Energy-And-Buildings-74-111-119.Pdf

Energy and Buildings 74 (2014) 111–119

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Energy and Buildings

j ournal homepage: www.elsevier.com/locate/enbuild

Energy performance of Trombe walls: Adaptation of ISO

13790:2008(E) to the Portuguese reality

a,b,∗ c d

Ana Briga-Sá , Analisa Martins , José Boaventura-Cunha ,

a,e a,b

João Carlos Lanzinha , Anabela Paiva

C-MADE–Centre of Materials and Building Technologies, University of Beira Interior, 6201-001, Covilhã, Portugal

ECT - School of Science and Technology, University of Trás-os-Montes e Alto Douro UTAD, Quinta de Prados, 5000-801 Vila Real, Portugal

c 1

Multinordeste, S.A., Multifunç ões em Engenharias e Construç ão, 5300-111, Braganç a, Portugal

INESC TEC - INESC Technology and Science (formerly INESC Porto) and ECT - School of Science and Technology, University of Trás-os-Montes e Alto Douro, Portugal

Faculty of Engineering of the University of Beira Interior, 6201-001, Covilhã, Portugal

a r t a b

i c l e i n f o s t r a c t

Article history: The improvement of energy performance in buildings can be achieved through the integration of a Trombe

Received 20 May 2013

wall system. The literature review reveals that more research work is still required to evaluate the real

Received in revised form

impact of this system on the building thermal performance. The study here presented aims to deﬁne a

18 September 2013

calculation methodology of the Trombe wall energy performance, based on ISO 13790:2008(E), adapted

Accepted 27 January 2014

to the Portuguese climatic conditions. The massive wall thickness, the ventilation system and the external

shutters inﬂuence in the system thermal performance is demonstrated. It was concluded that the highest

Keywords:

contributions to the global heat gains is given by the heat transfer by conduction, convection and radiation.

Trombe wall

However, the existence of a ventilation system in the massive wall has a signiﬁcant role in the thermal

Calculation methodology

performance of the Trombe wall, which contribution increases with the increasing of the massive wall

Thermal performance

Energy efﬁciency thickness. It was also applied the Portuguese thermal regulation to a residential building with this system.

It was concluded that energy heating needs can be reduced in 16.36% if a Trombe wall is added to the

building envelope. The results also showed that the proposed methodology provides a valid approach to

compute the Trombe wall thermal performance.

1. Introduction achieve the objectives of the EU, namely reducing greenhouse

gases emissions in 20%, achieve 20% energy savings and increase

Environmental issues and energy consumption are today an the use of renewable energy in 20% by 2020 [3].

increasing and global concern. The building sector is responsible So, it is essential to adopt solutions in order to obtain more

for the majority of energy consumption in the world. In Europe energy efﬁcient and sustainable new and existing buildings. The

it is responsible for 40% of the energy consumption and 36% of study of traditional buildings showed that some construction tech-

the CO2 emissions [1]. In 2002, the European Union (EU) created niques used in these buildings make them more sustainable, due

the Energy Performance of Buildings Directive-EPBD (Directive to the use of local materials such as granite, schist, wood and earth

2002/91/EC) [2], which aims increasing the energy performance (e.g. tabique, taipa and adobe) [4–6] and to the reuse of agriculture

of buildings, according to the climatic conditions of the member waste (e.g. corn cob) [7–9].

states. In 2010, a recast of this directive was adopted in order to The use of solar energy is another way to improve the energy

performance of buildings, which can be done through the integra-

tion of passive solar systems in the buildings envelope [10–14].

These systems were also commonly used in traditional buildings,

∗

Corresponding author at: ECT - School of Science and Technology, University of but have been lost a long time ago, due to the emergence of new

Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados, 5000-801 Vila Real, Portugal, materials and construction systems. So, nowadays, the inclusion of

www.utad.pt and C-MADE–Centre of Materials and Building Technologies, Univer-

these systems in buildings is still not very common, resulting from

sity of Beira Interior, 6201-001 Covilhã, Portugal. Tel.: +351 259350342;

the lack of information about their efﬁciency. The heat storage

fax: +351 259350356.

capacity of materials and construction systems is considered a

E-mail address: [email protected] (A. Briga-Sá).

www.utad.pt passive solar technology. Thick walls made of materials with

112 A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119

Nomenclature

t2 length of the cooling season (h)

Asw area of the Trombe Wall (m ) U0 heat transfer coefﬁcient of the Trombe wall

2 2 ◦

Asol,k effective collecting area of the Trombe wall (m ) (W/(m C))

btr,l reduction factor for the adjacent unconditioned Ui heat transfer coefﬁcient of the internal element in

space with internal heat source l, deﬁned in ISO the Trombe wall

13789 Ue heat transfer coefﬁcient of the external element in

e emissivity of the glazing surface the Trombe wall

Fsh,ob,k shading reduction factor for external obstacles

Fh shading reduction factor for obstacles from the hori- Greek Letters

zon or from other building elements ˛ solar absorption coefﬁcient of the massive wall

F0 shading reduction for obstacles from the horizontal exterior surface

elements overlapping the glazing ı ratio of the accumulated internal–external temper-

Ff shading reduction for obstacles from the vertical ature difference when the ventilation through the

elements overlapping the glazing vents is performed

Fr,k form factor between the Trombe wall and the sky sol,mn,u,l time-average heat ﬂow rate from internal heat

Fsh,gl shading reduction factor for movable shading source/in the adjacent unconditioned space (W)

devices r,k extra heat ﬂow due to thermal radiation to the sky

fsh,with fraction of time with the shading devices active from the Trombe wall (W)

FF glazed fraction al ratio between the solar heat gains and the heat loss

Gsul monthly average solar energy incident on South of the air layer

2 ◦

(kWh/m month) i temperature of the internal environment ( C)

◦

gw total solar energy transmittance of the glazing cov- 1 temperature of the air layer ( C)

◦

ering the air layer e temperature of the external environment ( C)

g⊥ glazing solar factor average difference between the external air temper-

g⊥100% glazing solar factor with the shading devices 100% ature and the apparent sky temperature (11K)

3 ◦

active aca heat capacity of air per volume (J/(m C))

◦

GD degrees day ( C days) ω adimensional parameter representative of the total

◦

H heat transfer coefﬁcient (W/ C) solar radiation ratio falling on the element when the

H0 heat transfer coefﬁcient of the non-ventilated air layer is open ◦

Trombe wall (W/(m C))

ht distance between the midpoints of the upper and

the bottom vents (m)

hr radiative surface heat transfer coefﬁcient in the air

high thermal mass to store heat obtained from the sun during 2 ◦

layer (W/(m C))

the day and release it gradually during the night is an ancient

hc convective surface heat transfer coefﬁcient in the air

technology that can be introduced nowadays in new buildings or 2 ◦

layer (W/(m C))

in the thermal rehabilitation of existing ones [15–17]. The Trombe

Iw solar irradiance, the mean energy of the solar irra-

wall is an example of a system with this capacity, whose concept

diation in the heating season (W Mseg/m )

was patented by Morse in 1881 and developed and popularized

Ir solar irradiance, the mean energy of the solar irra-

in 1957 by Félix Trombe and Jacques Michel. In 1967, in Odeillo,

diation in the cooling season (kWh/m )

France, they built the ﬁrst house using a Trombe wall [12]. This wall

Isol,k solar irradiance, the mean energy of the solar irra-

consists essentially of a single massive wall, an air layer and a glass

diation in the heating season (W/m )

on the outside. The massive wall should be made using materials

Ksw adimensional parameter function of the air ﬂow rate

with good heat storage capacity and a surface dark in colour, to

through the ventilated layer

increase the absorption of solar radiation [18,19]. This wall has the

M length of the heating season (months)

ability to accumulate the solar heat and transmit the accumulated

Qgn,sw solar heat gains (MJ)

heat to the interior spaces, by conduction, radiation and convection

Qht,al heat losses (MJ)

heat transfer mechanisms. Also, if a ventilation system exists in the

Qsol Solar heat gains (MJ)

massive wall it is possible to transfer the heat by air convection.

Qtrans heat transfer through the Trombe wall (MJ)

If there are vents in the massive wall and in the glazed surface,

qve,sw set value of the air ﬂow rate through the ventilated

the Trombe wall is optimized for heating and cooling seasons 3

layer (m /s)

[20–22]. In order to obtain an efﬁcient Trombe wall is essential to

Ri internal thermal resistance of the wall, between the

develop the study of the several variables involved in its design

2 ◦

air layer and the internal environment ((m C)/W)

and performance. The materials used and their thicknesses, the

2 ◦

Rsi superﬁcial internal thermal resistance ((m C)/W)

location and dimension of the air vents, the occlusion and shading

2 ◦

Rei thermal resistance of the massive wall ((m C)/W)

devices, as well as its use during the different seasons of the

2 ◦

R1 thermal resistance of the air layer ((m C)/W)

year should be adjusted and optimized depending on the local

Re external thermal resistance of the wall, between the

climate and the desired contribution of the Trombe wall for the

2 ◦

air layer and the external environment ((m C)/W)

building. Several works, using experimental setups and simulation

2 ◦

Rse superﬁcial external thermal resistance ((m C)/W)

models, have been conducted in this area in order to analyze the

2 ◦

Ree thermal resistance of the glazing ((m C)/W)

thermal behaviour of Trombe walls built with different materials

S area of the ventilation openings (m )

[23–29] and with or without installed ventilation systems [30–33].

t length of the considered season (Megaseconds)

However, there is still a lack of information in order to quantify the

t1 length of the heating season (h)

contribution of this type of systems to increase the energy efﬁciency

of the building adjusted to the different climatic conditions.

A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119 113

In Portugal, the application of this kind of passive solar sys- contribution will be included in the application of the Portuguese

tem is still rare and the stakeholders of the construction sector are thermal regulation to the building and the inﬂuence in the heating

unaware of this solution or do not have enough information about and cooling demands will be discussed.

its thermal performance and how to build it [29–31,34]. Also, the

Portuguese thermal legislation, speciﬁcally the regulation of the 2. Adaptation of the calculation methodology proposed by

characteristics of the buildings thermal behaviour (RCCTE) [35], ISO 13790:2008(E)

does not specify how to account the solar heat gains and losses

of this passive system. It is only mentioned that if there is a non The standard document ISO 13790:2008(E) [36] includes a set

ventilated Trombe wall in the building envelope, a properly jus- of equations to calculate the heat transfer and the solar heat

tiﬁed calculation method can be applied or a calculation program gains of ventilated Trombe walls. Those equations were organized,

can be used. However, the calculation program mentioned is not applied and adapted to obtain a methodology capable to evalu-

available in the market. Another possibility mentioned is to con- ate the performance of the ventilated and non-ventilated Trombe

sider this system as a neutral one. This means that it is considered wall, during heating and cooling seasons in Portugal [34]. The

that this type of systems contributes positively to warming in the adaptation required adjustments in the formulation presented in

cold season, so no heat losses through the system are accounted the international standard document, as well as the introduc-

and the minimum value of the heat transfer coefﬁcient required in tion of other equations to allow its application in accordance to

the regulation is not veriﬁed. However, it is necessary to fulﬁl the the Portuguese thermal regulations. The methodology presented

minimum requirements for shading in order to avoid overheating allows to calculate the global heat gains through the Trombe

and not penalize its use during the summer. This simpliﬁcation in wall, taking into account the losses and the heat gains. Also, the

the use of such systems disregards the high contribution that they way that Trombe wall’s construction details, such as the thick-

may have on the buildings energy consumption reduction and ends nesses and materials of the different layers and the ventilation

up to discourage their use by thermal comfort designers. system, inﬂuences its thermal performance can be achieved. In

The international standard ISO 13790:2008(E) [36], relative Fig. 1 is presented the constitution of the non-ventilated and

to the energy performance of buildings in what concerns to the the ventilated Trombe wall and some of the thermal parame-

calculation of energy use for space heating and cooling, presents ters taken into account in the calculation methodology, namely

a set of equations to obtain the heat transfer and solar heat gains thermal resistances of the different layers and temperatures. In Sec-

of special elements, that can be the base to deﬁne a calculation tion 2.1, will be presented the calculation methodology referred

methodology of the thermal performance of the Trombe wall. above and the changes made to ISO 13790:2008(E) [36] will be

The application and adaptation of this standard document to the explained.

Portuguese reality is essential for applying this system in buildings

envelope and will also be a useful contribute to ﬁll this gap in the 2.1. Calculation methodology

Portuguese thermal regulation. So, the research work presented

aims to deﬁne a calculation methodology for the ventilated and non 2.1.1. Global heat gains

ventilated Trombe wall during heating and cooling seasons based The standard document ISO 13790:2008(E) [36] presents the

on ISO 13790:2008(E). An application example of the referred calculation of the energy performance of the Trombe wall based

methodology will be also presented. Initially, the calculation on the contribution of the solar gains, Qsol, and heat transfer,

methodology will be applied to a ventilated and a non ventilated Qtrans. The physical equations used to calculate their values involve

Trombe wall subjected to the Portuguese climatic conditions. The coefﬁcients representing heat transfer by conduction, radiation

massive wall thickness, the ventilation system and the shading and convection through the Trombe wall system, adding the

devices inﬂuences will be analysed. It will be also studied the effect of air convection if there is a ventilation system in the

inﬂuence of the different parameters included in the equations and massive wall. In order to obtain a ﬁnal result of the Trombe’s wall

the contribution of the heat transfer by conduction, convection performance, the global heat gains through the system will be

and radiation and also by air convection through the vents in the deﬁned as Qgains and calculated by the addition of the contributions

massive wall. A second step in the research work corresponds to referred above, resulting in the Eq. (1), which is not presented in

the integration of the Trombe wall in the building envelope. Its ISO 13790:2008(E) [36].

Fig. 1. Trombe wall: (a) non-ventilated; (b) ventilated (classical model).

114 A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119

= +

Qgains Qsol Qtrans (MJ) (1) glazing area. In the ISO 13790:2008(E), the effective area of the

ventilated Trombe wall is given by Eq. (7):

The equations were ordained and will be presented separately

to calculate the heat gains achieved for the cases when is used a U0 Ri qve,sw 2

= · · · +

Asol,k Asw ˛ Fsh,gl FF.gw U0Re aca kswω (m )

ventilated and a non-ventilated Trombe wall, during the heating UiUe Asw

and the cooling seasons. (7)

where Fsh,gl is the shading reduction factor for movable shading

2.1.2. Ventilated Trombe wall

devices calculated according to Eq. (8)

2.1.2.1. Heating season.

− ⊥ +

(1 f )g f g⊥ 2.1.2.1.1. Solar gains. The calculation of the energy perfor- = sh,with sh,with 100%

Fsh,gl (8)

mance of the ventilated Trombe wall during the heating season g⊥

is based on the contribution of the solar gains and heat transfer

The value of fsh,with, accounted in the Eq. (8) to calculate Fsh,gl

through the massive wall and through the ventilation system pre-

is not deﬁned in the standard document for the climate conditions

viewed in the massive wall. According to ISO 13790:2008 (E) [36],

of Portugal. In the standard is only given its value for Paris, Rome

the solar gains, Qsol, in the considered building zone, for the heating

and Stockholm. In the adaptation for the Portuguese climatic con-

season are calculated by using Eq. (2):

ditions, it was assumed this value equal to 0.5, considering that

in winter the protections are active 50% of the time. The prod-

= + −

Qsol ˚sol,mn,k t 1 btr,l ˚sol,mn,u,l t (MJ) (2) uct Fsh,gl gw presented in Eq. (7) was modiﬁed according to RCCTE

⊥

k l [35], where it is designated by g . Thus, the Eq. (7) to calculate the

effective area changes to Eq. (9):

Ф where sol,mn,k is the time-average heat ﬂow rate from solar heat

U2R

source k, speciﬁcally, the Trombe wall, calculated in accordance 0 i qve,sw 2

= · · · +

Asol,k Asw ˛ FF g⊥ U0Re aca kswω (m ) (9)

with Eq. (3): UiUe Asw

= −

˚sol,mn,k Fsh,oh,kAsol,kIsol,k Fr,k˚r,k (W) (3) The standard document integrates the inﬂuence of heat transfer

by conduction, convection and radiation in the solar gains account-

In the research work developed, it was considered that the space

ing the thermal properties of the different layers that compose the

with the Trombe wall is surrounded by spaces with equal indoor

Trombe wall, represented by their thermal resistance or thermal

temperature, except in the facade that integrates the Trombe wall,

conductivity coefﬁcient values, deﬁned bellow. The parameter U0

which separates the space from the exterior environment. No heat

is the heat transfer coefﬁcient of the Trombe wall, calculated using

gains and losses from that surrounding spaces were accounted.

the Eqs. (10), (11) and (12):

So, the Eq. (2) was simpliﬁed being its second term equal to zero.

◦

Substituting the Eq. (3) in (2), the Eq. (4) is obtained: 2

U0 = (W/(m C)) (10)

+ +

Ri R1 Re

Q = (F A I − F ˚ )t (MJ) (4)

sol sh,oh,k sol,k sol,k r,k r,k 2 ◦

= +

Ri Rsi Rei ((m C)/W] (11)

According to ISO 13790:2008 (E) [36], Fsh,ob,k is the shading

= 2 ◦

Re Rse + Ree ((m C)/W) (12)

reduction factor for external obstacles for the solar effective col-

lecting area of the Trombe wall, which is deﬁned as the rate The Ui and Ue values represent the heat transfer coefﬁcients of

between the average solar irradiance actually received on the col- the internal and external elements in the Trombe wall obtained

lecting plane shaded by external obstacles and the average solar according to Eqs. (13) and (14), respectively. The internal element

irradiance on the collecting plane without shading. It is also referred is the massive wall and the external one is the glazing.

that the calculation of its value should be decided at national level,

depending on speciﬁc conditions to use a ﬁxed shading reduction Ui (13) +

Ri (R1/2)

factor for different windows in the building with the same orienta-

tion. Taking into account this, the equation deﬁned in the standard and

document was replaced by Eq. (5) in accordance with the Por- 1 2 ◦

Ue = (W/(m C)) (14)

tuguese thermal codes, the RCCTE [35]. Its value varies between

Re + (R1/2)

0 and 1 and depends on the shading from obstructions external

The inﬂuence of the ventilation system in the massive wall is

to the building and from horizontal and vertical building elements

considered including the air ﬂow rate due to air convection through

capable of reducing the solar irradiance incident in the Trombe wall.

the air vents. In the standard document this contribution is deﬁned

= × ×

Fsh,ob,k Fh Fo Ff (5) by the parameter qve,sw and is referred that should be determined

in accordance with the relevant standard or other appropriate doc-

Isol,k represents the solar irradiance in the heating season.

uments. To calculate the value of the air ﬂow rate through the air

According to the RCCTE [35] this value is deﬁned as Gsul and cal-

vents located at the bottom and at the top of the massive wall, with

culated for a south oriented surface, varying with the different

equal area, Eq. (15) is used [37]:

climatic regions and is presented in different units comparing with

the required in the standard. So, the value of I is obtained by

sol,k ht 3

qve,sw = 0.16S ( − ) (m /s) (15)

the Eq. (6), where M and Gsul are deﬁned in function of the winter 2 i 1

climatic zone.

According to the standard, the parameter k presented in Eq.

· sw

M Gsul 3 2

= × Isol,k 10 (W/m ) (6) (9) is deﬁned by the Eq. (16), where Z is a parameter determined

according to Eq. (17):

According to ISO 13790:2008(E) [36], the value of F is function

r,k −AswZ

k = 1 − exp (16)

of the heat ﬂow direction. In the case of the Trombe wall, the heat sw

acaqve,sw

ﬂux has a horizontal direction, taking the value 0.5.

1 hr 1 ◦

The solar gains are calculated taking into account the effective 2

= + (W/(m C) (17) +

Z h (h + 2h ) U U

collecting area of the surface that in this case corresponds to the c c r i e

A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119 115

Heat transfer by thermal radiation to the sky is also accounted given the seasonal climate change, namely the solar radiation inci-

in the effective area of the system by the external radiative heat dent on the cooling season, Isol,k, the effective solar surface, Asol,k,

transfer coefficient, hr, which to a first approximation, can be taken and the heat transfer coefficient, H. In this case, Isol,k is the value of

equal to 5ε, depending on the emissivity of the glazing surface of the the solar irradiance for the cooling season and is obtained according

Trombe wall. The effective collecting area of the Trombe wall is also to Eq. (28), based on the RCCTE (35):

calculated considering a parameter deﬁned as ω, which represents

= Ir × 3 2

the ratio of the total radiation falling on the element when the air Isol,k 10 (W/m ) (28)

layer is open to the total solar radiation. The standard deﬁnes its

calculation by graphical way or simply using an equation. In the During the cooling season, the best performance of the Trombe

calculation methodology presented, its determination is done using wall implies that the vents are closed and therefore, qve,sw = 0 m /s.

the Eq. (18) deﬁned in the standard. So, the calculation of Asol,k, involves only the heat transfer by con-

duction, convection and radiation through the system. In this case,

= − −

ω 1 exp( 2, 2al) (18)

the Eq. (8) takes the following form:

where al represents the ratio between the solar heat gains, Qgn,sw, 2

= · · ·

Asol,k Asw ˛ FF g⊥ [U0Re] (m ) (29)

and the heat loss of the air layer, Qht,al, during the calculation period,

which can be obtained by Eqs. (19) and (20). The value of the glazing solar factor, g⊥, also changes, since it is

considered in the developed work that the shading in summer is

Qgn,sw = IwAsw (MJ) (19)

promoted by external white shutters, which are active 70% of the

calculation period.

= −

Qht,al UeAsw(1 e)t (MJ) (20)

Regarding heat transfer, as the vents are closed, the compo-

The solar heat gains, Q , depends on the solar radiation, I ,

gn,sw w nent related to the heat transfer by convection is equal to zero and

and its calculation is not deﬁned in the standard document for Por-

therefore H = 0. The Eq. (22) takes the following form:

tuguese climatic conditions. So, the principles deﬁned in the RCCTE

◦

H = H (W/ C) (30)

[35] to obtain its value were used, resulting in the Eq. (21): 0

Iw = 3.6 × M × G (W Ms/m ) (21)

sul 2.1.3. Non-ventilated Trombe wall

In order to calculate the thermal performance of the non-

Finally, to calculate the heat ﬂow rate, sol,mn,k, deﬁned in the

ventilated Trombe wall, the factors related to ventilation and heat

Eq. (2), it was also taken into account a component that refers to

transfer by air convection through the existing vents in the massive

the extra heat ﬂow due to the thermal radiation emitted from the

wall should not be considered. It is also necessary to adjust all the

Trombe wall to the sky, which is deﬁned in the standard document

values that varies with the heating and cooling seasons.

by the Eq. (22):

˚ = R U A h (W) (22)

r,k se 0 sw r 3. Methodology application

2.1.2.1.2. Heat transfer. The heat transfer through the Trombe

3.1. Constitution of the Trombe wall

wall is addressed in the standard document by the calculation of

the heat transfer coefﬁcient, H, using Eq. (23).

The calculation methodology previously presented was applied

◦

= +

H H0 H (W/ C) (23) to a ventilated and a non ventilated Trombe wall submitted to win-

ter and summer climatic conditions of the city of Vila Real, in the

In the present study, it was deﬁned an equation to calculate

north of Portugal.

the heat transfer gains through the Trombe wall, according to the 2

The analysed Trombe wall has 7.5 m of area and follows the

RCCTE [35], depending on the heat transfer coefﬁcient, H, and the

model identiﬁed in Fig. 1. It is composed by: a concrete massive wall

climatic conditions that characterize the considered climatic zone,

painted black on its outer surface, an air layer with 10 cm of thick-

represented by the days degree value, GD. This gains were deﬁned

ness and a double glazing on the outside. It was also considered the

as Qgn,sw and can be obtained using Eq. (24).

existence of external white shutters. The ventilation system in the

Qtrans = 0.0864 · H · GD (MJ) (24) massive wall was provided by the existence of openings at the top

and at the bottom of the wall. The area of the air vents corresponds

The calculation of the heat transfer coefﬁcient, H, includes the

to 3% of the total area of the Trombe wall. The constitution of the

contribution of two components, represented by the parameters H0

studied Trombe wall was deﬁned based in previous work devel-

and H. The heat transfer coefﬁcient of the non-ventilated Trombe

oped by other authors, namely in what concerns to the air layer

wall, H0, results from the heat transfer by conduction, convection

thickness and the area of ventilation system [18,19,21,38–45].

and radiation by the system being given by the Eq. (25).

The calculation methodology was carried out for the Trombe

◦

wall deﬁned above by varying the thickness of the concrete massive

H0 = U0 · Asw (W/ C) (25)

wall. Its behavior was studied for the thicknesses of 15 cm, 20 cm,

The additional heat transfer coefﬁcient due to the convection 25 cm, 30 cm, 35 cm and 40 cm. The ventilated and non-ventilated

phenomena through the air vents on the massive wall, H, is Trombe wall with a concrete massive wall thickness of 40 cm were

obtained by Eqs. (26) and (27): integrated into a building envelope and the thermal Portuguese

2 regulation was applied in order to analyze its contribution on the

Ue ◦

H c · q ı · k (W/ C) (26) thermal performance of the building during the heating and cooling a a ve,sw U sw i seasons.

= + −

ı 0.3al 0.03(0.0003 1) (27)

3.2. Parameters and climate values used in the models

2.1.2.2. Cooling season. The calculation of the ventilated Trombe

wall thermal performance for the cooling season is based on the The calculation methodology of the energy performance of the

formulation previously indicated for winter in Section 2.1.2.1. How- Trombe wall previously deﬁned involves the achievement of sev-

ever, there are some parameters whose adaptation is essential, eral parameters, namely related with the thermal characteristics of

116 A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119

Table 1

Thermal characteristics of the Trombe wall materials [46].

Parameters Value

2 ◦

Superﬁcial internal thermal resistance (Rsi) 0.13 m C/W

2 ◦

Superﬁcial external thermal resistance (Rse) 0.04 m C/W

◦

Concrete’s thermal conductivity 1.5 W/(m C)

2 ◦

Air layer’s thermal resistance (R1) 0.18 m C/W

2 ◦

Glazing’s thermal resistance (Ree) 0.29 m C/W

2 ◦

External white shutter’ thermal resistance 0.17 m C/W

the different materials that compose the system and with the cli-

matic conditions of the place where the application of the Trombe

wall is studied. In what concerns to the thermal characteristics of

the various layers, it was considered for the calculation the val-

ues of the thermal conductivities and thermal resistances shown

in Table 1. Another parameter that inﬂuences the performance of

the system is the absorption capacity of the materials. When the

external shutter is active, the value of the absorption coefﬁcient, ˛,

Fig. 2. Trombe wall global heat gains, Qgains, depending on the thickness of the

depends on its white color, which corresponds to a value of 0.4. If

concrete massive wall.

the external shutter is not active, the black painted external surface

of the massive wall contributes to the increasing of the heat store

If the Trombe wall is non-ventilated, the heat gains depends

capacity of the system because the value of ˛ changes to 0.8.

only from the storage characteristics of the massive wall [47] and

The ability of the glazing to emit heat by radiation was taken

decreases when the thickness increases because heat transfer takes

into account introducing its emissivity in the calculation. It was

place only by conduction, convection and radiation through the

considered the value of 0.89 for the parameter e, which is the typical

wall. The thicker the wall is, the longer it takes the heat to reach

value for the current glass. As mentioned previously, the shading

the interior of the room. This situation results from the delay in

reduction factor, Fsh,ob,k, was calculated according to the RCCTE [35].

the return of heat that features this type of heat storage systems.

In this case study of the methodology application, it was considered

The obtained results are in agreement with other research work,

that there are no obstacles from the horizon and from horizontal

revealing that the increase of massive wall’s thickness can dampen

and vertical elements. So, the value of Fh corresponds to 0.9 and

the wide range heat charge and discharge ﬂuctuation from out-

the product F0 Ff is equal to 0.9, for the heating season. For the

door [48]. Thus, in the case of the ventilated Trombe wall, when

cooling season, the value of Fh changes to 1. The parameter that

the massive wall thickness increases, the heat gains achieved by

refers to the glass fraction, FF, takes the value of 0.7 because the

conduction, convection and radiation through the massive wall

glazing frame has no grids. The parameter g⊥ is 0.75 for the glazing

decrease and the heat gains obtained by air circulation through

and when the white shutters are closed it takes the value 0.04, and

the vents increase. In the calculation methodology, the parameters

it is designated as g⊥100%.

Asol,k and H are responsible for this results, as it can be observed

The methodology application also requires the introduction of

in Figs. 3 and 4. The values of the effective collecting area of the

temperature values. It is necessary the values of the temperatures

Trombe wall show that, for a 15 cm massive wall thickness, the con-

of the outdoor and indoor environments, e and i, and the tem-

tribution of heat transfer by conduction, convection and radiation

perature in the air layer between the glazing and the massive wall,

corresponds to 28.96% and the remaining 71.04% result from heat

1. For the air temperature in the exterior, e, it was considered an

◦ transmission by convection through the air vents. As the thickness

average value of 7.6 C based on the available data in the Meteorol-

increases, the values of heat transmission through the openings

ogy and Geophysics Institute for the city of Vila Real. The value of

◦ increases and the gains by conduction, convection and radiation

the indoor air temperature, i, was assumed 20 C which, according

through the massive wall decreases. A differential of 11.21% in those

to Portuguese legislation, corresponds to the comfort temperature

for the heating season. For the temperature 1 was taken an average

◦

value of 45 C, based on the literature review [12]. The introduc-

tion of these values in the calculation methodology allowed to

obtain the global heat gains through the Trombe wall, which were

accounted in the RCCTE application.

3.3. Results and discussion

3.3.1. Trombe’ wall global heat gains

The application of the proposed methodology allows obtain-

ing the gains of a Trombe wall using concrete in the massive wall.

The global heat gains, Qgains, for heating and cooling seasons were

obtained for the ventilated and non-ventilated Trombe wall with

different thicknesses in the massive wall, as it is shown in Fig. 2. The

obtained results indicate that, for the heating season, the heat gains

through the Trombe wall are higher when the massive wall is ven-

tilated. This is due to the fact that the transmission of heat occurs

by conduction, convection and radiation through the massive wall

and also by air convection through the vents. In this case, the heat

gains increase with the increasing of the massive wall thickness. Fig. 3. Heat transmission contribution in Asol value.

A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119 117

Fig. 6. Heat transmission contribution in Qgains value.

Fig. 4. Heat transmission contribution in H value.

massive wall has a signiﬁcant role in the thermal performance of

the Trombe wall, which contribution increases with the increasing

values are obtained for a massive wall with 40 cm, Fig. 3. Something

of the massive wall thickness. These results are extremely impor-

similar occurs with the values obtained for the heat transfer coef-

tant to optimize the constructive details and the operation of the

ﬁcient, despite the difference between the two considered forms

Trombe wall under different climatic conditions, during the heat-

of heat transmission be further reduced. For a thickness of 15 cm,

ing and cooling seasons. During the cooling season, the ventilation

69.36% of the heat transfer is obtained by conduction, convection

system must be closed to reduce the gains and therefore it is consid-

and radiation, and the remaining is due to the ventilation system.

ered only the behavior of non-ventilated Trombe wall. As shown in

For a 40 cm thickness, this value decreases to 47.17%, and the higher

Fig. 2, the values of the heat gains are considerably lower than those

contribution is ensured by air movement through the vents, reach-

obtained in winter for ventilated and non-ventilated Trombe wall.

ing the value of 52.83%. In this case, comparing the values obtained

This situation is due to the fact that the use of the external white

for 15 cm and 40 cm thicknesses, there is a differential of 22.19%,

shutter reﬂects the incident solar radiation and increases the ther-

Fig. 4. Those parameters are determinant in the values of Qsol and

mal resistance of the wall to the heat ﬂux. It can be also concluded

Qtrans and therefore in the global heat gains, Qgains. In Fig. 5, the

that the heat gains decrease with the increasing of massive wall

heat transfer associated to Qsol and Qtrans and its contribution in

thickness, as it happens in winter for the non-ventilated Trombe

the global heat gains are presented. It can be concluded that the

wall, which brings beneﬁts for its use during this season. The inﬂu-

solar gains are responsible for 79.11% of the global heat gains, which

ence of the massive wall thickness, the existence of the ventilation

59.44% corresponds to heat from conduction, convection and radia-

system and the introduction of the external shutters in the thermal

tion through the massive wall. The heat gains by transfer represents

performance of the Trombe wall was clearly demonstrated in this

20.89% of the global heat gains, resulting 14.49% from conduction,

application example. So, the values obtained for the ventilated and

convection and radiation through the massive wall and 6.40% from

non-ventilated Trombe wall gains during the heating and cooling

air convection due to the existence of the ventilation system. So, the

seasons lead to the conclusion that the proposed methodology pro-

analysis of these parameters included in the calculation method-

vides a valid approach to the thermal performance of this passive

ology leads to the conclusion that the highest contribution in the

system.

thermal performance of the Trombe wall is given by the heat trans-

fer by conduction, convection and radiation, as it can be observed

3.3.2. Trombe wall’s Integration in building envelope

in Fig. 6. However, the existence of a ventilation system in the

After applying the calculation methodology of the Trombe wall’s

thermal performance, this system was integrated in the building

envelope in order to analyze its contribution to the thermal per-

formance of a residential building. The Trombe wall previously

analysed, composed by a concrete massive wall with 40 cm of thick-

ness, was included in the south facade of a room. It was considered

the construction of a Trombe wall with 7.5 m of area in a build-

ing with a ﬂoor area of 234.45 m . The Trombe wall is 3.20% of the

building ﬂoor area and 18.89% of the south facade area.

The Portuguese thermal regulation, RCCTE [35], was applied to

the building with and without a Trombe wall system. The energy

heating and cooling demands were calculated for both cases.

The calculated energy heating and cooling needs are deﬁned

as Nic and Nvc, respectively, and the required limits to the con-

sidered climatic zone as Ni and Nv. In Table 2, their values are

presented. The results lead to the conclusion that the integration of

the Trombe wall increases the thermal performance of the building.

If the Trombe wall is ventilated, the value of Nic decreases in 16.36%

comparing with the value obtained for the building with no Trombe

wall. With a non-ventilated Trombe wall, there is an improvement

Fig. 5. Heat transmission contribution in Qsol, Qtrans and Qgains values. of 9.46% in the thermal behaviour of the building during the heating

118 A. Briga-Sá et al. / Energy and Buildings 74 (2014) 111–119

Table 2

Thermal performance of the building with the integration of the Trombe wall.

Thermal performance of the building Without Trombe wall Ventilated Trombe wall Non-ventilated Trombe wall

Heating season

Nic (kWh/m year) 121.52 101.64 110.02 2

Ni (kWh/m year) 138.05

Nic/Ni (%) 88.03% 73.63% 79.70%

Cooling season

Nvc (kWh/m year) 2.84 3.41 2

Nv (kWh/m year) 18.00

Nvc/Nc (%) 15.78% 18.95%

season. During the cooling season, the energy needs, Nvc, increases a signiﬁcant role in the thermal performance of the Trombe wall,

in 20.00% with the integration of a non-ventilated Trombe wall. which contribution increases with the increasing of the massive

However, this value is still considerably lower than the required wall thickness. The application of the Portuguese thermal regula-

value for the climate zone under analysis, which is 18 kWh/m year. tion to a residential building with a ventilated Trombe wall, whose

This behaviour can also be minimized by combining the use of nat- area corresponds to only 3.20% of the building ﬂoor area, reveals

ural cross ventilation during the night periods. These results shows that the energy heating demands can be reduced in16.36%. So, the

that the inclusion of a Trombe wall, with an area that corresponds inclusion of a Tombe wall system in the building envelope improves

only to 3.20% of the building ﬂoor area, can contribute to the reduc- its energy efﬁciency. However, experimental work should be devel-

tion of energy consumption in the building. This is considered a oped to determine temperature ﬂuctuations along the different

valid result taking into account other theoretical and experimental layers, heat ﬂuxes and delay in the return of heat. These data may

studies that shows that the indoor comfort is improved as well as eliminate some gaps in the standard, particularly regarding to the

the annual heating energy needs due to the integration of a Trombe air layer temperatures. It will also be a useful contribution to the

wall [18,49–51]. For example, in the Visitor Center at Zion National optimization of the presented methodology.

Park, 20% of the annual heating was supplied by a concrete Trombe

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