the urn cnopy lyer), solr het fluxes over the horizontl, nd incoming longwve rdition or equivlent sky temperture. The inputs of the model re construction nd geometric informtion, internl het gins, indoor therml nd humidity set-points, supply ir temperture of the HVAC system, mximum sensile cooling lod clculted through itertion of the model, CHTC of the different surfces, nd exchnge velocity etween the urn cnyon nd the tmosphere clculted through itertion of the model (see Tle for specific inputs). The outputs of the model re the verge diurnl cycles of node tempertures, het fluxes, uilding energy demnd, nd wste het emissions for the simultion period. Tle Inputs of the RC model used in the comprison of the model with the Coupled Scheme. This configurtion represents the dense urn centre of Toulouse (Frnce). The term fl indictes tht mximum sensile cooling lod refers to the used re of the uilding. diurnl cycles clculted y the RC model nd the CS for fifteen dys in summer nd fifteen dys in winter re compred. 3.. Building energy demnd Settings Loction Toulouse (Ltitude: 43.48 ; Longitude:.3 ) Simultion time-step 8 s Simultion period Summer: 7/5e7/3 Winter: 2/e2/6 Averge uilding height 2 m Building density.68 Verticl-to-horizontl urn.5 re rtio Floor height 3m Glzing rtio.3 COP of the cooling system 2.5 Frction of wste het mixed. with the urn cnyon ir Indoor ir temperture Summer: 25 C Winter: 2 C Indoor reltive humidity 5% Supply temperture of the 4 C cooling system Internl het gins Residentil: 6.25 W m 2 (fl) Commercil: 3.75 W m 2 (fl) Rdint frction of internl.2 het gins Ltent frction of internl.2 het gins Indoor convective het 2. W m 2 K trnsfer coefficient (CHTC) Indoor rditive het 6. W m 2 K trnsfer coefficient CHTC rod-ir 5 W m 2 K CHTC wll-ir 25 W m 2 K CHTC roof-ir 2 W m 2 K Indoor therml mss construction Concrete e 2 cm, k ¼ 2. W m K, rc p ¼.874$ 6 Jm 3 K Wll nd roof construction Inner lyer: Insultion e 3 cm, k ¼.3 W m K, rc p ¼ 5.23$ 4 Jm 3 K Outer lyer: Brick e 3 cm, k ¼.5 W m K, rc p ¼.58$ 6 Jm 3 K, ¼.68 Rod construction Ground e.25 m, k ¼.4 W m K, rc p ¼.4$ 6 Jm 3 K, ¼.92 Window construction s ¼.6; U ¼ 2.5 W m 2 K Infiltrtion.5 ACH Fig. 2 compres the sensile cooling energy demnd in summer nd the heting energy demnd in winter clculted y the RC model nd the CS. The root men squre error (RMSE) nd men is error (MBE) of the comprison is presented in Tle 3. As cn e seen, the RC model is le to reproduce the uilding energy 3. Simultion-sed model evlution In this section, the RC model is compred with the EnergyPlus- TEB Coupled Scheme (CS) [8]. The CS ws evluted with field dt from the experiment CAPITOUL conducted in Toulouse (Frnce) from Ferury 24 to Mrch 25 [2]. The sme cse study is used for the evlution of the RC model. Tle descries the inputs of the RC model used in this study. Three different cse studies re compred (Tle 2). The first two cses re summertime simultions of residentil nd commercil uilding, respectively. The third cse corresponds to wintertime simultion of residentil uilding. The verge Tle 2 Cse studies used in the comprison of the RC model with the Coupled Scheme, nd inputs of the RC model otined through itertion for ech cse study. The term fl indictes tht mximum sensile cooling lod refers to the used re of the uilding. In winter, the model ssumes tht there re no wste het emissions from the HVAC system, nd the mximum sensile cooling lod is not used in the simultion. Prmeter Cse Cse 2 Cse 3 Seson Summer Summer Winter Internl het gins Residentil Commercil Residentil Prmeters otined through itertion Exchnge velocity.29 m s.3 m s.3 m s Mximum sensile cooling lod.3 W m 2 (fl) 32. 3 W m 2 (fl) e

2 B. Bueno et l. / Building nd Environment 54 (22) 6e25 which evlute errors. The RMSE ssocited with the trnsmitted solr rdition clculted y oth models rnges etween.3 nd.8 W m 2 of floor re. Negtive MBE vlues of trnsmitted solr rdition indicte tht the RC model overestimtes this prmeter systemticlly. In ddition, the solr trnsmission error is high compred to its reference vlue, which cn e explined y the simplifictions mde in the RC model for its clcultion. Interior wll nd mss surfce tempertures re well cptured y the RC model with RMSE etween. nd.6 K. 3.2. HVAC wste het emissions Fig. 3 shows the verge diurnl cycle of wste het emissions in summer clculted y the RC model nd the CS. As cn e seen, the RC model is le to reproduce the wste het emissions predicted y the CS with RMSE round 6.5 W m 2 of urn re, where the verge wste het flux clculted y the CS is 55 W m 2 for the residentil cse nd 22 W m 2 for the commercil cse. 3.3. Urn ir tempertures Fig. 2. Averge diurnl cycle of sensile cooling energy demnd of () cse nd () cse 2 for summer, July 5eJuly 3, nd verge diurnl cycle of heting energy demnd of (c) cse 3 for winter, Ferury eferury 6, clculted y the RC model nd y the Coupled Scheme. performnce predicted y the CS with RMSE etween.3 nd.8 W m 2 of floor re. These vlues re much lower thn the verge uilding energy demnd clculted y the CS for the simultion period, which is tken s the reference vlue (REF) to Fig. 4 represents the verge diurnl cycle of ir tempertures inside the urn cnyon clculted y the RC model, the CS, nd the TEB scheme. In cse, in which wste het emissions re round 55 W m 2 of urn re, the three models predict similr urn ir tempertures. The RMSE etween the RC model nd the CS is.4 K, where the verge temperture difference etween the cnyon nd the tmosphere is.2 K. Cse 2 presents wste het emissions of round 22 W m 2 of urn re, nd the urn ir tempertures clculted y the RC model nd the CS re round K higher thn those clculted y the TEB model, which does not ccount for wste het emissions. The RMSE etween the RC model nd the CS is lso.4 K, eing the reference vlue 2. K. These reltive errors re cceptle given the importnt uncertinties relted to urn climte predictions. In winter (cse 3), the three models predict similr urn ir tempertures. The RMSE etween the RC model nd the CS is.5 K, for which the reference cnyon-tmosphere temperture difference is.7 K. Although the reltive difference etween the error nd the reference vlue is higher in wintertime, the fct tht for the three cses the error is very similr suggests tht this is systemtic nd proly relted to the different methods used to clculte exchnge velocities. A systemtic error will cncel when compring different simultions with the RC model, s in the prmetric nlyses of the following sections. In terms of wll nd rod surfce tempertures, the RMSE etween RC nd CS rnges etween.7 K nd.6 K. The reference Tle 3 Root men squre error (RMSE), men is error (MBE), nd reference vlue (REF) of the comprison etween the Coupled Scheme (CS) nd the RC model. The reference vlue of outdoor ir temperture is the verge of the difference etween the outdoor ir temperture clculted y the CS nd the tmospheric temperture. The reference vlue of indoor nd outdoor surfce tempertures is the verge of the difference etween the surfce tempertures clculted y the CS nd the indoor nd outdoor ir temperture, respectively. The reference vlue of energy nd het fluxes is the verge of the energy nd het fluxes clculted y the CS. The term ur indictes unit of urn re nd the term fl indictes unit of used re of the uilding. Cse Cse 2 Cse 3 Prmeter RMSE MBE REF RMSE MBE REF RMSE MBE REF Urn ir temperture (K).4.2.2.4. 2..5.5.7 Rod surfce temperture (K).7.7 2.7.6.4 2.6.6.4.7 Exterior wll surfce temperture (K).2.3.2.3.6..5.4.6 Wste het emissions (W m 2 ur) 6.8 5.4 55.2 6.2.5 29.9 Interior wll surfce temperture (K).7.3.3.8.3.3.7 Mss surfce temperture (K).8.2.2.8.6.6.7 Trnsmitted solr rdition (W m 2 fl).8.7 2.6.8.7 2.6.3.2.9 Building energy demnd (W m 2 fl).2. 6.3.8.7 26.6.3.2 6.4

B. Bueno et l. / Building nd Environment 54 (22) 6e25 2 Air temperture (C) 45 4 35 3 25 2 RC CS TEB Air temperture (C) 5 4 8 2 6 2 45 4 35 3 25 2 RC CS TEB Fig. 3. Averge diurnl cycle of HVAC wste het emissions of () cse nd () cse 2 for summer, July 5eJuly 3, clculted y the RC model nd y the Coupled Scheme. vlues for these prmeters cn e of the sme mgnitude or even lower, which cn e explined y the generic vlues of CHTC used s inputs of the model. A etter greement of surfce tempertures cn e otined y using the verge CHTC clculted y the CS. However, our simultions show tht these differences in surfce tempertures do not hve significnt effect on urn ir tempertures. 4. Impct of the UHI effect on the energy performnce of uildings In this section, the RC model is used to nlyse the impct of the UHI effect on the energy performnce of uildings. A series of simultions is crried out imposing outdoor conditions (T ur ) to the RC model. This is chieved y using outdoor tempertures s oundry conditions t the top of the urn cnyon nd introducing high exchnge velocity etween the urn cnyon nd the tmosphere. The outdoor conditions used in this nlysis correspond to UHI scenrio mesured during the CAPITOUL experiment (Tle 4). The dependence of the uilding energy performnce to other UHI scenrios is lso tested. Five cse studies re nlysed (Tle 5). The first three cses re simulted using summer outdoor conditions nd the lst two using winter outdoor conditions. Cses, 2, 4, nd 5 correspond to residentil uilding with nd without insulted wlls. Cse 3 corresponds to commercil uilding with insulted wlls. Fig. 5 shows the dily-verge chnge in sensile energy demnd due to the UHI effect for different uilding glzing rtios. In Fig. 5, the energy demnd chnge is divided y the ctul energy demnd of the uilding. The grphs show the solute vlue of the chnge in energy demnd, which is positive in summer nd negtive in winter. Fig. 5 shows tht the UHI effect hs greter impct on the uilding energy performnce for higher glzing rtios. As expected, the slope is lower for the cses in which wlls re not insulted, nd there is convergence in energy demnd c Air temperture (C) 5 4 8 2 6 2 25 2 5 5 RC CS TEB 4 8 2 6 2 Fig. 4. Averge diurnl cycle of urn ir tempertures of () cse nd () cse 2 for summer, July 5eJuly 3, nd of (c) cse 3 for winter, Ferury eferury 5, clculted y the RC model, y the Coupled Scheme, nd y the Town Energy Blnce scheme. chnge etween insulted nd uninsulted cses for higher glzing rtios. The fct tht the rtio of energy demnd chnge due to the UHI effect is decresing in summer for higher glzing rtios is explined y the fct tht the overll uilding energy demnd increses fster thn the energy demnd chnge due to the UHI effect for higher glzing rtios. The results show smll influence of the glzing rtio nd wll insultion on the rtio of energy demnd chnge due to the UHI effect. Fig. 6 shows the dily-verge rtio of energy demnd chnge due to the UHI effect for different infiltrtion irflow rtes nd Tle 4 Mesured urn nd rurl outdoor ir tempertures used to nlyse the impct of the UHI effect on the energy performnce of uildings. Summer Winter Design dy 7/3/4 2/26/5 Mximum urn-rurl Night 4. 5.3 temperture difference (K) Dy.3.9

22 B. Bueno et l. / Building nd Environment 54 (22) 6e25 Tle 5 Cse studies used to nlyse the interctions etween uildings nd the urn environment. In the insulted cses, the uilding wll is composed of 3 cm rick nd n inner lyer of 3 cm insultion. In the uninsulted cses, the uilding wll is composed of 3 cm rick. Internl het gin vlues for the residentil nd commercil cses, s well s other uilding nd urn prmeters re defined in Tle. Cses Insultion Building use Design dy Yes Residentil Summer 2 No Residentil Summer 3 Yes Commercil Summer 4 Yes Residentil Winter 5 No Residentil Winter Rtio of energy demnd chnge.5.4.3.2. verticl-to-horizontl uilding re rtios. Infiltrtion het gins cn e n importnt frction of the uilding energy demnd, ove ll in winter when the temperture difference etween indoor nd outdoor environments is high. The UHI effect modifies the het gin due to infiltrtion, incresing the cooling energy demnd in summer nd decresing the heting energy demnd in winter. The verticl-to-horizontl uilding re rtio determines the reltive mount of uilding surfce re exposed to the outdoor environment nd, therefore, ffected y the UHI effect y mens of het trnsmission through wlls nd windows. The grphs show significnt influence of the infiltrtion level nd wek dependence on the verticl-to-horizontl uilding re rtio. Hving more uilding surfce exposed to the outdoor environment usully Rtio of energy demnd chnge.5.5 Infiltrtion (ACH).5.4.3.2. 5 5.5.5 2 2.5 3 Verticl-to- horizontl uilding re rtio Fig. 6. Dily-verge chnge in sensile energy demnd due to the UHI effect divided y the overll sensile uilding energy demnd for different () infiltrtion irflow rtes nd () verticl-to-horizontl uilding re rtios. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; 3. summer, commercil, insulted wlls; 4. winter, residentil, insulted wlls; nd 5. winter, residentil, uninsulted wlls. Other prmeter settings re Tin ¼ 22 C, GR ¼.4, VH ld ¼ 2, nd Vo ¼.5 ACH. Rtio-of energy demnd chnge.2.4.6.8 Glzing rtio.5.4.3.2..2.4.6.8 Glzing rtio implies more infiltrtion through opening crcks, ut this effect is not tken into ccount in this nlysis. The results suggest tht the min mechnism y which the UHI effect influences the indoor environment is the outdoor ir entering the uilding, which cn e produced y infiltrtion ut lso y nturl or forced ventiltion. The UHI impct from the conductive het trnsfer through the uilding enclosure is reltively smll. The rtio of energy demnd chnge for different UHI effect scenrios (Fig. 7) is represented in Fig. 8, which shows liner reltionship. For residentil uildings in summer, the results show 5% increse in cooling energy demnd per K increse in the mximum UHI effect t night. A similr order of mgnitude decrese in heting energy demnd is lso produced y n equivlent wintertime UHI effect. Commercil uildings, usully dominted y internl het gins, re less influenced y the outdoor environment, nd therefore not significntly ffected y the UHI effect if they do not hve uilding systems with close interction with the outdoor environment such s economizers or nturl ventiltion. Fig. 5. Dily-verge chnge in sensile energy demnd due to the UHI effect for different uilding glzing rtios. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; 3. summer, commercil, insulted wlls; 4. winter, residentil, insulted wlls; nd 5. winter, residentil, uninsulted wlls. Results re given in () solute form nd () reltive form divided y the overll sensile uilding energy demnd. Other prmeter settings re Tin ¼ 22 C, VH ld ¼ 2, nd Vo ¼.5 ACH. 5. Impct of the energy performnce of uildings on the outdoor environment In this section, prmetric nlysis is crried out with the RC model to investigte the impct of the indoor energy performnce

B. Bueno et l. / Building nd Environment 54 (22) 6e25 23 4 35 Tle 6 Meteorologicl conditions ove the urn cnyon used to nlyse the impct of the energy performnce of uildings on the outdoor environment. Summer Winter 3 25 =K =2K =4K =6K =9K Design dy 7/3/4 /26/5 Mximum ir temperture 35. C.2 C Dily ir temperture rnge 5.6 K 2.8 K Averge wind speed 5. m s 5. m s 2 5.. Effect of the indoor environment without wste het emissions 5 4 8 2 6 2 5 5 =K =2K =4K =6K =9K Without considering wste het emissions, chnge in the indoor therml conditions cn ffect the outdoor environment y het conduction through the uilding enclosure, which modifies outdoor surfce tempertures nd end up ffecting outdoor ir tempertures y convective het trnsfer. A chnge in the indoor environment cn lso hve n impct on outdoor ir tempertures through exfiltrtion. Assuming tht ll the ir tht enters uilding through infiltrtion leves it t indoor ir temperture, there is n exfiltrtion het flux ssocited with the indooreoutdoor temperture difference, which would e more importnt in winter thn in summer. 5 4 8 2 6 2 Fig. 7. Diurnl cycles of urn ir temperture in () summer nd in () winter for different mximum urn-rurl ir temperture difference. on urn ir tempertures. Tle 6 summrizes the oundry conditions ove the urn cnyon used in this nlysis. The summer nd the winter design dys correspond to hot nd cold dy, respectively, mesured in Toulouse during the CAPITOUL experiment. The verge wind speed ove the urn cnyon is set up to 5 m s. The dependence of outdoor tempertures to this prmeter is lso tested. The sme five cse studies presented in the previous section re nlysed (Tle 5). Air temperture chnge (K).8.6.4.2.2.4.6.8 Glzing rtio Rtio of energy demnd chnge.5.4.3.2. 2 4 6 8 Urn Het Islnd (K) Fig. 8. Dily-verge rtio of energy demnd difference for different mximum urnrurl ir temperture difference. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; 3. summer, commercil, insulted wlls; 4. winter, residentil, insulted wlls; nd 5. winter, residentil, uninsulted wlls. Other prmeter settings re Tin ¼ 22 C, GR ¼.4, VH ld ¼ 2, nd Vo ¼.5 ACH. Air temperture chnge (K).8.6.4.2 2 22 24 26 28 Indoor tempeture (C) Fig. 9. () Dily-verge difference in outdoor ir temperture due to chnge in indoor ir temperture from 22 Cto27 C in summer nd from 7 Cto22 Cin winter for different uilding glzing rtions. () Dily-verge outdoor ir temperture difference due to chnge in exfiltrtion irflow rte from. to.5 ACH for different indoor ir tempertures in summer nd in winter. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; 3. summer, commercil, insulted wlls; 4. winter, residentil, insulted wlls; nd 5. winter, residentil, uninsulted wlls. Other prmeter settings re r ld ¼.5, VH ur ¼, GR ¼.4, f wste ¼., nd Vo ¼. ACH.

24 B. Bueno et l. / Building nd Environment 54 (22) 6e25 Fig. 9 shows the dily-verge difference in outdoor ir temperture due to n increse in the indoor ir temperture of 5 K in summer nd in winter for different uilding glzing rtios. As cn e seen, indoor ir tempertures hve smll influence on the outdoor environment when there re no wste het emissions from ir-conditioning systems nd no exfiltrtion het. Fig. 9 shows the dily-verge difference in outdoor ir temperture due to chnge in the exfiltrtion irflow rte from. to.5 ACH for different indoor ir tempertures. As cn e seen, exfiltrtion hs n unimportnt influence on the outdoor environment in summer, ut it might e relevnt in some winter situtions. Due to the high indooreoutdoor temperture difference, the exfiltrtion het flux cn e compred to other urn fluxes in cloudy dy in winter. Air temperture chnge (K) 3 2.5 2.5.5.2.4.6.8 Building density 5.2. Effect of wste het emissions 3 Wste het emissions from HVAC systems re significnt sources of het in the energy lnce of n urn cnyon. Fig. shows the dily-verge difference in outdoor ir temperture due to the wste het from ir-conditioning systems in summer for different indoor ir temperture vlues. Dily-verge wste het emissions re represented in Fig.. Commercil uildings, due to their high internl het gins, hve greter impct on the outdoor environment. Fig. represents the dily-verge difference in outdoor ir temperture due to wste het emissions for different uilding densities. This prmeter, typiclly used in urn plnning, hs Wste het (W m 2 ) 25 2 5 5.2.4.6.8 Building density Air temperture chnge (K) 3 2.5 2.5.5 2 22 24 26 28 Indoor tempeture (C) Fig.. Dily-verge () difference in outdoor ir temperture due to wste het emissions nd () wste het emissions in summer for different uilding densities. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; nd 3. summer, commercil, insulted wlls. Other prmeter settings re VH ur ¼, Vo ¼.5 ACH, GR ¼.4, nd Tin ¼ 22 C. significnt impct on outdoor ir tempertures. This cn e seen y the fct tht to condition igger indoor spces in summer implies pumping more het into smller outdoor environment, nd therefore outdoor ir tempertures sor. The wind speed ove the urn cnopy ffects the het exchnge rte etween the urn cnyon nd the tmosphere through the verge exchnge velocity used in the RC model. Fig. 2 3 3 Wste het (W m 2 ) 25 2 5 5 Air temperture chnge (K) 2.5 2.5.5 2 22 24 26 28 Indoor tempeture (C) 2 4 6 8 Forcing wind speed (m s ) Fig.. Dily-verge () difference in outdoor ir temperture due to wste het emissions nd () wste het emissions in summer for different indoor ir tempertures. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; nd 3. summer, commercil, insulted wlls. Other prmeter settings re r ld ¼.5, VH ur ¼, Vo ¼.5 ACH, nd GR ¼.4. Fig. 2. Dily-verge difference in outdoor ir temperture due to wste het emissions in summer for different wind speeds ove the urn cnopy lyer. The following cses re nlysed:. summer, residentil, insulted wlls; 2. summer, residentil, uninsulted wlls; nd 3. summer, commercil, insulted wlls. Other prmeter settings re r ld ¼.5, VH ur ¼, Vo ¼.5 ACH, GR ¼.4, nd Tin ¼ 22 C.

B. Bueno et l. / Building nd Environment 54 (22) 6e25 25 shows the dependence of the urn cnyon ir temperture chnge due to wste het emissions on the wind speed ove the urn cnopy. For the residentil cses, in which wste het emission re round W m 2 of urn re, the increse in outdoor temperture rnges etween.5 K for wind speed of m s nd K for wind speed of 2 m s. For the commercil cse, in which the verge wste het flux is 22 W m 2 of urn re, the increse in outdoor temperture rnges etween.2 K for wind speed of m s nd 2.2 K for wind speed of 2 m s. It cn e concluded tht, for uilding densities lower thn.6, the increse in outdoor ir temperture is pproximtely proportionl to the het flux per unit of urn re relesed into the urn cnyon with reltion of K per W m 2 for low wind speeds nd.5 K per W m 2 for high wind speeds. 6. Conclusion A simple urn cnopy nd uilding energy model, sed on therml network of constnt resistnces nd cpcitnces, hs een presented. The urn RC model represents the fundmentl physicl reltions tht govern the energy interctions etween uildings nd their urn environment. The model is evluted ginst coupled scheme etween uilding simultion progrm, EnergyPlus, nd n urn cnopy model, TEB, for summer nd winter conditions nd for different uilding configurtions. The model is then used in series of prmetric nlyses to investigte the impct of the UHI effect on the energy consumption of uildings. For residentil uildings in summer, 5% increse in cooling energy demnd cn e expected per K increse in the mximum UHI effect (usully t night). A similr order of mgnitude decrese in heting energy demnd of residentil uilding cn e expected y n equivlent wintertime UHI effect. Commercil uildings re not significntly ffected y the UHI effect if they re not nturlly-ventilted. Depending on the proportion of cooling nd heting dys of ech prticulr climte nd the type of system used to meet uilding energy demnds, the UHI effect cn hve positive or negtive impct on the overll energy consumption of cities. The min mechnism y which the UHI effect influences the indoor energy performnce is infiltrtion nd ventiltion; the impct from the conductive het trnsfer through the uilding enclosure is reltively smll. This result highlights the importnce of considering the UHI effect in the design nd nlysis of uilding systems, such s nturl ventiltion or economizers, in which the outdoor ir entering the uilding plys criticl role. The RC model is lso used to investigte the dominnt mechnisms y which the indoor environment ffects outdoor ir tempertures. In wintertime, exfiltrtion het fluxes cn hve noticele effect on outdoor ir tempertures. Wste het emissions from HVAC systems re the min mechnism y which the energy performnce of uildings ffects outdoor therml conditions. This nlysis shows tht, for uilding densities lower thn.6, the increse in outdoor ir temperture is pproximtely proportionl to the het flux per unit of urn re relesed into the urn cnyon with reltion of K per W m 2 for low wind speeds nd.5 K per W m 2 for high wind speeds. Given its simplicity nd computtionl efficiency, nd the fct tht it runs in widely used numericl pltform such s Mtl, the RC model cn e useful tool for uilding engineers nd urn plnners interested in introducing the interctions etween uildings nd the urn environment s nother spect of their design process. Acknowledgements This reserch ws funded y the Singpore Ntionl Reserch Foundtion through the Singpore-MIT Allince for Reserch nd Technology (SMART) Centre for Environmentl Sensing nd Modelling (CENSAM), nd y the French Ntionl Reserch Agency under the MUSCADE project referenced s ANR-9-VILL-3. References [] Houet T, Pigeon G. Mpping urn climte zones nd quntifying climte ehviors e n ppliction on Toulouse urn re (Frnce). 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