Ventilated facades energy performance in summer cooling of buildings

Solar Energy 75 (2003) 491–502 www.elsevier.com/locate/solener

Ventilated facades energy performance in summer cooling of buildings M. Ciampi, F. Leccese, G. Tuoni

*

Department of Energetica ‘‘L. Poggi’’, Faculty of Engineering, University of Pisa, Via Diotisalvi 2, 56126 Pisa, Italy Received 30 September 2002; received in revised form 21 August 2003; accepted 2 September 2003

Abstract The use of ventilated facades and roofs can help to reduce summer thermal loads and, therefore, the energy consumption due to air-conditioning systems. This paper discusses a simple analytical method for the calculation of the energy saving achievable by using ventilated facades in which the air flow inside the air duct is due to stack effect. Two particular cases of outstanding importance are investigated. The first in which the inner masonry wall is given, and the air duct and the outer facing have to be optimized. The second in which the outer facing is given, and the inner masonry wall and the air duct have to be optimized. The first case can occur in existing buildings renovation, while the second case can occur during the design process. Finally, the influence of the variation of some quantities necessary for calculation on the energy performance of ventilated facades is investigated. In particular, the energy performance of such facades results to be strongly influenced by the air duct width, the insulating material distribution, the solar radiation intensity, the wall outer surface thermal resistance and the roughness of the slabs delimiting the air duct.
2003 Elsevier Ltd. All rights reserved. Keywords: Ventilated facades; Energy performance of buildings; Energy saving; Summer cooling; Solar radiation

1. Introduction The recent European Directive on the energy performance of buildings (Directive 2002/91/EC) focuses its attention on the fact that the air-conditioning plants have become, in the last few years, widespread systems, in particular in the countries of Southern Europe. This creates considerable problems at peak load times; in June 2002 in Italy the power required at the summer peak equalled the one required at the winter peak. For this reason the Directive suggests adopting priority strategies which enhance the thermal performance of buildings during the summer period. For instance, passive cooling techniques could be developed to a greater extent in order to improve the indoor climatic conditions and the microclimate around buildings. Ventilated walls,

*

Corresponding author. Tel.: +39-50-569642; fax: +39-50569604. E-mail address: [email protected] (G. Tuoni).

facades and roofs, if well designed, can help to reduce considerably the summer thermal loads due to direct solar radiation (Ciampi et al., 2003a,b, 2002a–d; Leccese, 2002; Afonso and Oliveira, 2000; Balocco, 2002; Bartoli et al., 1997a,b; Ciampi and Tuoni, 1995, 1998; Gan, 1998; Mootz and Bezian, 1996). Ventilated facades can be used even in cases of renovation of existing buildings, for instance, in the absence of rules relating to historic-architectural preservation. Ventilated structures can prove useful also for the cooling of photovoltaic panels (PV) in order to increase their efficiency (Brinkworth et al., 2000; Mei et al., 2003). A complete thermofluid dynamic analysis of a ventilated air duct requires an accurate knowledge of heat transfer coefficients, friction factors and thermophysical properties of the materials; the determination of such quantities is, unfortunately, not so easy and values currently used for them are often quite uncertain. In particular, the uncertain knowledge of heat transfer coefficients and the head loss inside the air duct can reduce, in many cases, the reliability of the use of

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2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2003.09.010

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M. Ciampi et al. / Solar Energy 75 (2003) 491–502

Nomenclature absorptivity to solar radiation, dimensionless b roughness of the surfaces inside the air duct (m) cp air specific heat at constant pressure (J kg
1 K
1 ) C ¼ m_ cp =‘L specific heat capacity rate (W K
1 m
2 ) d thickness of the air duct (m) D hydraulic diameter (m) Ec , Ep kinetic and potential energy for mass unit (J kg
1 ) g acceleration due to gravity (m s
2 ) m_ mass flow rate (kg s
1 ) H radiative correction factor, dimensionless k thermal conductivity (W m
1 K
1 ) G solar radiation intensity (W m
2 ) ‘ width of the air duct (m) L length of air duct (m) peL external air pressure at x ¼ L (Pa) pe0 external air pressure at x ¼ 0 (Pa) p0 air pressure inside the duct at x ¼ 0 (Pa) pL air pressure inside the duct at x ¼ L (Pa) p air pressure (Pa) Pr ¼ gcp =k Prandtl number q, q1 , q2 heat fluxes (W m
2 ), Eqs. (5) Q heat flux coming into the room (W m
2 ), Eq. (13) Q0 heat flux coming into the room with closed air duct (W m
2 ), Eq. (14) rA , rB convection resistance inside the air duct (m2 K W
1 ), Fig. 1 r1 , r2 thermal resistances (m2 K W
1 ), Eqs. (1) ri inner surface thermal resistance (m2 K W
1 ) re outer surface thermal resistance (m2 K W
1 ) rp equivalent resistance (m2 K W
1 ), Eq. (7) R thermal resistance (m2 K W
1 ), Eq. (1) RA , RB conductive thermal resistance, respectively of the slabs A and B (m2 K W
1 ) Rcd resistance to heat flux along a closed duct (m2 K W
1 ) Re , Ri thermal resistance (m2 K W
1 ), Eqs. (2) Rt ¼ Re þ Ri total thermal resistance of the ventilated facades (m2 K W
1 ) a

sophisticated and complex calculation methods, such as the ones based on the computational fluid dynamics (CFD). Note that in most cases the precise value of energy saving, achievable by using a given ventilated facade, is of little interest compared to the criteria, even qualitative, concerning the positioning of the insulating layer, the air duct dimensions, and the materials to be used for the construction of the inner and outer slabs.

total thermal resistance of the ventilated facades with closed air duct (m2 K W
1 ) RW thermal resistance (m2 K W
1 ), Eq. (7) R ¼ rA þ rB þ C thermal resistance (m2 K W
1 ) S energy saving, dimensionless t temperature at node O (K), Fig. 1c
t mean temperature (K), Eq. (13) T1 , T2 temperature of the air duct’s inner faces, respectively of the slabs A and B (K), Fig. 1b–c Ti indoor air temperature (K) Te sol–air temperature (K) T0 outdoor air temperature in the shade (K); air temperature at duct inlet (K) TL air temperature at duct outlet (K) T ¼ T ðxÞ air temperature (K) Tm mean temperature (K), Eq. (10) T average air temperature inside the duct (K), Eq. (12) Tb ¼ ðT1 þ T2 Þ=2 arithmetical mean temperature (K) W0 air velocity at the duct inlet (m s
1 ) x longitudinal coordinate (m) z ¼ Re =Rt dimensionless parameter, Eq. (3) Rtnv

Greek symbols c ¼ CRtnv dimensionless parameter, Eqs. (15) C radiative resistance between the slabs A and B of the air duct (m2 K W
1 ), Fig. 1b e1 , e2 emissivity of the air duct’s inner faces, respectively of the slabs A and B g air dynamic viscosity (kg m
1 s
1 ) g0 air viscosity at duct inlet (kg m
1 s
1 ) k friction factor, dimensionless kin friction factor at duct inlet, dimensionless kou friction factor at duct outlet, dimensionless l dimensionless quantity, defined by Eq. (9) q air density (kg m
3 ) q0 air density at duct inlet (kg m
3 ) qL air density at duct outlet (kg m
3 ) r Stefan–Boltzmann constant (W m
2 K
4 ) u dimensionless environmental parameter, Eqs. (15) v ¼ Rtnv =Rt dimensionless parameter, Eqs. (15)

This paper discusses a simple analytical method for design applications, able to provide all the useful criteria for choosing the most suitable ventilated facade to be used in case of forced ventilation (due to the action of a fan) and natural ventilation (stack effect). Two particular cases of outstanding importance are investigated. The first in which the inner masonry wall is given, and the air duct and the outer facing have to be optimized.

M. Ciampi et al. / Solar Energy 75 (2003) 491–502

The second in which, the outer facing is given, and the air duct and the inner masonry wall have to be optimized. Finally, the influence of the variation of some quantities necessary for calculation such as the heat transfer coefficients of the outer facing and the roughness of the slabs delimiting the air duct, on the energy performance of ventilated facades, is investigated.

Re ¼ RA þ re þ r1 ;

493

Ri ¼ RB þ ri þ r2 ;

Rt ¼ Re þ Ri ð2Þ

with RA and RB conductive thermal resistances of the slabs A and B, re and ri respectively outer and inner surface thermal resistances. The following resistance ratio should also be introduced: z ¼ Re =Rt

2. Mathematical model The ventilated facade is schematized as consisting of two slabs A (outer) and B (inner) delimiting an air duct into which air flows. Let L be the length of the structure (in the direction of the air flow), ‘ the width and d the thickness of the air duct; a reference axis x, orientated as in Fig. 1a, is assumed. The air flows into the air duct from the inlet section (x ¼ 0) to the outlet section (x ¼ L).

The radiative heat transfer within the air duct can be characterized (by linearization) with a thermal resistance C; the convective heat transfer within the air duct can be characterized with the thermal resistances rA and rB (see Fig. 1b). All thermal resistances refer to per surface unit. T1 and T2 are assumed to be the temperatures of the air duct’s inner faces, respectively of the slabs A and B, while T is assumed to be the temperature of the air flowing into the air duct (see Fig. 1b); these temperatures obviously vary with x. It is convenient to replace the triangular mesh among the temperatures T1 , T2 and T ðxÞ of Fig. 1b with the equivalent star one, of Fig. 1c, among the same temperatures, by introducing the resistances r1 , r2 and R: r2 ¼ rB  C=R;

Let Ti be the indoor air temperature and Te the sol–air temperature defined by: Te ¼ T0 þ are G with T0 the air temperature in the shade, a the absorption coefficient to solar radiation of the outer face of the slab A and G the incident solar radiation intensity. Indicating by tðxÞ the temperature inside the node O of Fig. 1c, the following local relations are valid for the energy balance of the air duct: C dT ¼ ðt
T Þdx=LR;

q ¼ q1
q2

ð4Þ

where heat fluxes are given by:

2.1. Heat transfers

r1 ¼ rA  C=R;

ð3Þ

R ¼ rA rB =R

ð1Þ

with R ¼ rA þ rB þ C. The following relations have to be set:

q ¼ ðt
T Þ=R;

q1 ¼ ðTe
tÞ=Re ;

q2 ¼ ðt
Ti Þ=Ri ð5Þ

By C the air heat capacity rate per surface unit, relating to the whole heat transfer surface area ‘ L, has been indicated; we have: C ¼ m_ cp =‘L where m_ is the mass flow rate and cp the specific heat at constant pressure of air (mean value for the temperatures of interest). Notice that radiation has two distinct influences: it changes the purely convective resistances rA and rB in the corresponding surface thermal resistances r1 and r2 , and introduces a thermal resistance R for the heat flux absorbed (q) by the fluid in the air duct (see Fig. 1c). More precisely, it is convenient to introduce the dimensionless parameter H : H¼


 
1 R RW ¼ rp RW þ C 1 þ Rt rA þ rB

ð6Þ

Fig. 1. Schematization of the ventilated facade (a) and of thermal resistances inside the air duct: triangular mesh (b); star mesh (c).

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M. Ciampi et al. / Solar Energy 75 (2003) 491–502

with:

with: rp ¼ rA rB =ðrA þ rB Þ;

RW ¼ RA þ RB þ ri þ re

ð7Þ

From Eq. (6) it follows that the higher the radiation resistance C is the smaller H is. In particular, for C ! 1 (negligible radiation) H ! 0 is obtained and for C ! 0 (dominant radiation) H ¼ rp =RW is obtained. Hence, the physical meaning of H turns out to be evident: it is a dimensionless parameter, 0 < H < rp =RW , measuring the radiative effects not quantified by the surface thermal resistances r1 and r2 . From Eqs. (5) and from the second of Eqs. (4) it follows that: t ¼ ½HTm þ zð1
zÞT =½H þ zð1
zÞ

ð8Þ

while the first of Eqs. (4) becomes: dT =dx ¼ lðTm
T Þ=L

ð9Þ

having introduced the dimensionless quantity: l ¼ 1=½CRt ðH þ zð1
zÞÞ and the temperature Tm defined by: Tm ¼ zTi þ ð1
zÞTe

ð10Þ

Tm is immediately acknowledged to represent the mean value of the temperatures Ti and Te weighed on the conductances 1=Ri and 1=Re . Integrating Eq. (9), with the obvious boundary condition T ðx ¼ 0Þ ¼ T0 , we obtain: T ðxÞ ¼ Tm þ ðT0
Tm Þ  e
lx=L

Rtnv ¼ RA þ RB þ re þ ri þ Rcd where Rcd is the thermal resistance of the closed air duct. The percentage energy saving S, due to the facade ventilation, can be defined by the following relation: S¼

Q0
Q Q0

It is useful to introduce the dimensionless parameters u, v and c defined by: u¼

Te
T0 ; Te
Ti

v ¼ Rtnv =Rt > 1;

c ¼ CRtnv ¼ m_ cp

Rtnv ‘L ð15Þ

The ratio u can be interpreted as an ‘‘environmental parameter’’ characterizing thermal field and solar radiation. The resistive ratio v quantifies the thermal resistance decrease within the air duct, due to the air flow inside the duct. It still results that v > 1, even if values of v differing significantly from 1 refer to badly thermal insulated structures. The parameter c represents the product between the air heat capacity rate, C, and the total thermal resistance of the closed air duct, Rtnv . From Eqs. (13)–(15), the energy saving S can be put in the following form:
  v S ¼ 1
v þ czðu
zÞ 1
exp
c½H þ zð1
zÞ

ð11Þ

ð16Þ

which provides the temperature trend of the air flowing into the air duct. The mean value of the T ðxÞ throughout the air duct is: Z L T ¼ ð1=LÞ T ðxÞ dx

From Eq. (16) it follows that, in spite of the problem complexity and the large number of physical quantities influencing a ventilated facade thermal behaviour, it is possible to resume its energy performance using a unique formula, having as input quantities just five dimensionless parameters: u, z, v, c and H. The influence of the five parameters on S has been studied in Ciampi et al. (2002a), where the behaviour of some ventilated facades and roofs, chosen among those of simplest construction, has also been investigated. In summer ðTe > Ti Þ and for rooms provided with an air-conditioning plant, we have, generally, Ti < T0 . Then it results: u < 1; observe, however, that in some cases (for example, rooms not provided with an air-conditioning plant) we can have Ti > T0 and then u > 1. In the absence of insolation we obviously have Te ¼ T0 (u ¼ 0) and from Eq. (16) it follows that S 6 0: therefore, the ventilated structure does not prove to be efficient from an energy point of view. In presence of insolation the ventilation is efficient (S > 0) only for z < u; under these conditions S rises as c increases. In other words: for u > 1 the air duct ventilation is efficient for any value of z; for high values of c the heat flux Q may result to become negative, i.e. a heat removal from

0

¼ Tm þ ðT0
Tm Þ  ð1
e
l Þ=l

ð12Þ

By using Eqs. (8) and (12) the mean heat flux coming into the room through the ventilated structure results to be: Z L Q ¼ ð1=LÞ q2 dx ¼ ð
t
Ti Þ=Ri 0

¼ ðTe
Ti Þ=Rt
zCðTL
T0 Þ

ð13Þ

with TL ¼ T ðx ¼ LÞ. Eq. (13) points out the role of the heat flux zCðTL
T0 Þ, removed by ventilation from the room, which is the useful effect of the structure under examination. In absence of ventilation, the heat flux coming into the room is: Q0 ¼

Te
Ti Rtnv

ð14Þ

M. Ciampi et al. / Solar Energy 75 (2003) 491–502

the room might occur; in such a situation a value of S higher than unit is formally obtained. For u < 1 ventilation is never efficient (S < 0) for air ducts with z > u. In winter and for rooms provided with a heating plant we have Ti > T0 and, generally, Te < Ti ; in these conditions we have u < 0 and it results that S < 0. In winter the ventilated structure does not prove to be energy efficient. In winter it is advisable to close the air duct with self-regulating dampers or rather to allow a small ventilation in order to facilitate the draining of condensation effects.

If the dependence of the density on the pressure is disregarded and if the mass balance (qW ¼ q0 W0 ) is used, we have: qL ¼ q0 T0 =TL ;

þ q0 W02 k

dp þ q dEc þ q dEp þ q dL ¼ 0

ð18Þ

Connected with the outlet section at x ¼ L a localized head loss of friction factor kou occurs. While passing through this section the air velocity changes from the value WL at the duct outlet to the zero value on the outside, the pressure changes from the value pL to the outdoor value peL and, as well as in Eq. (18), the following can be written: peL
pL þ ð1=2ÞqL WL2 ð1
kou Þ ¼ 0

ð20Þ

L T ¼0 2D T0

ð21Þ

with T given by Eq. (12) and with: Z L h1=T i ¼ ð1=LÞ dx=T ¼ ½1 þ ð1=kÞ  lnðTL =T0 Þ=Tm 0

where Eq. (11) has been used. From Eqs. (18), (19) and (21) and using the obvious relation pe0 ¼ peL þ q0 gL we have:  

1
1 kin
1 Lk T kou þ 1 TL  þ  W02 ¼ gL  1
T0 þ T 2 2D T0 2 T0 ð22Þ Since the velocity W0 is known, the mass flow rate of the air flowing into the duct has to be calculated by the obvious relation: m_ ¼ q0 W0 d‘.

ð17Þ

where dp, dEc ¼ dW 2 =2, dEp ¼ g dx represent, respectively, the pressure, the kinetic energy and the potential variations, and dL ¼ kW 2 dx=2D expresses the work due to friction. Connected with the inlet section (x ¼ 0) a localized head loss of friction factor kin occurs. While passing through this section, the air velocity changes from the zero value on the outside to the value W0 at the duct inlet, pressure changes from the value pe0 on the outside to the value p0 at the duct inlet, while the density (q0 ), the temperature (T0 ) and the height remain unvaried; from Eq. (17) we should have: p0
pe0 þ ð1=2Þq0 W02 ð1 þ kin Þ ¼ 0

WL ¼ W0 TL =T0

with qL being the air density in the air duct at x ¼ L. Integrating Eq. (17) from section x ¼ 0 to section x ¼ L, considering k as independent of T and using Eq. (20) we obtain:     TL 1
1 þ gLq0 T0 pL
p0 þ q0 W02 T0 T

2.2. The air flow inside the air duct The mass flow rate m_ of the air flowing into the duct can be considered as an independent variable in cases of forced ventilation, i.e. when the ventilation is provided by using suitable electric fans. In case of natural ventilation the flow rate is determined by the heat field, the air duct geometry, the fluid dynamic head losses and the external atmospheric conditions (in particular, wind velocity and direction). If we neglect the effect of the wind, which is hard to quantify, a valuation of the air flow rates setting in by stack effect in ventilated facades can be made as follows. Let W be the outflow velocity in the duct, q the air density, g the acceleration of gravity, D ¼ 2‘d=ð‘ þ dÞ the hydraulic diameter and k the friction factor of the duct inner faces. With reference to Fig. 1a, the Bernoulli equation for a length dx can be written in the following form:

495

ð19Þ

3. Solution procedure The friction factors and heat transfer coefficients are assumed to be constant along the length of the duct. This is convenient, as it allows an analytical (exponential) expression to be obtained for the heat flux Q and it is, in our case, justified by the fact that the ratio of the duct length to thickness ðL=dÞ is, in any studied case, greater than 50. In the calculations the Haaland relation (Haaland, 1983) has been used for the friction factor k, the Gnielinski formula (Rohsenow et al., 1985) for the convective heat transfer coefficients. The Gnielinski formula is valid for rough ducts and for Reynolds numbers higher than 2300 (this condition is satisfied in all the examined cases). The Haaland and Gnielinski relations require, as input data, the roughness b of the air duct. Generally, the roughness value of the air duct is assumed to be quite high in order to take into account the presence of supports (i.e. reticular rafters, stirrups. . .) inside the air duct; in this respect, in a standard situation it has been estimated as b ¼ 0:02 m. For the radiative thermal resistance between the two slabs the following relation has been considered:

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M. Ciampi et al. / Solar Energy 75 (2003) 491–502

C ¼ ð1=e1 þ 1=e2
1Þ=4r Tb 3 with r the Stefan–Boltzmann constant, Tb the mean temperature between T1 and T2 , e1 and e2 the emissivity of the air duct’s inner faces, respectively of the two slabs A and B. For the air specific heat the mean value cp ¼ 1005 J kg
1 K
1 has been considered; the air density has been evaluated referring to an isobaric transformation for a perfect gas, while for the dependence of the air dynamic viscosity g on the temperature following relation has pthe ffiffiffiffiffiffiffiffiffiffiffiffiffi been considered: gðT Þ ¼ g0 T =300 with g0 ¼ 1:85  10
5 kg m
1 s
1 (at 300 K). The Prandtl number value (Pr) has been considered to be constant and the air thermal conductivity has been obtained by the relation cp gðT Þ=Pr with Pr ¼ 0:719. For a standard situation in summer the following reference climatic conditions have been assumed: Ti ¼ 24 C, T0 ¼ 28 C and G ¼ 400 W m
2 to which the value u ¼ 0:74 corresponds for the environmental parameter (assuming a ¼ 0:70 and re ¼ 0:04 m2 K W
1 ). All the graphs reported hereinafter should be meant to refer, unless it is indicated otherwise, to such a value of the environmental parameter. All calculations have been developed in Maple 8 programming software. For the friction factors kin and kou the minimum values have been considered: kin ¼ 0:5 (sudden air inlet from the atmosphere) and kou ¼ 1 (sudden air outlet into the atmosphere); the presence of narrowings, obstructions, various shapings, protection grills, dirt accumulation, determines a considerable increase in these values. The values of the parameter H , for the limitation H < rp =RW , is small and usually remains lower than to 0.01; from Eq. (16) it follows that the influence of H on the ratio S is very restricted and the higher the value of H is, the smaller S is. The climatic conditions and duct geometry have been assumed to be fixed except for the air duct thickness; values assumed for calculation are indicated in Table 1. As reference values for the thermal resistances of the wall’s outer surface, re , of the wall’s inner surface, ri , and of the non-ventilated air duct, Rcd , the ones recommended by technical standard (EN ISO 6946, 1996) have been assumed. Therefore Rcd ¼ 0:18 m2 K W
1 has been considered for the air duct thickness varying from 0.06 to 0.30 m.

4. Assigned inner masonry wall This case can occur in existing buildings renovation, which represent, in Italy, a remarkable share of building activity. On this topic some recent regional rules (Umbria Region Local Rule n. 38/2000) allow a volumetric increase in order to achieve an energy behaviour im-

Table 1 Reference values for calculation Climatic conditions Outdoor air temperature, T0 Indoor air temperature, Ti Solar radiation intensity, G

28 C 24 C 400 W m
2

Wall’s outer surface Thermal resistance, re Absorptivity, a

0.04 m2 K W
1 0.70

Wall’s inner surface Thermal resistance, ri

0.13 m2 K W
1

Ventilation air duct Width, ‘ Length, L Thickness, d Closed air duct thermal resistance, Rcd Emissivity of surfaces, e Inlet friction factor, kin Outlet friction factor, kou Roughness, b

10 m 15 m 0.15 m 0.18 m2 K W
1 0.9 0.5 1 0.02 m

provement of a building, for example by applying layers of outer facing in order to construct a ventilated air duct (Ciampi et al., 2001). As an example of such a case six ventilated facades have been taken into account, labelled FBj (j ¼ 1; . . . ; 6) and characterized by the same inner masonry wall (slab B) made of hollow brick in blocks to which are anchored the most common types of outer facings (slab A); among them FB2 and FB5 are completely made of brick. In particular, FB1 has an outer facing made of copper plates; FB2 and FB5 present an outer facing made of brick (slabs or hollow flat blocks); FB3 is made of asbestos cement panels; FB4 is made of plates of fine porcelain stoneware; FB6 in plastic panels of reinforced polyester. Thermophysical and geometrical properties of the layers composing the six facades described are reported in Table 2. All facades present a thermal insulating layer (fibreglass in rigid panels) with a thickness of 0.04 m, located inside the air duct close to the inner masonry wall. In practice these are characterized by the same total thermal resistance without ventilation Rtnv ffi 2:0 m2 K W
1 ; the conductive resistance of the inner masonry wall is in any case RB ¼ 1:58 m2 K W
1 . Fig. 2 shows the energy saving S for each facade FBj as the air duct thickness d varies by 0:06 < d < 0:30 m (around the reference value 0.15 m, indicated in Table 1 and in brackets in Table 2). The facade FB2 , completely made of brick, turns out to be the best. Note, for example, that in order to obtain a 35% energy saving an air duct thickness of about 0.17 m is necessary for the facade FB1 , and of just 0.09 m for the facade FB2 . In order to better explain fluid dynamic aspects due to the thickness variation of the air duct Fig. 3 reports

M. Ciampi et al. / Solar Energy 75 (2003) 491–502

497

Table 2 Description of ventilated facades with the same inner masonry wall (RB ¼ 1:58 m2 K W
1 ) No. of layer

Description of layer

Thickness (m)

q (kg m
3 )

k (W m
1 K
1 )

Facade FB1 Rtnv ¼ 1:93 m2 K W
1

1 (Ext) 2 3 4 5 6 (Int)

Copper plates Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.006 (0.15) 0.04 0.015 0.25 0.015

8900 – 100 2000 1400 1800

380 – 0.038 1.40 0.50 0.90

Facade FB2 Rtnv ¼ 2:08 m2 K W
1

1 (Ext) 2 3 4 5 6 (Int)

Brick slabs Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.050 (0.15) 0.04 0.015 0.25 0.015

1 (Ext) 2 3 4 5 6 (Int)

Asbestos cement panels Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.053 (0.15) 0.04 0.015 0.25 0.015

1 (Ext) 2 3 4 5 6 (Int)

Slabs of ceramics Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.0145 (0.15) 0.04 0.015 0.25 0.015

2400 – 100 2000 1400 1800

1 (Ext) 2 3 4 5 6 (Int)

Brick hollow flat blocks Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.040 (0.15) 0.04 0.015 0.25 0.015

1400 – 100 2000 1800 1800

1 (Ext) 2 3 4 5 6 (Int)

Polyester panels Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.004 (0.15) 0.04 0.015 0.25 0.015

1800 – 100 2000 1400 1800

Facade FB3 Rtnv ¼ 1:99 m2 K W
1

Facade FB4 Rtnv ¼ 2:00 m2 K W
1

Facade FB5 Rtnv ¼ 2:01 m2 K W
1

Facade FB6 Rtnv ¼ 1:94 m2 K W
1

the variation of the air mean velocity W0 , inside the air duct, with d. The air velocity clearly results to be maximum by d ffi 0:20 m (Gan, 1998). Fig. 4a shows the variation of S with the solar radiation intensity by 150 < G < 800 W m
2 ; it is clear that the energy saving increases as G increases. In order to minimize summer thermal loads, the bigger the solar radiation is, the more ventilated facades turn out to be efficient.

800 –

0.33 –

100 2000 1400 1800

0.038 1.40 0.50 0.90

315 –

0.92 –

100 2000 1400 1800

0.038 1.40 0.50 0.90 1.00 – 0.038 1.40 0.50 0.90 0.50 – 0.038 1.40 0.50 0.90 0.50 – 0.038 1.40 0.50 0.90

For a better understanding of these graphs in Figs. 4b and 4c are also reported. The variation of Q with G is shown in Fig. 4b for the facades FB1 and FB2 . Notice that the variation of Q with G is quasi-linear for the considered facades. For comparison the linear trend of Q0 (corresponding to the closed air duct) is also reported; the facades FB1 and FB2 are characterized by similar values of the thermal resistance Rtnv . The trend of Q0 is, therefore, very similar for the two facades. The

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M. Ciampi et al. / Solar Energy 75 (2003) 491–502

Fig. 2. Variation of energy saving, S, with air duct thickness, d (m).

Fig. 3. Variation of air velocity, W (m s
1 ), with air duct thickness, d (m).

difference (Q0
Q) and, therefore, the reduction in summer thermal load, achievable by using a ventilated facade, increases sensibly as G increases; for instance, in the case of the facade FB2 , for G ¼ 700 W m
2 it results Q0
Q ffi 6:5 W m
2 , which is a considerable value being able to influence sensibly the thermal balance of buildings with wide-surface facades turned southward. In Fig. 4c the variation of S with G for two values of the difference DT ¼ T0
Ti has been reported for the facades FB2 and FB1 . We have considered: DT ¼ 4 and 6 C. The air properties inside the air duct actually depend on the temperature and in particular on T0 and Ti

and not only on DT ; calculations carried out realizing the same DT with different combinations of the values of T0 and Ti (obviously in the range of the values being of some interest for the examined problem) have pointed out that the energy saving S, for a given facade, depends essentially on DT and just a little on the values of T0 and Ti separately (in Fig. 4c this latter dependence has been neglected). From the graph it turns out to be clear that, for a given facade, S increases sensibly as DT decreases. It is interesting to investigate how to optimize the distribution of the insulating material inside the air duct. For this purpose the fraction e (0 < e < 1) of insulating material located on the outer facing is introduced. By e ¼ 0 all the insulating material is close to the inner masonry wall and we have the disposition reported in Table 2, while by e ¼ 1 all the insulating material is close to the outer facing. Fig. 5 shows the variation of S with e; from the graph it appears to be clear that the energy saving is maximum by e ffi 0:15 for the facade FB2 and by e ffi 0:30 for the facades FB1 , FB3 and FB4 . In any case, the usual positioning of the insulating material close to the inner masonry wall is more efficient than the one close to the outer facing. Finally, the influence of the variation of some quantities necessary for calculation such as the thermal resistance, re , of the wall’s outer surface and the roughness, b, of the slabs delimiting the air duct, on the energy performance of ventilated facades has been investigated. A ventilated facade and the same facade but nonventilated are considered. It is interesting to determine the additional thickness D of insulating material to be used in the non-ventilated facade so that the two facades, ventilated and non-ventilated ones, could show the same heat flux. D obviously depends on the solar radiation intensity G and increases as G increases. For example, where wall FB2 is concerned, the following can be found out by calculation: for G ¼ 300 W m
2 , D ¼ 0:04 m; for G ¼ 700 W m
2 , D ¼ 0:08 m. It appears to be clear that the additional thicknesses of insulating materials being necessary for compensating for the absence of ventilation may result to be considerable. In this respect, it should be noticed that other systems suitable for reducing the solar radiation effect on the building can be used to reduce cooling loads instead of increasing the facade thermal insulation. A possibility could be, for instance, to construct the outer facing using reflecting materials (special steels, titanium alloys, etc.) or to treat it with high-reflection-coefficient paints (Akbari et al., 1999). This system can be considered to be, to a great extent, as an alternative to ventilated facades. Fig. 6 shows the variation of S with re . In all cases, S increases as re increases and the re variation effect turns out to be quantitatively remarkable. Notice how rele-

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Fig. 4. (a) Variation of energy saving, S, with solar radiation intensity, G (W m
2 ). (b) Variation of heat flux coming into the room, Q (W m
2 ), with G (W m
2 ). The dotted line shows the heat flux coming into the room, Q0 (W m
2 ), without ventilation. (c) Variation of energy saving, S, with solar radiation intensity, G (W m
2 ), for two different values of DT : DT ¼ 4 C (solid line); DT ¼ 6 C (thin line).

Fig. 5. Variation of energy saving, S, with the fraction, e (%), of insulating material disposed on the outer facing.

vant is the uncertainty in the evaluation of re , both owing to variability of climatic conditions (i.e. wind velocity) and the difficulty to dispose of good correlations for very wide surfaces. It should be remembered that in the S definition the comparison is made between ventilated facade and closed-air-duct facade, Rtnv being equal; the re increase involves, i.e. a further energy saving in comparison with the one we have by increasing non-ventilated facade thermal resistance. It is clear that the reference value assumed for the roughness (b ¼ 0:02 m) results to be rather unreliable, therefore an analysis of its influence on the energy saving value S appears to be remarkable. Results are visualized in Fig. 7 where b ffi 0:015 m has been assumed as the smaller value of relative roughness b owing to the unavoidable presence of supports of the outer facing.

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Fig. 7. Variation of energy saving, S, with the roughness, b (m). Fig. 6. Variation of energy saving, S, with the thermal resistance, re (m2 K W
1 ) of wall’s outer surface.

5. Assigned outer facing This case can occur during the design process, when, owing to the particular architectural context in which a building is being built, some local rules are imposed on the kind of materials to be used for the construction of the facade. As an example three ventilated facades, labelled FAj (j ¼ 1; . . . ; 3) and characterized by the same outer facing (slab A) made of brick elements preassem-

bled in panels, have been taken into account; the conductive resistance of the outer facing is RA ¼ 0:15 m2 K W
1 . The three facades present a inner masonry wall (slab B) in blocks of lightened brick with density q equal to: 600 kg m
3 for the facade FA1 , 1200 kg m
3 for the FA2 and 2000 kg m
3 for the FA3 . Thermophysical and geometrical properties of layers composing the three described facades are reported in Table 3. Also in this case a thermal insulating layer (fibreglass in rigid panels) with a thickness of 0.04 m, positioned inside the air duct close to the inner masonry wall, has been taken into account.

Table 3 Description of ventilated facades with the same outer facing (RA ¼ 0:15 m2 K W
1 )

Facade FA1 Rtnv ¼ 2:58 m2 K W
1

Facade FA2 Rtnv ¼ 2:16 m2 K W
1

Facade FA3 Rtnv ¼ 1:86 m2 K W
1

No. of layer

Description of layer

Thickness (m)

1 (Ext) 2 3 4 5 6 (Int)

Brick slabs Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in lightened hollow blocks Lime mortar and cement plastering

0.05 (0.15) 0.04 0.015 0.25 0.015

1 (Ext) 2 3 4 5 6 (Int)

Brick slabs Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in hollow blocks Lime mortar and cement plastering

0.05 (0.15) 0.04 0.015 0.25 0.015

1 (Ext) 2 3 4 5 6 (Int)

Brick slabs Air (ventilation duct) Rigid fibreglass panels Cement mortar Brick in half-full blocks Lime mortar and cement plastering

0.05 (0.15) 0.04 0.015 0.25 0.015

q (kg m
3 ) 800 – 100 2000 600 1800 800 – 100 2000 1200 1800 800 – 100 2000 2000 1800

k (W m
1 K
1 ) 0.33 – 0.038 1.40 0.25 0.90 0.33 – 0.038 1.40 0.43 0.90 0.33 – 0.038 1.40 0.90 0.90

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Fig. 8 shows the energy saving S for each facade FAj as the air duct thickness varies by 0:06 < d < 0:3 m. The facade presenting the maximum value of S is the FA1 . In order to compare the energy requirements for cooling we can consider two different ventilated facades characterized, respectively, by energy saving S and S 0 and by different values of thermal resistances Rtnv and R0tnv . On the basis of the obvious meaning of symbols we have: Q0 ¼ ðTe
Ti Þ=Rtnv , Q00 ¼ ðTe
Ti Þ=R0tnv , while for the definition of S it results Q ¼ Q0 ð1
SÞ, Q0 ¼ Q00 ð1
S 0 Þ. From the previous relations it follows: Q0 ¼



Rtnv 1
S 0  R0tnv 1
S

 Q

ð23Þ

that allows to compare directly the energy requirements for cooling concerning the two considered ventilated facades. In the particular case in which the structures show the same thermal resistance Rtnv ¼ R0tnv , the previous relation becomes simply: Q0 ¼ Qð1
S 0 Þ=ð1
SÞ. Suppose, for example, by using the graphs in Fig. 8, that we wish to compare the energy performance of the facade FA3 (Rtnv ¼ 1:86 m2 K W
1 ) with facade FA1 (Rtnv ¼ 2:58 m2 K W
1 ), using an air duct thickness of 0.15 m. From Fig. 8, for d ¼ 0:15 m, we have S ¼ 0:37 for FA3 and S ¼ 0:40 for FA1 . The value put into brackets in Eq. (23) results to be equal to 0.68 and therefore, with the input conditions, the energy requirements in order to keep the room at the required temperature Ti , results to be for the facade FA1 equal to the 68% of the ones needed for the facade FA3 . In Fig. 9 the variation of S with the solar radiation intensity by 150 < G < 800 W m
2 is shown; obviously, in this situation also the energy saving strongly increases as G increases.

Fig. 8. Variation of energy saving, S, with air duct thickness, d (m) in case of facades with the same outer facing (see Section 5).

Fig. 9. Variation of energy saving, S, with the intensity, G (W m
2 ), of solar radiation in case of facades with the same outer facing (see Section 5).

6. Conclusions An analytical method has been illustrated, suitable for design applications, in order to evaluate the energy performance of ventilated facades. As an example of this method two particular cases of outstanding importance have been investigated. The first in which the inner masonry wall is given, and the air duct and the outer facing have to be optimized. The second in which the outer facing is given, and the air duct and the inner masonry wall have to be optimized. The first case can occur in existing buildings renovation in the absence of rules relating to historic-architectonical preservation; the second case can occur during the design process, when, owing to the particular architectural context in which building is being built, some local rules are imposed on the materials to be used for the construction of the facade’s outer facing. The achieved results can be resumed as follows. • In all cases, the energy saving increases as the air duct width d rises, and such a rise turns out to be particularly marked by d < 0:15 m. • The usual disposition of the insulating layer inside the air duct, close to the inner masonry wall, may not be the most efficient from an energy point of view. It is possible to find out an optimal insulating material distribution between the inner masonry wall and the outer facing by which the maximum energy saving can be reached. In all cases, the positioning of the insulating material close to the inner masonry wall is more efficient than the one close to the outer facing.

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• The energy saving increases remarkably as solar radiation intensity increases; the bigger the solar radiation is, the more efficient ventilated facades turn out to be from an energy saving point of view. The facades where the outer facing is made of reflecting materials (special steels, titanium alloys, etc.) strongly reduce the solar radiation influence and should be considered as an alternative to ventilated facades. • The energy saving increases sensibly as the difference between the outdoor and indoor temperatures decreases. • The use of carefully designed ventilated facades will allow, in summer cooling of buildings, an energy saving even exceeding 40%. • The energy saving S is remarkably influenced by the wall’s outer surface thermal resistance value and by relative roughness of the slabs delimiting the air duct. Such parameters, therefore, require an accurate evaluation.

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