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A resistance-capacitance network model for the analysis of the interactionsbetween the energy performance of buildings and the urban climate

Bruno Bueno a,b,*, Leslie Norford a, Grégoire Pigeon b, Rex Britter aaMassachusetts Institute of Technology, Cambridge, MA, USAbCNRM-GAME, Météo France and CNRS, Toulouse, France

a r t i c l e i n f o

Article history:Received 10 August 2011Received in revised form29 January 2012Accepted 31 January 2012

Keywords:Anthropogenic heatBuilding energy modelState-spaceUrban canopy modelUrban heat island

a b s t r a c t

This paper presents an urban canopy and building energy model based on a thermal network of constantresistances and capacitances. The RC model represents the fundamental physical relations that governthe energy interactions between buildings and their urban environment, retaining the sensitivity to thedesign parameters typically used in building energy and urban climate studies. The benefits of the RCmodel are its simplicity and computational efficiency. It allows for better understanding the physics ofthe problem and makes it possible to easily evaluate modelling hypotheses and the sensitivity ofdifferent parameters. In this study, the RC model is evaluated against advanced simulation tools that arewell accepted and evaluated within their individual scientific communities. The model is then used ina series of parametric analyses to investigate the impact of the Urban Heat Island effect on the energyconsumption of buildings in configurations that are parameterized in terms of internal heat gains,construction, geometry, glazing ratio, and infiltration level. The RC model is also used to investigate thedominant mechanisms by which the indoor environment affects outdoor air temperatures. Parameterssuch as indoor air temperatures, exfiltration heat, and waste heat from HVAC systems are analysed. Theconclusions obtained by this study can be applied to a wide range of urban configurations.

! 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Urbanization produces higher air temperatures in cities than inthe undeveloped rural surroundings [1,2]. This phenomenon,known as the Urban Heat Island (UHI) effect, is usually moreintense under cloudless sky and light wind conditions and is mainlycaused by the geometric and construction differences between theurban and rural surfaces [3] and the anthropogenic heat released inthe urban environment [4]. The UHI effect can increase coolingenergy consumption of buildings [5,6] but can also reduce theheating energy consumption in winter.

Different numerical models have been developed in the last twodecades to analyse the causes and consequences of the UHI effect.The Cluster Thermal Time Constant (CTTC) model [7] calculatesurban air temperatures from measurements at a rural meteoro-logical station, applying simple analytical expressions that take intoaccount the storage and release of heat in the built area. The modelrepresents the urban area as a lumped body characterized by a skyview factor and a CTTC parameter that measures its thermal inertia.

The new generation of urban canopy models is based on thesurface energy balance [8], which accounts for the area-averagedfluxes through the surface of an imaginary box that represents anurban canyon. The literature reports different urban canopymodels, which are based on physical or empirical approaches to thesurface energy balance. The Town Energy Balance (TEB) model[9e12] is a physically-based urban canopy model that considersa two-dimensional approximation of an urban canyon formed bythree generic surfaces: a wall, a road, and a roof. It calculates theclimate conditions, the drag force and energy fluxes of a town orneighbourhood formed by identical urban canyons, where all theorientations are possible and all exist with the same probability.

To represent the effect of the energy performance of buildingson the urban climate, simplified building energy models areimplemented in urban canopy models [13,14]. These models areable to capture the main heat transfer processes that occur insidebuildings and to calculate building energy demand, heating,ventilation and air-conditioning (HVAC) energy consumption andwaste heat emissions [15,16]. Given the inherent interrelationsbetween building energy and urban climate studies, a CoupledScheme (CS) between a detailed building energy program, Ener-gyPlus [17], and the TEB model has been developed [18] to moreprofoundly integrate both fields of study.

* Corresponding author. Massachusetts Institute of Technology, 77 MassachusettsAve., R.5-414, Cambridge, 02139 MA, USA. Tel.: þ1 857 654 0099.

E-mail address: bbueno@mit.edu (B. Bueno).

Contents lists available at SciVerse ScienceDirect

Building and Environment

journal homepage: www.elsevier .com/locate/bui ldenv

0360-1323/$ e see front matter ! 2012 Elsevier Ltd. All rights reserved.doi:10.1016/j.buildenv.2012.01.023

Building and Environment 54 (2012) 116e125

As a complement to the sophisticated models above mentioned,this paper presents an urban canopy and building energy modelbased on a thermal network of constant resistances and capaci-tances. The benefits of the RC model are its simplicity and compu-tational efficiency. The model represents the fundamental physicalrelations that govern the reciprocal energy interactions betweenbuildings and theurbanenvironment, retaining the sensitivity to thedesign parameters typically used in building energy and urbanclimate studies. The RC model is based on a state-space formulationthat can be very efficiently solved by a numerical program, such asMatlab. This allows for faster parametric analyses and makes itpossible to easily evaluate modelling hypothesis and the sensitivityof different parameters. The RCmodel can be used as a research anddidactic tool and has the potential to become an operational tool forthe design and analysis of buildings and urban areas.

In this paper, the RC model is described and evaluated againstthe CS for summer and winter and for different scenarios of wasteheat emissions. The model is then used in a series of parametricanalyses to investigate the impact of the UHI effect on the energyconsumption of buildings for different building configurations. Themodel is also used to investigate the dominant mechanisms bywhich the indoor environment and the energy performance ofbuildings affect outdoor air temperatures. The conclusions of thisstudy can be applied to a wide range of building and urbanconfigurations.

2. The urban RC model

Fig. 1 shows the thermal RC network model of the indoor andoutdoor environments. The indoor environment representsa single-zone building with an internal thermal mass. The outdoorenvironment represents an average-oriented urban canyon,composed of a generic façade and a generic road.

2.1. Physics

The RC model represents the following heat transferphenomena and calculations:

" Transient heat conduction through building walls and roof" Steady state heat conduction through windows

" Solar transmission through windows" Heat storage in intermediate floor constructions" Longwave radiant heat exchange among interior surfaces (wall,roof, and mass)

" Sensible heat balance of the indoor air, including the convec-tive heat fluxes from walls, windows, roof, and intermediatefloors, the convective fraction of internal heat gains, the heatfluxes due to infiltration and ventilation air, and the heat fluxesfrom the HVAC system.

" Sensible heat balance of the urban canyon air, including theconvective heat fluxes from walls, windows and the road, thesensible heat exchange between the canyon air and theatmosphere, the heat fluxes due to exfiltration and exhaust air,and the waste heat from HVAC equipment.

" Solar radiation absorbed by walls, roof, and road assuming anaverage orientation of an urban canyon [9]

" Heat storage in the road soil" Wall-sky, road-sky, roof-sky, and wall-road longwave radiantheat exchanges, taking into account the view factors betweeneach pair of elements. This represents the longwave trapping ofurban areas due to reduced sky view factors.

2.2. Assumptions

The objective of the RC model is to capture the fundamentalphysical relations that govern the indoor and outdoor energyinteractions, while keeping a state-space formulation that can beefficiently solved. This implies constant resistances and capaci-tances in the thermal network represented in Fig. 1.

The rate of heat exchange between the urban canyon air and theatmosphere is usually characterized by an exchange velocity (uex),which can be defined as:

uex ¼ QatmrcpðTurb % TatmÞ (1)

where Qatm is the sensible heat exchange between the urbancanyon and the atmosphere, Turb is the urban canyon mean airtemperature, and Tatm is the air temperature above the urbancanopy layer. Preliminary results obtained with the RC model

Nomenclature

C Capacitance W s K%1

CHTC Convective heat transfer coefficient W m%2 K%1

COP Coefficient of performance of an HVAC systemfwaste Fraction of waste heat released into the urban canyonGR Glazing ratiok Thermal conductivity W m%1 K%1

lv Water condensation heat J kg%1

_ms Mass flow rate kg s%1

Q Heat flux W/W m%2

R Resistance K W%1

t Time sT Temperature 'C, Kuex Exchange velocity m s%1

U Window U-factor W m%2 K%1

VHbld Vertical-to-horizontal building area ratio, defined asexterior vertical building area divided by building planarea, VHbld ¼ VHurb=rbld

VHurb Vertical-to-horizontal urban area ratio, defined asexterior vertical building area divided by the plan area

of the urban site (this parameter is an input in the TEBmodel)

Vo Infiltration/exfiltration airflow rate ACHw Specific humidity kg kg%1

a Solar absorptivityrbld Building density, defined as building plan area divided

by the plan area of the urban site (this parameter is aninput in the TEB model).

rcp Volumetric heat capacity J m%3 K%1

s Window transmittance

Subscriptsatm Atmosphereig Internal heat gainsin Indoor airHVAC Building energy demandlat Dehumidification energys Supplysol Solar radiationurb Conditions inside the urban canyonwaste Waste heat from HVAC systems

B. Bueno et al. / Building and Environment 54 (2012) 116e125 117

showed that urban canyon air temperatures are sensitive to thevalues of the exchange velocity. Different methods are proposed inthe literature to calculate exchange velocities. In this version of theRC model, the correlations of Louis (1979) [19] are used. In thismethod, exchange velocities depend on the Richardson number,which is a measure of the air stability inside the canyon and isa function of the canyon air temperature calculated by the RCmodel. Therefore, an iteration of the RC model is required to matchthe input and calculated exchange velocities.

As a consequence of the state-space formulation, the RCmodel assumes that the convection heat transfer coefficients(CHTC) and the exchange velocities remain invariant during thesimulation. In detailed building energy programs and urbancanopy models, the CHTC can be calculated by correlations asa function of the wind speed and surface-air temperaturedifference. Exchange velocities usually depend on geometry,roughness length for momentum and heat, wind speed, andatmospheric stability. Even so, the RC model is able to reproducethe average diurnal cycle of the results of more sophisticatedmodels by using the average exchange velocity calculated bycorrelations for the simulation period.

Other assumptions of the RC model include:

" Constant indoor air temperature." Constant infiltration and ventilation airflow rate." Constant internal heat gains." Single-zone building with intermediate floors represented asan internal thermal mass. The transmitted solar radiation andthe radiant fraction of internal heat gains are perfectly absor-bed by the internal thermal mass and then are released into theindoor environment.

" Adiabatic building floor. This condition is reasonable if the flooris well insulated.

" Ideal HVAC system: the energy supplied by the system equalsthe building energy demand, and the energy consumption iscalculated from a constant efficiency.

" Well-mixed air inside the urban canyon. This is a reasonableassumption for relatively homogenous urban canopiescomposed of low-rise to medium-rise buildings. Building, cars,and other heat sources keep a positive buoyancy level insideurban canyons, even at night, and enhance the mixing of airinside the urban canopy.

" Linearized radiation formulation and one-bounce approxima-tion for indoor and outdoor longwave radiative heat exchanges.

2.3. State-space formulation

The RC model is derived from energy conservation principles.For each capacitance node (Fig. 1), the rate of change of its internalenergy is related to the heat fluxes reaching the node. This can begenerally expressed as:

CjdTjdt

¼X

k

1Rk

!Tk % Tj

"þX

Qj (2)

where Cj and Tj represent the capacitance and temperature of thenode j, Rk and Tk represent the resistance and temperature of thenodes k that interact with the node j, and Qj represents the heatfluxes acting on the node j.

Using these relations, a state-space formulation can be set upand efficiently solved by a numerical simulation tool, such asMatlab. The general formulation can be written as:dTjðtÞdt

¼ A$TjðtÞ þ B$ujðtÞ (3)

where Tj(t) is a vector of state variables that correspond to each ofthe temperature nodes associated with a capacitance, uj(t) is

Fig. 1. Representation of an urban canopy and building energy model based on a thermal network of constant resistances and capacitances. A capacitance is associated with eachtemperature node. Nodes are connected by resistances. The heat sources of each node are represented by arrows. Four nodes are used to calculate the heat transfer through the wall,the roof and the road.

B. Bueno et al. / Building and Environment 54 (2012) 116e125118

a vector of inputs that can be known temperatures or heat fluxes,and A and B are coefficient matrices.

2.4. Heat fluxes

The transmitted solar radiation is obtained by multiplying thesolar radiation that reaches the average-oriented wall by a constantwindow transmittance provided by the user.

In the case of a cooling situation, waste heat from the outdoorequipment is released into the outdoor environment (Qwaste). Thewaste heat is calculated as a function of the cooling energy demandof the building (QHVAC) and the energy consumed by the HVACsystem to dehumidify the air that passes through the cooling coil(Qlat):

Qwaste ¼ f ðQHVAC þ QlatÞ (4)

where the function f depends on the coefficient of performance(COP) of the cooling system, f ¼ ð1þ 1=COPÞ. The dehumidifica-tion energy (Qlat) is obtained by assuming that the air enters thecooling coil at indoor conditions and leaves the cooling coil atsupply temperature and at 90% relative humidity. Then,

Qlat ¼ _mslvðwin %wsÞ (5)

where _ms is the supply mass flow rate; lv is the water condensationheat; ws is the supply specific humidity, calculated from the supplytemperature (Ts) and 90%RH; andwin is the specific humidity of theindoor air, calculated from the set-point of temperature and rela-tive humidity provided by the user. To obtain the supply mass flowrate, the model requires the maximum sensible cooling load of thebuilding, which is calculated through the simulation. Therefore, aniteration of the RCmodel is required in order to calculatewaste heatemissions.

2.5. Boundary conditions, inputs and outputs

As boundary conditions, the RC model requires time-step valuesof air temperatures and wind speed at the top of the urban canyon(above the urban canopy layer), solar heat fluxes over the hori-zontal, and incoming longwave radiation or equivalent skytemperature. The inputs of the model are construction andgeometric information, internal heat gains, indoor thermal andhumidity set-points, supply air temperature of the HVAC system,maximum sensible cooling load calculated through iteration of themodel, CHTC of the different surfaces, and exchange velocitybetween the urban canyon and the atmosphere calculated throughiteration of the model (see Table 1 for specific inputs). The outputsof the model are the average diurnal cycles of node temperatures,heat fluxes, building energy demand, and waste heat emissions forthe simulation period.

3. Simulation-based model evaluation

In this section, the RC model is compared with the EnergyPlus-TEB Coupled Scheme (CS) [18]. The CS was evaluated with field datafrom the experiment CAPITOUL conducted in Toulouse (France)from February 2004 to March 2005 [20]. The same case study isused for the evaluation of the RC model. Table 1 describes theinputs of the RC model used in this study.

Three different case studies are compared (Table 2). The firsttwo cases are summertime simulations of a residential anda commercial building, respectively. The third case corresponds toa wintertime simulation of a residential building. The average

diurnal cycles calculated by the RCmodel and the CS for fifteen daysin summer and fifteen days in winter are compared.

3.1. Building energy demand

Fig. 2 compares the sensible cooling energy demand in summerand the heating energy demand in winter calculated by the RCmodel and the CS. The root mean square error (RMSE) and meanbias error (MBE) of the comparison is presented in Table 3. As canbe seen, the RC model is able to reproduce the building energy

Table 1Inputs of the RC model used in the comparison of the model with the CoupledScheme. This configuration represents the dense urban centre of Toulouse (France).The term fl indicates that maximum sensible cooling load refers to the used area ofthe building.

Settings

Location Toulouse (Latitude: 43.48'; Longitude: 1.3')Simulation time-step 1800 sSimulation period Summer: 07/15e07/30 Winter: 02/01e02/16Average building height 20 mBuilding density 0.68Vertical-to-horizontal urban

area ratio1.05

Floor height 3 mGlazing ratio 0.3COP of the cooling system 2.5Fraction of waste heat mixed

with the urban canyon air1.0

Indoor air temperature Summer: 25 'C Winter: 20 'CIndoor relative humidity 50%Supply temperature of the

cooling system14 'C

Internal heat gains Residential: 6.25 W m%2(fl)Commercial: 31.75 W m%2(fl)

Radiant fraction of internalheat gains

0.2

Latent fraction of internalheat gains

0.2

Indoor convective heattransfer coefficient (CHTC)

2.0 W m%2 K%1

Indoor radiative heattransfer coefficient

6.0 W m%2 K%1

CHTC road-air 15 W m%2 K%1

CHTC wall-air 25 W m%2 K%1

CHTC roof-air 20 W m%2 K%1

Indoor thermal massconstruction

Concrete e 20 cm, k ¼ 2.0 W m%1 K%1,rcp ¼ 1.874$106 J m%3 K%1

Wall and roof construction Inner layer: Insulation e 3 cm,k ¼ 0.03 W m%1 K%1, rcp ¼ 5.203$104 J m%3 K%1

Outer layer: Brick e 30 cm, k ¼ 1.15 W m%1 K%1,rcp ¼ 1.58$106 J m%3 K%1, a ¼ 0.68

Road construction Ground e 1.25 m, k ¼ 0.4 W m%1 K%1,rcp ¼ 1.4$106 J m%3 K%1, a ¼ 0.92

Window construction s ¼ 0.6; U ¼ 2.5 W m%2 K%1

Infiltration 0.5 ACH

Table 2Case studies used in the comparison of the RC model with the Coupled Scheme, andinputs of the RC model obtained through iteration for each case study. The term fl

indicates that maximum sensible cooling load refers to the used area of the building.Inwinter, the model assumes that there are no waste heat emissions from the HVACsystem, and the maximum sensible cooling load is not used in the simulation.

Parameter Case 1 Case 2 Case 3

Season Summer Summer WinterInternal heat gains Residential Commercial ResidentialParameters obtained through iterationExchange velocity 0.29 m s%1 0.31 m s%1 0.30 m s%1

Maximum sensible coolingload

11.3 W m%2

(fl)32. 3 W m%2

(fl)e

B. Bueno et al. / Building and Environment 54 (2012) 116e125 119

performance predicted by the CS with RMSE between 0.3 and1.8 W m%2 of floor area. These values are much lower than theaverage building energy demand calculated by the CS for thesimulation period, which is taken as the reference value (REF) to

which evaluate errors. The RMSE associated with the transmittedsolar radiation calculated by both models ranges between 1.3 and1.8 W m%2 of floor area. Negative MBE values of transmitted solarradiation indicate that the RC model overestimates this parametersystematically. In addition, the solar transmission error is highcompared to its reference value, which can be explained by thesimplifications made in the RC model for its calculation. Interiorwall and mass surface temperatures are well captured by the RCmodel with RMSE between 0.0 and 0.6 K.

3.2. HVAC waste heat emissions

Fig. 3 shows the average diurnal cycle of waste heat emissions insummer calculated by the RC model and the CS. As can be seen, theRC model is able to reproduce the waste heat emissions predictedby the CS with RMSE around 6.5 W m%2 of urban area, where theaverage waste heat flux calculated by the CS is 55 W m%2 for theresidential case and 220 W m%2 for the commercial case.

3.3. Urban air temperatures

Fig. 4 represents the average diurnal cycle of air temperaturesinside the urban canyon calculated by the RCmodel, the CS, and theTEB scheme. In case 1, in which waste heat emissions are around55 W m%2 of urban area, the three models predict similar urban airtemperatures. The RMSE between the RC model and the CS is 0.4 K,where the average temperature difference between the canyon andthe atmosphere is 1.2 K. Case 2 presents waste heat emissions ofaround 220 W m%2 of urban area, and the urban air temperaturescalculated by the RC model and the CS are around 1 K higher thanthose calculated by the TEB model, which does not account forwaste heat emissions. The RMSE between the RC model and the CSis also 0.4 K, being the reference value 2.1 K. These relative errorsare acceptable given the important uncertainties related to urbanclimate predictions.

In winter (case 3), the three models predict similar urban airtemperatures. The RMSE between the RC model and the CS is 0.5 K,for which the reference canyon-atmosphere temperature differ-ence is 0.7 K. Although the relative difference between the errorand the reference value is higher inwintertime, the fact that for thethree cases the error is very similar suggests that this is systematicand probably related to the different methods used to calculateexchange velocities. A systematic error will cancel when comparingdifferent simulations with the RC model, as in the parametricanalyses of the following sections.

In terms of wall and road surface temperatures, the RMSEbetween RC and CS ranges between 1.7 K and 0.6 K. The reference

Table 3Root mean square error (RMSE), mean bias error (MBE), and reference value (REF) of the comparison between the Coupled Scheme (CS) and the RCmodel. The reference valueof outdoor air temperature is the average of the difference between the outdoor air temperature calculated by the CS and the atmospheric temperature. The reference value ofindoor and outdoor surface temperatures is the average of the difference between the surface temperatures calculated by the CS and the indoor and outdoor air temperature,respectively. The reference value of energy and heat fluxes is the average of the energy and heat fluxes calculated by the CS. The term urb indicates unit of urban area and theterm fl indicates unit of used area of the building.

Case 1 Case 2 Case 3

Parameter RMSE MBE REF RMSE MBE REF RMSE MBE REF

Urban air temperature (K) 0.4 0.2 1.2 0.4 %0.1 2.1 0.5 0.5 0.7Road surface temperature (K) 1.7 0.7 2.7 1.6 0.4 2.6 0.6 %0.4 %0.7Exterior wall surface temperature (K) 1.2 %0.3 1.2 1.3 %0.6 1.1 1.5 1.4 0.6Waste heat emissions (W m%2 urb) 6.8 %5.4 55.2 6.2 1.5 219.9 0 0 0Interior wall surface temperature (K) 0 0 0.7 0.3 0.3 1.8 0.3 %0.3 %1.7Mass surface temperature (K) 0 0 0.8 0.2 0.2 1.8 0.6 %0.6 %0.7Transmitted solar radiation (W m%2

fl) 1.8 %1.7 2.6 1.8 %1.7 2.6 1.3 %1.2 0.9Building energy demand (W m%2

fl) 1.2 %1.1 6.3 1.8 %1.7 26.6 0.3 0.2 6.4

Fig. 2. Average diurnal cycle of sensible cooling energy demand of (a) case 1 and (b)case 2 for summer, July 15eJuly 30, and average diurnal cycle of heating energydemand of (c) case 3 for winter, February 1eFebruary 16, calculated by the RC modeland by the Coupled Scheme.

B. Bueno et al. / Building and Environment 54 (2012) 116e125120

values for these parameters can be of the same magnitude or evenlower, which can be explained by the generic values of CHTC usedas inputs of the model. A better agreement of surface temperaturescan be obtained by using the average CHTC calculated by the CS.However, our simulations show that these differences in surfacetemperatures do not have a significant effect on urban airtemperatures.

4. Impact of the UHI effect on the energy performance ofbuildings

In this section, the RC model is used to analyse the impact of theUHI effect on the energy performance of buildings. A series ofsimulations is carried out imposing outdoor conditions (Turb) to theRC model. This is achieved by using outdoor temperatures asboundary conditions at the top of the urban canyon and intro-ducing a high exchange velocity between the urban canyon andthe atmosphere. The outdoor conditions used in this analysiscorrespond to a UHI scenario measured during the CAPITOULexperiment (Table 4). The dependence of the building energyperformance to other UHI scenarios is also tested.

Five case studies are analysed (Table 5). The first three cases aresimulated using summer outdoor conditions and the last two usingwinter outdoor conditions. Cases 1, 2, 4, and 5 correspond toa residential building with and without insulated walls. Case 3corresponds to a commercial building with insulated walls.

Fig. 5a shows the daily-average change in sensible energydemand due to the UHI effect for different building glazing ratios. InFig. 5b, the energy demand change is divided by the actual energydemand of the building. The graphs show the absolute value of thechange in energy demand, which is positive in summer andnegative in winter. Fig. 5a shows that the UHI effect has a greaterimpact on the building energy performance for higher glazingratios. As expected, the slope is lower for the cases in which wallsare not insulated, and there is a convergence in energy demand

change between insulated and uninsulated cases for higher glazingratios. The fact that the ratio of energy demand change due to theUHI effect is decreasing in summer for higher glazing ratios isexplained by the fact that the overall building energy demandincreases faster than the energy demand change due to the UHIeffect for higher glazing ratios. The results showa small influence ofthe glazing ratio and wall insulation on the ratio of energy demandchange due to the UHI effect.

Fig. 6 shows the daily-average ratio of energy demand changedue to the UHI effect for different infiltration airflow rates and

0000 0400 0800 1200 1600 200015

20

25

30

35

40

45

Air

tem

pera

ture

(C)

RC

CS

TEB

0000 0400 0800 1200 1600 200015

20

25

30

35

40

45

Air

tem

pera

ture

(C)

RC

CS

TEB

0000 0400 0800 1200 1600 20000

5

10

15

20

25

Air

tem

pera

ture

(C)

RC

CS

TEB

a

b

c

Fig. 4. Average diurnal cycle of urban air temperatures of (a) case 1 and (b) case 2 forsummer, July 15eJuly 30, and of (c) case 3 for winter, February 1eFebruary 15,calculated by the RC model, by the Coupled Scheme, and by the Town Energy Balancescheme.

Table 4Measured urban and rural outdoor air temperatures used to analyse the impact ofthe UHI effect on the energy performance of buildings.

Summer Winter

Design day 07/31/04 02/26/05Maximum urban-rural

temperature difference (K)Night 4.1 5.3Day 0.3 0.9

Fig. 3. Average diurnal cycle of HVAC waste heat emissions of (a) case 1 and (b) case 2for summer, July 15eJuly 30, calculated by the RC model and by the Coupled Scheme.

B. Bueno et al. / Building and Environment 54 (2012) 116e125 121

vertical-to-horizontal building area ratios. Infiltration heat gainscan be an important fraction of the building energy demand, aboveall in winter when the temperature difference between indoor andoutdoor environments is high. The UHI effect modifies the heat gaindue to infiltration, increasing the cooling energy demand insummer and decreasing the heating energy demand in winter. Thevertical-to-horizontal building area ratio determines the relativeamount of building surface area exposed to the outdoor environ-ment and, therefore, affected by the UHI effect by means of heattransmission through walls and windows. The graphs showa significant influence of the infiltration level and weak depen-dence on the vertical-to-horizontal building area ratio. Havingmore building surface exposed to the outdoor environment usually

implies more infiltration through opening cracks, but this effect isnot taken into account in this analysis. The results suggest that themain mechanism by which the UHI effect influences the indoorenvironment is the outdoor air entering the building, which can beproduced by infiltration but also by natural or forced ventilation.The UHI impact from the conductive heat transfer through thebuilding enclosure is relatively small.

The ratio of energy demand change for different UHI effectscenarios (Fig. 7) is represented in Fig. 8, which shows a linearrelationship. For residential buildings in summer, the results showa 5% increase in cooling energy demand per 1 K increase in themaximum UHI effect at night. A similar order of magnitudedecrease in heating energy demand is also produced by an equiv-alent wintertime UHI effect. Commercial buildings, usually domi-nated by internal heat gains, are less influenced by the outdoorenvironment, and therefore not significantly affected by the UHIeffect if they do not have building systems with a close interactionwith the outdoor environment such as economizers or naturalventilation.

5. Impact of the energy performance of buildings on theoutdoor environment

In this section, a parametric analysis is carried out with the RCmodel to investigate the impact of the indoor energy performance

0 0.2 0.4 0.6 0.80

50

100

150

Glazing ratio

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

Glazing ratio

Rat

io-o

f ene

rgy

dem

and

chan

ge

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

a

b

Fig. 5. Daily-average change in sensible energy demand due to the UHI effect fordifferent building glazing ratios. The following cases are analysed: 1. summer, resi-dential, insulated walls; 2. summer, residential, uninsulated walls; 3. summer,commercial, insulated walls; 4. winter, residential, insulated walls; and 5. winter,residential, uninsulated walls. Results are given in (a) absolute form and (b) relativeform divided by the overall sensible building energy demand. Other parameter settingsare Tin ¼ 22 'C, VHbld ¼ 2, and Vo ¼ 0.5 ACH.

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

Infiltration (ACH)

Rat

io o

f ene

rgy

dem

and

chan

ge

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

Vertical-to- horizontal building area ratio

Rat

io o

f ene

rgy

dem

and

chan

ge

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

a

b

Fig. 6. Daily-average change in sensible energy demand due to the UHI effect dividedby the overall sensible building energy demand for different (a) infiltration airflowrates and (b) vertical-to-horizontal building area ratios. The following cases areanalysed: 1. summer, residential, insulated walls; 2. summer, residential, uninsulatedwalls; 3. summer, commercial, insulated walls; 4. winter, residential, insulated walls;and 5. winter, residential, uninsulated walls. Other parameter settings are Tin ¼ 22 'C,GR ¼ 0.4, VHbld ¼ 2, and Vo ¼ 0.5 ACH.

Table 5Case studies used to analyse the interactions between buildings and the urbanenvironment. In the insulated cases, the building wall is composed of 30 cm brickand an inner layer of 3 cm insulation. In the uninsulated cases, the building wall iscomposed of 30 cm brick. Internal heat gain values for the residential andcommercial cases, as well as other building and urban parameters are defined inTable 1.

Cases Insulation Building use Design day

1 Yes Residential Summer2 No Residential Summer3 Yes Commercial Summer4 Yes Residential Winter5 No Residential Winter

B. Bueno et al. / Building and Environment 54 (2012) 116e125122

on urban air temperatures. Table 6 summarizes the boundaryconditions above the urban canyon used in this analysis. Thesummer and the winter design days correspond to a hot and a coldday, respectively, measured in Toulouse during the CAPITOULexperiment. The average wind speed above the urban canyon is setup to 5 m s%1. The dependence of outdoor temperatures to thisparameter is also tested. The same five case studies presented in theprevious section are analysed (Table 5).

5.1. Effect of the indoor environment without waste heat emissions

Without considering waste heat emissions, a change in theindoor thermal conditions can affect the outdoor environment byheat conduction through the building enclosure, which modifiesoutdoor surface temperatures and end up affecting outdoor airtemperatures by convective heat transfer. A change in the indoorenvironment can also have an impact on outdoor air temperaturesthrough exfiltration. Assuming that all the air that enters a buildingthrough infiltration leaves it at indoor air temperature, there is anexfiltration heat flux associated with the indooreoutdoor temper-ature difference, which would be more important in winter than insummer.

0000 0400 0800 1200 1600 2000−5

0

5

10

15

UHImax

=1K

UHImax

=2K

UHImax

=4K

UHImax

=6K

UHImax

=9K

a

b

0000 0400 0800 1200 1600 200015

20

25

30

35

40

UHImax

=1K

UHImax

=2K

UHImax

=4K

UHImax

=6K

UHImax

=9K

Fig. 7. Diurnal cycles of urban air temperature in (a) summer and in (b) winter fordifferent maximum urban-rural air temperature difference.

2 4 6 80

0.1

0.2

0.3

0.4

0.5

Urban Heat Island (K)

Rat

io o

f ene

rgy

dem

and

chan

ge

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

Fig. 8. Daily-average ratio of energy demand difference for different maximum urban-rural air temperature difference. The following cases are analysed: 1. summer, resi-dential, insulated walls; 2. summer, residential, uninsulated walls; 3. summer,commercial, insulated walls; 4. winter, residential, insulated walls; and 5. winter,residential, uninsulated walls. Other parameter settings are Tin ¼ 22 'C, GR ¼ 0.4,VHbld ¼ 2, and Vo ¼ 0.5 ACH.

Table 6Meteorological conditions above the urban canyon used to analyse the impact of theenergy performance of buildings on the outdoor environment.

Summer Winter

Design day 07/31/04 01/26/05Maximum air temperature 35.1 'C %0.2 'CDaily air temperature range 15.6 K 2.8 KAverage wind speed 5.0 m s%1 5.0 m s%1

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

1

Glazing ratio

Air

tem

pera

ture

cha

nge

(K)

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

20 22 24 26 280

0.2

0.4

0.6

0.8

1

Indoor tempeature (C)

Air

tem

pera

ture

cha

nge

(K)

Sum−Res−InsSum−Res−NonSum−Com−InsWin−Res−InsWin−Res−Non

a

b

Fig. 9. (a) Daily-average difference in outdoor air temperature due to a change inindoor air temperature from 22 'C to 27 'C in summer and from 17 'C to 22 'C inwinter for different building glazing rations. (b) Daily-average outdoor air temperaturedifference due to a change in exfiltration airflow rate from 0.0 to 0.5 ACH for differentindoor air temperatures in summer and in winter. The following cases are analysed: 1.summer, residential, insulated walls; 2. summer, residential, uninsulated walls; 3.summer, commercial, insulated walls; 4. winter, residential, insulated walls; and 5.winter, residential, uninsulated walls. Other parameter settings are rbld ¼ 0.5,VHurb ¼ 1, GR ¼ 0.4, fwaste ¼ 0.0, and Vo ¼ 0.0 ACH.

B. Bueno et al. / Building and Environment 54 (2012) 116e125 123

Fig. 9a shows the daily-average difference in outdoor airtemperature due to an increase in the indoor air temperature of 5 Kin summer and inwinter for different building glazing ratios. As canbe seen, indoor air temperatures have a small influence on theoutdoor environment when there are nowaste heat emissions fromair-conditioning systems and no exfiltration heat.

Fig. 9b shows the daily-average difference in outdoor airtemperature due to a change in the exfiltration airflow rate from 0.0to 0.5 ACH for different indoor air temperatures. As can be seen,exfiltration has an unimportant influence on the outdoor envi-ronment in summer, but it might be relevant in some winter situ-ations. Due to the high indooreoutdoor temperature difference, theexfiltration heat flux can be compared to other urban fluxes ina cloudy day in winter.

5.2. Effect of waste heat emissions

Waste heat emissions from HVAC systems are significant sour-ces of heat in the energy balance of an urban canyon. Fig. 10a showsthe daily-average difference in outdoor air temperature due to thewaste heat from air-conditioning systems in summer for differentindoor air temperature values. Daily-average waste heat emissionsare represented in Fig. 10b. Commercial buildings, due to their highinternal heat gains, have a greater impact on the outdoorenvironment.

Fig. 11 represents the daily-average difference in outdoor airtemperature due to waste heat emissions for different buildingdensities. This parameter, typically used in urban planning, has

a significant impact on outdoor air temperatures. This can be seenby the fact that to condition bigger indoor spaces in summerimplies pumping more heat into a smaller outdoor environment,and therefore outdoor air temperatures soar.

The wind speed above the urban canopy affects the heatexchange rate between the urban canyon and the atmospherethrough the average exchange velocity used in the RCmodel. Fig. 12

20 22 24 26 280

0.5

1

1.5

2

2.5

3

Indoor tempeature (C)

Air

tem

pera

ture

cha

nge

(K)

Sum−Res−InsSum−Res−NonSum−Com−Ins

20 22 24 26 280

50

100

150

200

250

300

Indoor tempeature (C)

Was

te h

eat (

W m

−2)

Sum−Res−InsSum−Res−NonSum−Com−Ins

a

b

Fig. 10. Daily-average (a) difference in outdoor air temperature due to waste heatemissions and (b) waste heat emissions in summer for different indoor air tempera-tures. The following cases are analysed: 1. summer, residential, insulated walls; 2.summer, residential, uninsulated walls; and 3. summer, commercial, insulated walls.Other parameter settings are rbld ¼ 0.5, VHurb ¼ 1, Vo ¼ 0.5 ACH, and GR ¼ 0.4.

0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

3

Building density

Air

tem

pera

ture

cha

nge

(K)

Sum−Res−InsSum−Res−NonSum−Com−Ins

0.2 0.4 0.6 0.80

50

100

150

200

250

300

Building density

Was

te h

eat (

W m

−2)

Sum−Res−InsSum−Res−NonSum−Com−Ins

a

b

Fig. 11. Daily-average (a) difference in outdoor air temperature due to waste heatemissions and (b) waste heat emissions in summer for different building densities. Thefollowing cases are analysed: 1. summer, residential, insulated walls; 2. summer,residential, uninsulated walls; and 3. summer, commercial, insulated walls. Otherparameter settings are VHurb ¼ 1, Vo ¼ 0.5 ACH, GR ¼ 0.4, and Tin ¼ 22 'C.

2 4 6 8 100

0.5

1

1.5

2

2.5

3

Forcing wind speed (m s−1)

Air

tem

pera

ture

cha

nge

(K)

Sum−Res−InsSum−Res−NonSum−Com−Ins

Fig. 12. Daily-average difference in outdoor air temperature due to waste heat emis-sions in summer for different wind speeds above the urban canopy layer. The followingcases are analysed: 1. summer, residential, insulated walls; 2. summer, residential,uninsulated walls; and 3. summer, commercial, insulated walls. Other parametersettings are rbld ¼ 0.5, VHurb ¼ 1, Vo ¼ 0.5 ACH, GR ¼ 0.4, and Tin ¼ 22 'C.

B. Bueno et al. / Building and Environment 54 (2012) 116e125124

shows the dependence of the urban canyon air temperature changedue to waste heat emissions on the wind speed above the urbancanopy. For the residential cases, in which waste heat emission arearound 100 W m%2 of urban area, the increase in outdoortemperature ranges between 0.5 K for a wind speed of 10 m s%1 and1 K for a wind speed of 2 m s%1. For the commercial case, in whichthe average waste heat flux is 220 W m%2 of urban area, theincrease in outdoor temperature ranges between 1.2 K for a windspeed of 10 m s%1 and 2.2 K for a wind speed of 2 m s%1. It can beconcluded that, for building densities lower than 0.6, the increasein outdoor air temperature is approximately proportional to theheat flux per unit of urban area released into the urban canyonwitha relation of 1 K per 100 W m%2 for low wind speeds and 0.5 K per100 W m%2 for high wind speeds.

6. Conclusion

A simple urban canopy and building energy model, based ona thermal network of constant resistances and capacitances, hasbeen presented. The urban RC model represents the fundamentalphysical relations that govern the energy interactions betweenbuildings and their urban environment. The model is evaluatedagainst a coupled scheme between a building simulation program,EnergyPlus, and an urban canopy model, TEB, for summer andwinter conditions and for different building configurations.

The model is then used in a series of parametric analyses toinvestigate the impact of the UHI effect on the energy consumptionof buildings. For residential buildings in summer, a 5% increase incooling energy demand can be expected per 1 K increase in themaximumUHI effect (usually at night). A similar order ofmagnitudedecrease in heating energy demand of a residential building can beexpected by an equivalent wintertime UHI effect. Commercialbuildings are not significantly affected by the UHI effect if they arenot naturally-ventilated.Dependingon theproportionof cooling andheating days of each particular climate and the type of system usedto meet building energy demands, the UHI effect can have a positiveor negative impact on the overall energy consumption of cities.

The main mechanism by which the UHI effect influences theindoor energy performance is infiltration and ventilation; theimpact from the conductive heat transfer through the buildingenclosure is relatively small. This result highlights the importanceof considering the UHI effect in the design and analysis of buildingsystems, such as natural ventilation or economizers, in which theoutdoor air entering the building plays a critical role.

The RC model is also used to investigate the dominant mecha-nisms by which the indoor environment affects outdoor airtemperatures. In wintertime, exfiltration heat fluxes can havea noticeable effect on outdoor air temperatures. Waste heat emis-sions from HVAC systems are the main mechanism by which theenergy performance of buildings affects outdoor thermal condi-tions. This analysis shows that, for building densities lower than0.6, the increase in outdoor air temperature is approximatelyproportional to the heat flux per unit of urban area released into theurban canyon with a relation of 1 K per 100 W m%2 for low windspeeds and 0.5 K per 100 W m%2 for high wind speeds.

Given its simplicity and computational efficiency, and the factthat it runs in awidely used numerical platform such as Matlab, theRC model can be a useful tool for building engineers and urban

planners interested in introducing the interactions betweenbuildings and the urban environment as another aspect of theirdesign process.

Acknowledgements

This research was funded by the Singapore National ResearchFoundation through the Singapore-MIT Alliance for Research andTechnology (SMART) Centre for Environmental Sensing andModelling (CENSAM), and by the French National Research Agencyunder the MUSCADE project referenced as ANR-09-VILL-003.

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