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Solar Energy 114 (2015) 303–313

A fast assessment method for thermal performance ofnaturally ventilated double-skin facades during cooling season

Fei Xue, Xiaofeng Li ⇑

Department of Building Science, School of Architecture, Tsinghua University, Beijing, China

Received 31 July 2014; received in revised form 5 November 2014; accepted 25 January 2015

Communicated by: Associate Editor Ursula Eicker

Abstract

Double-skin facades (DSFs) are promising and attractive building envelopes. DSFs can reduce the undesired heat gain during coolingseason. However, due to complicated air flow and heat transfer in a DSF, economical and practical methods suitable for evaluating thethermal performance of a naturally ventilated DSF for the duration of a cooling season are still lacking. A large number of computa-tional fluid dynamics (CFD) simulations are required to reach an assessment for a naturally ventilated DSF. This paper proposes a newfast calculation method. The proposed method significantly reduces the CFD simulation workload by establishing a correlation betweenindoor heat gain and solar radiation intensity. The novel calculation method demonstrated good computational accuracy. The resultswere verified by CFD models and were then applied to obtain the total indoor heat gain for a cooling season. This method could beused in optimization of DSFs.� 2015 Elsevier Ltd. All rights reserved.

Keywords: Double-skin facades; Thermal performance; Indoor heat gain; Computational fluid dynamics

1. Introduction

Double-skin facades are effective building envelopetechniques and have been widely applied in commercialbuildings (Poirazis, 2004). A DSF is comprised of twoglasses with a ventilated cavity between them; it could havetwo air vents and shading devices placed in the cavity. Withthe ventilated cavity functioning as a thermal buffer, DSFsare able to reduce undesired heat gain during the coolingseason and heat loss during the heating season. Therefore,it is important to study the performance and optimizationof DSFs.

The three working modes for a DSF can be classified byventilation modes and air flow path (Fig. 1) (Saelens et al.,

http://dx.doi.org/10.1016/j.solener.2015.01.040

0038-092X/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +86 10 62779993; fax: +86 10 62773461.E-mail address: xfli@mail.tsinghua.edu.cn (X. Li).

2008). Type A and B modes are normally mechanicallyventilated (Type A could also be naturally ventilated ifused as a Trombe wall (Ruiz-Pardo et al., 2010)) and canbe integrated within the ventilation system of indoorspaces, i.e. being part of Heating Ventilation and Air-Conditioning (HVAC) system of a building. They are usu-ally used to pre-heat the outdoor air or exhaust the indoorair. Type C is called naturally ventilated DSF. The cavity isnaturally ventilated with exterior air. It can be used as asupply air window for natural ventilation (when the win-dow on the inner glass is open) or as an insulation envelopefor an air-conditioned room (when the window on theinner glass is closed), which increases thermal resistance(Saelens et al., 2008).

DSFs may be suitable building envelopes for moderncommercial buildings (Zhou and Chen, 2010). Experiments(Baofeng, 2004) and theory analyses (Chen et al., 2005;

Nomenclature

A DSF area, m2

A’ solar altitude angle, degreec specific heat of air, J/(kg K)D DSF width, mg gravity coefficient, m/s2

G ventilation quantity, m3/sh convective heat transfer coefficient, W/(m2 K)H height of DSF or region received short-wave

radiation on inner glass, mJ radiation intensity, W/m2

Dp pressure differential between inlet and outlet ofDSF, Pa

q heat gain, W/m2

Q heat gain in cooling season, MJ/m2

RCI Radiation Conversion Index, W1/3/m2/3

S DSF resistance coefficient, (m kg)�1

T absolute temperature, KU overall coefficient of heat transfer, W/(m2 K)

Greek symbols

d thickness, me emissivity

k thermal conductivity, W/(m K)q ambient air mass density, kg/m3

s transmittance

Subscripts

b bottom of DSFcav cavityconv convectiondiff diffuse radiationdir direct radiationes exterior surfaceig inner glassis interior surfacelr long-wave radiationog outer glassout outletre once-reflected radiations shading devicesr shortwave radiation

Fig. 1. Schematic representation of the three typologies for DSFs (Saelenset al., 2008).

304 F. Xue, X. Li / Solar Energy 114 (2015) 303–313

Jiang and Long, 2006) are now being conducted to studythe performance of DSFs. Li recommended a type CDSF after conducting a series of experiments for differentDSF types with different ventilation modes in Wuhan, atypical Chinese city (Baofeng, 2004). Other research foundthat the heat loss through the conventional opaque wall inheating season was 89.1% more than that of a DSF, whilethe heat gain of the opaque wall in cooling season was 30%less (Jiang and Long, 2006). As such, the annual energyconsumption for DSF buildings is less than a conventionalenvelope; however, during the heating season the energyconsumption is more. A study by Saelens et al. (2003)reached similar conclusions. Therefore, as a priority, thethermal performance of DSFs in cooling seasons shouldbe analyzed and optimized. For the reasons outlinedabove, it is important to design an economical and practi-cal method to evaluate the best thermal performance ofnaturally ventilated DSFs for the duration of a cooling sea-son. This design objective is also the main focus of this cur-rent work. However, due to the complicated structures andheat transfer, DSFs are different from conventional build-ing envelopes; as such, the assessment method should alsobe different. Previous research mentioned multiple assess-ment indicators for DSFs, including Solar Hear GainCoefficient (SHGC), U-value, Total Solar Energy Trans-mittance (Chou et al., 2009; Manz, 2004), cavity airflowrate (Pappas and Zhai, 2008), and heating/cooling load(Fallahi et al., 2010; Saelens et al., 2003). Energy perfor-mance of a facade is traditionally expressed with SHGCand U-value, which are steady-state concepts that ignore

the dynamic aspects of facade behaviors. For this reason,they cannot be directly applied to DSFs (Corgnati et al.,2003; Faggembauu et al., 2003). The building load indica-tor (indoor heat gain) is most suited to measuring the ther-mal performance of DSFs for the duration of a coolingseason. Specifically, the minimum indoor heat gain reflectsthe maximum ability in thermal insulation of a DSF; assuch, it is used as the thermal performance indicator in thisresearch.

F. Xue, X. Li / Solar Energy 114 (2015) 303–313 305

Building load calculations require DSF modeling. Mod-els used for the prediction and analysis of DSF perfor-mance include analytical and lumped models (Park et al.,2004), non-dimensional analysis (Balocco, 2004), networkmodels (Tanimoto and Kimura, 1997), zonal models (Jiruand Haghighat, 2008) and airflow network models coupledwith energy simulation (Gratia and De Herde, 2004; Stecand Paassen, 2005). Detailed studies have also been con-ducted using CFD for mechanically ventilated facades(Jiru et al., 2011; Manz et al., 2004) and for naturally ven-tilated facades (Manz, 2004; Safer et al., 2005; Zeng et al.,2012). The CFD simulation approach provides detailedaccurate results, especially for the dynamic aspects. How-ever, a single CFD simulation can only provide one resultunder a given condition. Hence, multiple simulations arerequired to obtain the thermal performance for the dura-tion of a cooling season. This paper presents a new methodbased on the CFD approach for rapidly calculating the bestthermal performances of naturally ventilated DSFs in anymeteorological condition. It also provides the minimumindoor heat gain through a DSF for the duration of awhole cooling season.

2. Proposed calculation method

This section introduces a fast method for calculating thethermal performance of a naturally ventilated DSF duringa cooling season. Indoor heat gain through a DSF wasseparated into two parts. One is the shortwave radiationtransmission heat gain, and can be calculated based onthe radiation intensity, DSF structure and optical proper-ties of each surface of the DSF. The other part is a functionof the radiation intensity, heat transfer coefficient, and thetemperature difference between indoor and outdoor. In thefunction, there is only one undetermined coefficient, whichcan be calculated by introducing CFD method. This coef-ficient is unaffected by meteorological conditions and solelydependent on the characteristic of DSF. As such, the total

Fig. 2. Energy fl

indoor heat gain under any given meteorological conditioncan be calculated immediately, and so the indoor heat gainduring the whole cooling season is obtained. The detailedderivation and description of the calculation method areas follow.

2.1. Energy flow of DSF

The energy flow of a DSF is complex because it involvesreflection, transmission, absorption, convection heat trans-fer, heat exhausting, and other aspects (Fig. 2).

A DSF affects the indoor cooling load in three ways:transmission of direct and diffused solar radiation (short-wave radiation); long-wave radiation heat exchangebetween the inner glass and indoor objects; and free con-vection heat transfer between the inner glass and indoorair:

q ¼ qsr þ qlr þ qconv ð1Þ

where q, qsr, qlr and qconv are the heat transfer rates of totalindoor heat gain, shortwave radiation transmission heatgain, long-wave radiation heat gain and convection heatgain, respectively. The three aspects of heat gain can beseparately treated.

The long-wave radiation heat gain is:

qlr ¼ hlrðT ig;is � T roomÞ ð2Þ

where hlr is the linearized radiative heat transfer coefficientbetween the interior surface of the inner glass and the sur-faces of the indoor objects; Tig,is is the mean temperature ofthe interior surface of the inner glass; and Troom is the tem-perature of the indoor objects (taken as the indoor airtemperature).

The free convection heat gain is:

qconv ¼ hig;isðT ig;is � T roomÞ ð3Þ

where hig,is is the convective heat transfer coefficient of theinterior surface of the inner glass.

Thus, the total indoor heat gain is:

ow of DSFs.

306 F. Xue, X. Li / Solar Energy 114 (2015) 303–313

q ¼ qsr þ ðhlr þ hig;isÞðT ig;is � T roomÞ¼ qsr þ UðT ig;es � T roomÞ ð4Þ

where Tig,es is the temperature of the exterior surface of theinner glass and U is the overall U-value between the exteri-or surface of the inner glass and the indoor air or objects,such that:

U ¼ 1dig

kigþ 1

hig;isþhlr

ð5Þ

where dig and kig are the thickness and thermal conductivityof the inner glass, respectively.

Eq. (4) shows that in order to obtain the total indoorheat gain, qsr and Tig,es must be solved because the overallU-value is obtained by empirical values; Troom is anassumed value. Thus, qsr and UðT ig;es � T roomÞ can beseparately calculated.

2.2. Calculation of qsr

The calculation of qsr is based on radiation intensity,DSF structure and the optical properties of each surfaceof the DSF. Taking into account the properties of the dif-ferent surfaces, the short-wave radiation received by theinner glass is separated into three parts to approximateqsr: diffuse radiation, direct radiation and once-reflectedradiation (Fig. 3). Normally, the top and bottom surfacesof the cavity are not made of reflective materials (Chan

Fig. 3. Short-wave radiation received by inner glass.

et al., 2009; Xu and Ojima, 2007), mostly with reflectancesunder 0.3. Therefore, over 90% of the solar radiation ener-gy will be absorbed after reflected twice or more, whichmeans the intensity of the radiation reflected multiple timesby the two surfaces is at least an order of magnitude lessthan solar radiation. So, it is a tiny impact on qsr, andwas ignored in this calculation. This kind of separationof short-wave radiation have also been adopted in recentDSF researches (Jiru and Haghighat, 2008; Xu andYang, 2008). After the separation and simplification, theqsr can be calculated by the regions on the inner glass thatreceive the above three kinds of radiation and the accord-ing radiation intensities.

The diffuse radiation is received by the whole inner glassevenly, while the direct radiation and once-reflected radia-tion are influenced by solar altitude and shaded by the DSFstructure. Therefore, only the regions on the inner glassthat receive the direct radiation and once-reflected radia-tion need to be calculated separately. With given DSF sizesand solar altitude angle, the two regions can be easilyobtained according to the geometrical relationship(Fig. 3), as the following two equations:

Hdir ¼H � D tan A0 ;D tan A0 < H

0 ;D tan A0 P H

�ð6Þ

Hre ¼D tan A0 ;D tan A0 < H

2H � D tan A0 ;H 6 D tan A0 < 2H

0 ;D tan A0 P 2H

8><>: ð7Þ

where H is the DSF height; D is the DSF width; A’ is thesolar altitude angle; Hdir is the region that receives directradiation; and Hre is the region that receives once-reflectedradiation.

The radiation intensities of the three parts mentionedabove can be calculated by solar diffuse, direct radiationintensity, solar altitude angle and the optical propertiesof each surface. Common types of inner blinds includecloth curtain and venetian blinds. The transmittance ofthe inner blind can be treated as a constant value. Otherconstants include the transmittance of the inner and outerglasses and the reflectance of the bottom of the DSF.

The transmission radiation intensities on the inner glassare measured as:

J sr;diff ¼ J og;diff sogsssig ð8Þ

J sr;dir ¼ J og;dirsogsssig ð9Þ

J sr;re ¼ J og;dirsogsssigqb ð10Þ

where Jog,diff and Jog,dir are the intensities of diffusion anddirect radiation on the exterior surface of the outer glass,respectively; sog, ss, and sig are the average transmittancesof the outer glass, shading device and inner glass plain,respectively; and qb is the average reflectance of the bottomof the DSF.

For Eqs. 9, 10, the structure transmittances should beconsidered when calculating area-averaged values. Eqs.

F. Xue, X. Li / Solar Energy 114 (2015) 303–313 307

(6)–(10) can calculate qsr under any solar radiation condi-tions, such that:

qsr ¼ ðHJ sr;diff þ HdirJ sr;dir þ HreJ sr;reÞ=H ð11Þ

2.3. Calculation of U(Tig,es � Troom)

Tig,es is affected by both solar radiation intensity and dif-ferences between the inside and outside temperatures. Assuch, Tig,es is related to the fluid dynamics process in theDSF, making it difficult to calculate. Therefore, a mathe-matical relationship between ðT ig;es � T outsideÞ and the solarradiation intensity on the exterior DSF surface (Jog, whichequals J og;dir þ J og;diff ) must first be established. This math-ematical relationship can then be used to reduce the work-load of the calculation. It is derived from the heat balanceequation as follows.

Assuming that the cavity is in a steady-state heat trans-fer condition and the DSF is well thermal-insulated to theadjacent exterior wall (adiabatic boundary), based on theenergy flow described in Section 2.1, the heat balance inthe DSF cavity is:

AsogJ og ¼ cGðT cav;out � T outdoorÞ þ Aqog þ Aqsr þ Aqlr

þ Aqconv ð12Þ

where A is the DSF area; c is the specific air temperature; G

is the ventilation quantity; Tcav,out is the air temperature atthe outlet of the cavity; and qog is the heat transfer throughthe outer glass.

Eq. (12) contains all the heat gains and losses of the cav-ity. The left side of Eq. (12) is the heat gain of the cavity,which is the solar radiation transmission through the outerglass; the right side are the heat losses of the cavity, includ-ing heat exhausting and both convection and radiationheat transfer through the outer and inner glass.

The wind pressures of the inlet and outlet areapproximately equal because the two DSF vents are onthe same surface; as such, the assumption is made that onlythermal pressure ventilation exists in the DSF cavity.According to the basic principles of thermal pressure ven-tilation, the pressure differential between the two vents is(ASHRAE Handbook, 2009):

Dp ¼ qgHðT cav � T outdoorÞ=T outdoor ð13Þ

where q is the ambient air mass density; g is the gravitycoefficient; and Tcav is the mean air temperature in thecavity.

There are four resistance components in the DSF: theinlet and outlet openings, inner gap (between the shadingdevice and inner glass), and outer gap (between the shadingdevice and outer glass). The airflow at the inlet and outletopenings is turbulent and obeys the quadratic resistancelaw. In the inner gap the airflow is also a turbulent flow,while in the outer gap the laminar and turbulent contribu-tions are in the same order of magnitude (Chan et al.,2009). Therefore, the laminar flow is only a small part,

and the whole DSF was simplified as a flow path wherethe airflow is turbulent and is in the region of the quadraticresistance law. Thus, the ventilation quantity fits:

G ¼ffiffiffiffiffiffiDpS

rq ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq3gHðT cav � T outdoorÞ

ST outdoor

sð14Þ

where S is the resistance coefficient of the DSF.The relations between the temperature differences are

(Chan et al., 2009):

T cav;out � T outdoor ¼ ð1� e�H=H0ÞðT ig;es � T outdoorÞ ð15Þ

T cav � T outdoor ¼ 1� H 0

Hð1� e�H=H0Þ

� �ðT ig;es

� T outdoorÞ ð16Þ

where H0 is the characteristic height, which is dependent onthe DSF form.

Zeng et al. used experimental and simulation results toshow that during a cooling season, heat exhaustingoccupies a vast majority of total heat loss inside the cavity,(typically, at least 70%) (Zeng et al., 2012). Here, heat loss-es can be ignored, except for the heat exhausting in Eq.(12). By substituting Eqs. (15) and (16), the heat balanceof the cavity can be written as:

AsogJ og ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqgH ½1� H0

H ð1�e�H=H0 Þ�ð1� e�H=H0 Þ2

ST outdoor

sðT ig;es�T outdoorÞ3=2 ð17Þ

In Eq. (17), for a given DSF, the variables (except Jog andTig,es) are either constant or nearly constant. Thus, Jog is

proportional to ðT ig;es � T outdoorÞ3=2 such that

ðT ig;es � T outdoorÞ is proportional to J 2=3og . Setting the propor-

tionality factor as RCI/U, UðT ig;es � T roomÞ can be nowwritten as:

UðT ig;es � T roomÞ ¼ UðT ig;es � T outdoorÞ þ UðT outdoor

� T roomÞ¼ RCI � J 2=3

og þ UðT outdoor � T roomÞ ð18Þ

where RCI refers to the Radiation Conversion Index. Eq.(18) suggests that the indoor heat gain without short-waveradiation, UðT ig;es � T roomÞ, can be separated into twoparts, U(Toutdoor � Troom) and U(Tig,es � Toutdoor). The firstpart, U(Toutdoor � Troom), is the heat gain caused by tem-perature between indoor and outdoor, so U(Tig,es � Tout-

door) can be regarded as the heat gain caused by solarradiation. Therefore, RCI is the factor between this partof heat gain and solar radiation intensity. So RCI repre-sents the average level of heat gain through the inner glassconverted from Jog for a given DSF. Theoretically, whenEq. (18) is validated, the RCI of a given DSF can beobtained by a single CFD simulation.

By substituting Eqs. (18) into (4), the total indoor heatgain can be written as:

q ¼ qsr þ RCI � J 2=3og þ UðT outdoor � T roomÞ ð19Þ

308 F. Xue, X. Li / Solar Energy 114 (2015) 303–313

According to the proposed calculation methods, every vari-able in Eq. (19) can be obtained under any given meteoro-logical condition as long as the determinate value of RCI isobtained based on the CFD results. Therefore, the hour-by-hour indoor heat gain can be calculated based on asmall number of CFD simulations, which allows the totalheat gain for a whole cooling season to be obtained.

3. CFD simulation

Some assumptions and approximations were made forthe derivation steps of the proposed calculation: the resis-tance coefficient and the convective heat transfer coefficientwere constant; the radiative heat transfer coefficient waslinearized; and the mean values of the temperatures andair density were applied. However, none of these assump-tions were used in the CFD method. As such, these meth-ods can be used to verify the proposed calculationapproach. Further, field experiments cannot adequatelyprovide the required separated heat gain values, whereasCFD methods can be verified by field experiments. There-fore, an experimentally validated CFD method was adopt-ed. Simulations of two types of naturally ventilated DSFswith different vents were completed. Twenty differentmeteorological conditions were applied to represent thevarious conditions throughout a cooling season. Theresults were used to perform a verification of the proposedfast calculation method as well as the equations provided inSection 2.

Fig. 4. DSF test room in Beijing, China (Zeng et al., 2012).

3.1. DSF model description

Two two-dimensional models of naturally ventilatedDSFs were constructed. The DSF models emulated secondfloor based DSFs with a height of 3 m and a width of 0.8 m(with the lower edge of the facade at 3 m). Two air vents(inlet and outlet) were located at the top and bottom ofthe outer glass, both 0.1 m in height. In actual conditions,double pane glass would commonly be used as the innerglass; however, for the experiment, this was simplified assingle pane glass with the U-value of double pane glass.

The shading device is a key component of the DSF. Themanagement of shading devices greatly influences the ther-mal performance of a DSF; shading can be up or down andthe slats of the shading device can change. All the abovechanges result in altered DSF configurations, making itimpossible to use inspiration the proposed fast calculationapproach. However, given that this assessment focused oninsulation performance during the cooling season, the max-imum ability for reducing heat gain was measured as thefirst priority. Hence, the DSF model was fixed, with ventsopened and the shading device closed. Therefore, the shad-ing device model was simplified as a semi-transparentboard, which emulated a completely closed roller blind orvenetian blind. The shading devices for both models were0.1 m apart from the upper and lower edges of the DSF,

acting as the air passages. The distance between the shad-ing device and inner glass was also 0.1 m.

Model 1 had no block in the air inlet and outlet; Model2 had three bafflers in each opening of the outer glass(Fig. 5). The opening angle of the bafflers was set to 30�and the inlet and outlet structures were the same.

The two sets of DSFs were located on the second floor,3 m above the ground. The upper boundary of the ambientregion was 10 m above the upper edge of the DSF. The leftboundary of the ambient region was 10 m away from theouter glass. Both of the DSFs faced south.

3.2. Simulation settings

The physical properties of the facades, shading device,and other surfaces were established (Table 1). The radia-tion properties were separately set using both shortwaves(0.1–3 lm) and long-waves (3–100 lm).

The detailed building model was not included in oursimulation. In the CFD model, the interfaces of the wallsand double-skin facade cavity were adiabatic. The interfaceof the room and inner glass was simplified as a third typeboundary condition. We assumed the room was underair-conditioning, and the temperatures of both the roomair and object surfaces were 26�C. The natural convectionheat transfer coefficient and linearized long-wave radiationheat transfer coefficient between the indoor and glass sur-face were 8 W/(m2 K) and 5.5 W/(m2 K), respectively.

20 different meteorological conditions were simulated.Because a DSF typically operates on clear sunny days,the diffuse solar radiation flux was set as 100 W/m2 to emu-late cloudless conditions; Table 2 shows the settings of theother meteorological parameters.

The two main radiation models are the surface-to-sur-face model (S2S) and the participating media radiationmodel. This study utilized the S2S radiation model, whichmade it possible to simulate the thermal radiation exchangebetween diffuse surfaces forming a closed set. The medium

Fig. 5. Configuration of two simulation models.

Table 1Thermal and optical properties settings.

Surface Material d (mm) ssr esr slr elr k (W/m K)

Outer glass Glass 10 0.7 0.1 0 0.9 0.7Inner glass Glass 20 0.7 0.1 0 0.9 0.1Shading device Fabric 20 0.1 0.6 0 0.9 0.5Sky – – 1 0 0 1 –Other surfaces – – 0 0.7 0 1 –

Note: d is the thickness; ssr and slr are the transmittances for shortwaveand long-wave radiation; esr and elr are the emissivities for shortwave andlong-wave radiation; k is the thermal conductivity.

F. Xue, X. Li / Solar Energy 114 (2015) 303–313 309

that filled the space between the surfaces was non-participating; as such, it did not absorb, emit or scatterradiation. Under these circumstances, the amount of radia-tion received and emitted by each surface was uniquelydefined by the surface radiation properties and the thermalboundary conditions imposed on it. The surface propertieswere quantified in terms of emissivity, reflectance, transmit-tance, and radiation temperature. These properties werenot dependent on direction (Yalcintas, 2006). The multi-band radiation model was also chosen in this study; itseparated the waveband into two bands, long-wave (3–100 lm) and shortwave (0.1–3 lm). The optical propertiesin the two wavebands were different and the optical perfor-mances in the two wavebands were separately calculated.

The turbulence model adopted the standard two-layerk-e model, which combines the standard k-e model andthe two-layer approach. The standard two-layer k-e model

can function with low-Reynolds number types (y+ � 1) aswell as wall-function type meshes (y+ > 30) (Yalcintas,2006). The two-layer, total y+ wall treatment (Yalcintas,2006) was applied as the wall treatment model; it employeda blended wall law to estimate shear stress and providedacceptable results for both coarse meshes (y+ > 30) and finemeshes (y+ � 1).

The CFD simulations applied the steady state mode,finite volume method, second-order upwind convectionscheme and the SIMPLE solution algorithm (Yalcintas,2006). Commercial CFD software (STAR-CCM+4.04.011) was used in the mathematical calculations(Yalcintas, 2006). The accuracy of the method has beenverified by Zeng et al. who ran a series of experiments ina DSF test room (Fig. 4). The DSF was constructed ofouter glass (with two openings to the outdoor space), cav-ity, venetian blind, and inner glass. The DSF cavity was2.0 m in height, 0.8 m in distance between the two glassesand 3.0 m in east–west direction width. Both two openingsin the outer glass were 0.2 m wide. Thermocouples wereused to monitor the temperature in the cavity at 6 differentheights. Tracer gas (SF6) was used to measure the ventila-tion rate. The simulated results were then compared withexperimental data. The validation showed good computa-tional accuracy for the numerical calculation approach,with main temperature errors kept below 2 �C and ventila-tion rate errors below 0.1 kg/s (Zeng et al., 2012). There-fore, this CFD method was considered reliable and wasused to validate the fast calculation method proposedabove.

Table 2Meteorological parameters.

Case A0 (�) Jdir (W/m2) Jog,dir (W/m2) Jog (W/m2) toutdoor (�C)

1 71 880 286.5 386.5 222 69 1000 358.4 458.4 243 71 880 286.5 386.5 244 84 570 59.6 159.6 225 76 890 215.3 315.3 276 73 1000 292.4 392.4 297 76 890 215.3 315.3 308 89 610 10.6 110.6 289 75 890 230.3 330.3 28

10 72 1000 309.0 409 2911 75 890 230.3 330.3 3012 88 590 20.6 120.6 2913 67 880 343.8 443.8 2714 64 1000 438.4 538.4 2915 67 880 343.8 443.8 3016 77 550 123.7 223.7 2917 54 870 511.4 611.4 2318 53 1000 601.8 701.8 2519 54 870 511.4 611.4 2620 57 500 272.3 372.3 24

Note: Jdir is the radiosity of direct solar radiation; Jog,dir is the radiosity of direct radiation on the outer surface, which equals Jdir�sinA’.

Fig. 6. Simulation results of Model 1.Fig. 7. Simulation results of Model 2.

310 F. Xue, X. Li / Solar Energy 114 (2015) 303–313

3.3. Simulation results

The values of qsr, qlr and qconv were calculated from thesimulations. In order to separate UðT ig;es � T outdoorÞ andUðT outdoor � T roomÞ, models with outdoor air temperatureidentical to the indoor temperature (26 �C) were simulated;other parameters remained unchanged. Hence, the heatgain through the inner glass was UðT ig;es � T outdoorÞ andthe difference between the two heat fluxes wasUðT outdoor � T roomÞ. This approach provided each part ofthe indoor heat gain. Figs. 6 and 7 shows a summaryresults for the two DSF models.

4. Validation

The simulation results were used to validate the pro-posed calculation method. In the method, the RCI value,

U value, and transmittance of the DSF need to be deter-mined. The RCI value was obtained from the simulationresults by curve fitting according to Eq. (18). Transmit-tance of the DSF and the heat transfer coefficient of theinner glass were calculated. Thus, according to the pro-posed fast calculation method, the indoor heat gainthrough a DSF under any meteorological condition wasmeasurable without requiring additional CFD simulations.

4.1. RCI calculation

Eq. (18) shows that curve fitting of the RCI was success-fully accomplished; the RCI values of the two differentmodels were obtained. Figs. 8 and 9 show the curve fittingresults. The RCI for Model 1 and 2 equaled 0.560 and0.742, respectively. A larger RCI represented a higher level

U (Tig,es-Toutdoor)=0.560Jog2/3

0

10

20

30

40

50

60

70

0 200 400 600 800

U( Tig,es-T

outdoor)

(W/m

2 )

Jog (W/m2)

fitted curve computed results

Fig. 8. Fitted results of RCI of Model 1.

U (Tig,es-Toutdoor)=0.742Jog2/3

0

10

20

30

40

50

60

70

0 200 400 600 800

U(Tig,es-T

outdoor)

(W/m

2 )

Jog (W/m2)

fitted curve computed results

Fig. 9. Fitted results of RCI of Model 2.

F. Xue, X. Li / Solar Energy 114 (2015) 303–313 311

of heat flux through the inner glass converted from Jog,which was caused by different ventilation opening struc-tures. Model 2 had three bafflers in each opening of theouter glass, while Model 1 had none. Bafflers acted as resis-tances for airflow, leading to poor heat exhausting and ahigher inner glass temperature, eventually resulting in larg-er heat gain through the inner glass.

Fig. 10. Results comparison for Model 1.

4.2. Selection of transmission parameters

The value of qsr was calculated according to Section 2.2.The configuration and optical parameters are provided inSection 3.1 and 3.2. Over 99% of the solar radiation energywas in the shortwave spectrum (0.1–3 lm) (Gates, 1966);therefore, qsr can be obtained when based on shortwaveoptical properties.

Fig. 11. Results comparison for Model 2.

4.3. U calculation

Table 1 shows the values of dig and kig. Values for hlr andhig,is were estimated based on empirical values. For thegiven conditions, which were natural convection heattransfer and long-wave radiation heat transfer betweenthe indoor and glass surface, the values of hig,is and hlr weretreated as 8 W/(m2 K) and 5.5 W/(m2 K), respectively.

Thus, according to Eq. (5), U was calculated as 3.65 W/(m2 K).

Based on the results, all the parameters for calculatingindoor heat gain were solved. In order to validate theindoor heat gain in different meteorological conditions, acalculation and comparison with CFD simulation resultswas performed (Figs. 10 and 11; simulation results on left).

Table 3 summarizes deviations of the 20 cases, includingthe largest absolute deviations of the three parts of indoorheat gain described in Section 2.3 ðqsr;UðT ig;es

�T outdoorÞ; and UðT outdoor � T roomÞÞ, as well as the largestand average absolute deviations of the total indoor heatgain q. It shows few differences between the CFDsimulation results and the proposed calculation method.The proposed fast calculation method showed consistencywith CFD results, especially UðT outdoor � T roomÞ andUðT ig;es � T outdoorÞ. Based on these comparisons of heatfluxes of the two CFD models, the computational accuracyof the proposed method was proved to be acceptable.

Table 3Summary of the deviations of the 20 compared cases.

Deviation W/m2 Largest deviation Average deviation

qsr UðT outdoor � T roomÞ UðT ig;es � T outdoorÞ q q

Model 1 �3.21 0.31 �1.44 �4.55 �1.91Model 2 �3.21 �0.64 �1.24 �4.16 �0.84

312 F. Xue, X. Li / Solar Energy 114 (2015) 303–313

Practically, the indoor heat gain was separately calculated.Furthermore, all the required calculation parameters couldbe obtained without CFD simulations (except RCI, whichcould still be fitted with only a small number of CFDsimulations). Hence, the indoor heat gain through a DSFcould be calculated quickly for any meteorologicalconditions.

5. Application

The proposed method was applied to the assessment andcomparison of the two DSF models above. Based on theresults in Section 4 as well as hourly meteorological data(Beijing, China), the total indoor heat gain for Model 1and 2 throughout the entire cooling season were calculated.Based on relevant conventions, the cooling season in Bei-jing was designated as 15 May to 15 September. Consider-ing the working schedule of people in commercialbuildings, daytime was defined as the hours between8:00 am and 6:00 pm. The proposed calculation methodsuccessfully provided the area-averaged daytime heat gain(computed according to the results in Section 4 as well asthe hourly meteorological data). Among the meteoro-logical parameters, the south horizontal solar diffuse anddirect radiation intensities were obtained from historicaldata (Song et al., 2005) and the solar altitude angle was cal-culated according to the orbit and rotation of the earth(Reda and Andreas, 2004). Hence, each part of the heatgain for each day of the cooling season (Model 1 and 2)was separately calculated. The total heat gain in the coolingseason was obtained by summing up the results.

Table 4 shows the results of the total indoor heat gainfor Model 1 and 2. Model 2 had a larger heat transferthrough the inner glass as well as a smaller solar radiationtransmission compared with Model 1 (because the bafflerand shading device increased airflow resistance). Accordingto the total indoor heat gain for the daytime during a cool-ing season, the air resistance effect was the most pre-dominant factor. The heat gain for Model 2 was 12.3%larger than for Model 1. The results also showed that therewas 7.4% more short-wave radiation transmission in

Table 4Results summary of total indoor heat gain for Model 1 and 2 duringcooling season.

Unit: MW h/m2 Qsr Qlr + Qconv Q

Model 1 69.98 82.30 152.28Model 2 65.16 105.78 170.94

Model 2 than in Model 1. As such, the proposed methodwas applied to the assessment of the two DSF models.

6. Discussions

In the proposed calculation method, an exponentialrelationship between U(Tig,es � Toutdoor) and Jog was dis-covered. However, as shown in Figs. 8 and 9, the relation-ship becomes almost linear when Jog is greater than 100 W/m2. Similar result was also presented by other researchers(Perez-Grande et al., 2005), who studied the influence ofglass properties on the performance of DSFs with Jog ran-ged from 100 to 500 W/m2 under the same temperatureindoor and outdoor (U(Toutdoor � Troom) equals 0). Theirresult suggested a linear relationship between total indoorheat gain and Jog, which corresponded to ours. However,they did not make further research about the mechanism,while we found the exponential relationship and adoptedit in our fast assessment method.

The double-skin facade model in this study needs about8 h to reach convergence (about 2500 iterations) at ourworkstation (Intel i7 octa-core CPU). The workload of cal-culating the hour-by-hour indoor heat gain by CFDmethod is enormous, and no one has ever done that. How-ever, the proposed method has made the hour-by-hourCFD results practical to obtain. According to the curve fit-ting results in the validation, the goodness-of-fit for bothcases were over 0.99, suggesting that the power law corre-lation was validated. So RCI is the only one undeterminedcoefficient in the correlation. Theoretically, only onesimulation is enough to get the RCI value. Even if the pos-sible deviation is considered, we believe that three simula-tions are enough. So the simulation can be finishedwithin one day. This is a significant advantage in reducingthe simulation time and makes the method much morepractical.

Moreover, RCI is an indicator independent of meteoro-logical conditions including wind, temperature, and radia-tion. RCI is solely dependent on the structure, materialcharacteristics of the DSF itself, so RCI could also serveas a unique parameter to evaluate DSFs’ thermal perfor-mance. However, as described in Section 3.2, RCI is calcu-lated with vents fully opened and shading device fullyclosed, but in real cases, DSFs are not always fixed andmay have different utilization factors due to different time(Ruiz-Pardo et al., 2010). So RCI can only be used inassessing the best thermal performance of DSFs, but notin calculation of the real hour-by-hour heat gain, becausethe utilization factors of vents and shading device may vary

F. Xue, X. Li / Solar Energy 114 (2015) 303–313 313

from time to time. This flaw will be the next major problemto be solved in further research.

7. Conclusion

This paper proposed a novel approach for performing afast calculation on the indoor heat gain of a naturally ven-tilated DSF during a cooling season. This approach sig-nificantly reduced the amount of required CFDsimulations without compromising accuracy. It calculatedhourly indoor heat gain through the DSF according tothe CFD simulations. This proposed method separatedthe indoor heat gain through the DSF into two parts. Bothparts of the heat gain were separately analyzed and calcu-lated; the Radiation Conversion Index (RCI) was thenapplied to the calculation. RCI represented the averagelevel of heat flux through the inner glass converted fromJog; it was unaffected by meteorological conditions. Therelationship between Jog and the indoor heat gain was thenestablished. Additionally, RCI was obtained using only asmall number of CFD simulations; this overcame the diffi-culty of calculating thermal performance for the durationof a cooling season and also significantly reduced the work-load. Verifications were conducted and the proposedmethod was accurate. As such, the proposed method canbe applied to both thermal performance analysis and opti-mal design for the naturally ventilated DSFs. Moreover,RCI could potentially serve as a unique indicator to evalu-ate DSFs’ thermal performance.

References

ASHRAE Handbook, 2009. Fundamentals (Vol. 111). Atlanta: AmericanSociety of Heating, Refrigerating and Air Conditioning Engineers.

Balocco, C., 2004. A non-dimensional analysis of a ventilated doublefacade energy performance. Energy Build. 36 (1), 35–40.

Baofeng, L., 2004. The Research on Climatic-active Design strategy ofBuilding Skin in Hot-summer and Cold-winter Zone. TsinghuaUniversity, Doctoral Dissertation, Beijing, pp. 37–45.

Chan, A.L.S., Chow, T.T., Fong, K.F., Lin, Z., 2009. Investigation onenergy performance of double skin facade in Hong Kong. EnergyBuild. 41 (11), 1135–1142.

Chen, H., Jiang, Q., Zhang, J., Guo, K., Zhang, Z., Cui, C., 2005. Finiteanalysis calculation method of the hot air flow inside the doublecurtain wall. Acta Sci. Nat. Univ. Sunyatseni 44 (1), 34–37.

Chou, S.K., Chua, K.J., Ho, J.C., 2009. A study on the effects of doubleskin facades on the energy management in buildings. Energy Convers.Manage. 50 (9), 2275–2281.

Corgnati, S.P., Perino, M., Serra, V., 2003. September 14–18. Energyperformance evaluation of an innovative active envelope: results froma year round field monitoring. Paper Presented at the 2nd Interna-tional Conference on Building Physics.

Faggembauu, D., Costa, M., Soria, M., Oliva, A., 2003. Numericalanalysis of the thermal behaviour of glazed ventilated facades inMediterranean climates. Part II: Applications and analysis of results.Sol. Energy 75 (3), 229–239.

Fallahi, A., Haghighat, F., Elsadi, H., 2010. Energy performanceassessment of double-skin facade with thermal mass. Energy Build.42 (9), 1499–1509.

Gates, D.M., 1966. Spectral distribution of solar radiation at the earth’ssurface. Science 151 (3710), 523–529.

Gratia, E., De Herde, A., 2004. Natural ventilation in a double-skinfacade. Energy Build. 36 (2), 137–146.

Jiang, Q., Long, W., 2006. Energy efficiency and design optimization ofdouble-skin facade buildings. J. HV AC (36), 58–63.

Jiru, T.E., Haghighat, F., 2008. Modeling ventilated double skin facade –a zonal approach. Energy Build. 40 (8), 1567–1576.

Jiru, T.E., Tao, Y.-X., Haghighat, F., 2011. Airflow and heat transfer indouble skin facades. Energy Build. 43 (10), 2760–2766.

Manz, H., 2004. Total solar energy transmittance of glass double facadeswith free convection. Energy Build. 36 (2), 127–136.

Manz, H., Schaelin, A., Simmler, H., 2004. Airflow patterns and thermalbehavior of mechanically ventilated glass double facades. Build.Environ. 39 (9), 1023–1033.

Pappas, A., Zhai, Z., 2008. Numerical investigation on thermal perfor-mance and correlations of double skin facade with buoyancy-drivenairflow. Energy Build. 40 (4), 466–475.

Park, C.-S., Augenbroe, G., Messadi, T., Thitisawat, M., Sadegh, N.,2004. Calibration of a lumped simulation model for double-skin facadesystems. Energy Build. 36 (11), 1117–1130.

Perez-Grande, I., Meseguer, J., Alonso, G., 2005. Influence of glassproperties on the performance of double-glazed facades. Appl. Therm.Eng. 25 (17–18), 3163–3175.

Poirazis, H., 2004. Double Skin Facades for Office Buildings. LundUniversity.

Reda, I., Andreas, A., 2004. Solar position algorithm for solar radiationapplications. Sol. Energy 76 (5), 577–589.

Ruiz-Pardo, A., Dominguez, S.A., de la Flor, F.J.S., Lissen, J.M.S., 2010.Simulation model for some types of double envelope elements. Int. J.Vent. 9 (3), 227–239.

Saelens, D., Carmeliet, J., Hens, H., 2003. Energy performance assessmentof multiple-skin facades. HVAC&R Res. 9 (2), 167–185.

Saelens, D., Roels, S., Hens, H., 2008. Strategies to improve the energyperformance of multiple-skin facades. Build. Environ. 43 (4), 638–650.

Safer, N., Woloszyn, M., Roux, J.J., 2005. Three-dimensional simulationwith a CFD tool of the airflow phenomena in single floor double-skinfacade equipped with a venetian blind. Sol. Energy 79 (2), 193–203.

Song, F., Zhu, Q., Wu, R., 2005. Meteorological Data for China BuildingThermal Environment Analysis. China building industry press,Beijing.

Stec, W., Paassen, A.v., 2005. Symbiosis of the double skin facade with theHVAC system. Energy Build. 37 (5), 461–469.

Tanimoto, J., Kimura, K.-I., 1997. Simulation study on an air flowwindow system with an integrated roll screen. Energy Build. 26 (3),317–325.

Xu, L., Ojima, T., 2007. Field experiments on natural energy utilization ina residential house with a double skin facade system. Build. Environ.42 (5), 2014–2023.

Xu, X.-L., Yang, Z., 2008. Natural ventilation in the double skin facadewith venetian blind. Energy Build. 40 (8), 1498–1504.

Yalcintas, M., 2006. An energy benchmarking model based on artificialneural network method with a case example for tropical climates. Int.J. Energy Res. 30 (14), 1158–1174.

Zeng, Z., Li, X., Li, C., Zhu, Y., 2012. Modeling ventilation in naturallyventilated double-skin facade with a venetian blind. Build. Environ.57, 1–6.

Zhou, J., Chen, Y., 2010. A review on applying ventilated double-skinfacade to buildings in hot-summer and cold-winter zone in China.Renew. Sustain. Energy Rev. 14 (4), 1321–1328.