Modeling the influence of glazed openings percentage and type of glazing on the thermal zone...

Modeling the influence of glazed openings percentage and typeof glazing on the thermal zone behavior

K.J. Kontoleon, D.K. Bikas*

Laboratory of Building Construction and Physics, Department of Civil Engineering, Aristotle University of Thessaloniki, 540-06 Thessaloniki, Greece

Received 27 August 2001; received in revised form 28 August 2001; accepted 28 August 2001

Abstract

The selection of the type of glazing as well as its proportion to the total wall area are very important towards achieving a desirable indoor

environment. This paper uses a dynamic thermal-circuit zone model to study the influence of the glazed openings percentage (GOP) and

type of glazing on the maximum and minimum indoor temperatures, during and after solar hours. The model comprises of four major

structural heat-flow paths, corresponding to the external and internal walls, glazing and horizontal slabs. The simulation is performed for

winter and summer seasons and for a zone with and without a power plant, with an external wall having south orientation. In the latter case,

the optimum GOP leading to the minimum energy consumption is determined. The zone formation comprises masonry walls with

insulation in the center plane, concrete horizontal slabs with and without insulation and three different types of glazing (double, double with

low emissivity (low-e) coating and double with reflective film). As GOP varies, computer results show how the type of glazing and the

insulation of the slabs affect the indoor zone temperatures and energy efficiency. # 2002 Elsevier Science B.V. All rights reserved.

Keywords: Thermal-circuit zone model; Glazing; Indoor temperature; Energy consumption

1. Introduction

Solar energy is an inexhaustible energy source reaching

earth in the form of electromagnetic waves. Glazed openings

ranging from typical windows to large glazed building

surfaces, have become a common feature in architecture,

allowing natural light into the building, visual communica-

tion with outdoors and a reduced wall load on the supporting

structure. Although present day glazing systems provide

good solutions for cold climates, and fairly effective ones

for warm conditions, there is still no system with the

flexibility required to provide a comfortable environment

and an efficient energy response in climates where heating is

essential in winter and cooling is required in summer. Thus,

in buildings with near south (SE to SW) orientation, having

large glazed openings, overheating is often observed. Etzion

and Erell [1] proposed a ventilated reversible glazing system

in response to the demands of winter and summer condi-

tions. As they report, the summer configuration of the

proposed reversible system may prevent overheating. The

overheating observed in passive solar buildings has been

studied by many researchers. In [2], some specific results are

given in relation to the optimum aspect ratios for south

window sizes, from a thermal performance point of view. An

overview of computational methods is given in [3], where

more specifically the positive effect of the thermal mass on

the indoor conditions, during summer and winter, is pre-

sented. As shown, the thermal mass causes a time lag of heat

release to the indoor air and a time shift of the peak of

cooling load. In [4], the impact of thermal mass, in terms of

thermophysical properties and thickness of a wall, on time

lag is specifically studied. Athienitis et al. [5] in their

experimental study have used phase change materials

(PCM) to store thermal energy. Their simulation and experi-

mental results showed a significant reduction of mean room

temperature.

From the view of the above referred literature, it is clear

that the extent of glazed areas in building surfaces, as well as

their internal thermal mass, are directly affecting their

indoor ambience. This paper considers the influence of

the type of glazing and the glazed openings percentage

(GOP) in the south wall of a zone in winter and summer,

with and without a power plant. The main objectives of the

present study are the following:

1. to model the zone in order to determine the influence of

GOP on the maximum and minimum indoor tempera-

tures during and after the solar hours, respectively;

Energy and Buildings 34 (2002) 389–399

* Corresponding author. Tel.: þ30-31-995763, 995777;

fax: þ30-31-420628.

E-mail address: [email protected] (D.K. Bikas).

0378-7788/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 7 7 8 8 ( 0 1 ) 0 0 1 2 5 - 6

2. to find the impact of horizontal slab insulation and that

of various glazing types, such as double-glazing,

double-glazing with low emissivity (low-e) coating and

double-glazing with reflective film, on the maximum

and minimum indoor temperatures;

3. to examine the influence of GOP on the energy

consumption.

To accomplish the above objectives, the well-known analo-

gies between the thermal and electrical laws [6–9] are

employed, deriving a zone thermal-circuit model compris-

ing four heat-flow paths: the external and internal walls, the

glazed area and the horizontal slabs (floor, ceiling). The

model parameters are self-adjusting to cope with the variable

percentage of glazed openings. The thermal-circuit is ana-

lyzed in a computer program, which was developed for this

purpose, using the non-linear nodal approach. The solution

of non-linear equations is iterative, taking into account

the dependence of convection and radiation coefficients

from the indoor and surface temperatures. The dynamic

behavior of the thermal model is assessed in discrete time-

steps. The model formulation and a general description of

the computer program are given in the following sections.

Computer results from the application of the model in

different outdoor environmental conditions (winter and

summer), various types of glazing and percentages of glazed

areas are presented in detail.

2. Outline of the zone modeling

Various models have been used for the prediction of

thermal behavior, as for example those in [7–11] and the

references quoted therein. In this study, the modeling of the

thermal zone dynamic behavior is employing a lumped

capacitance one-dimensional network model in which dis-

tributed thermal resistances and capacitances are connected

to each other via a number of nodes. The one-dimensional

and three-dimensional representations of an external wall-

section with thickness dx and a cube of it with dimensions

dx, dy, dz are shown in Fig. 1(a) and (b); for simplicity, we

will refer to the sections on the x, y, z axes as dx, dy and dz

sections. As seen, the one-dimensional section is modeled

using three nodes. The elements denoted by dRx, dRy and dRz

represent the thermal resistances of a section at node i; Ci is

the thermal capacitance at node i. The number of sections in

the axes (i.e. the number of nodes) must, generally, be large

enough to ensure a good accuracy. As shown in Fig. 1(c), the

series combination of two adjacent sections in the x-axis

(e.g. nodes i and j) in order to model larger parts of the wall

materials is straightforward. The simplification of one-

dimensional models is generally applied in many thermal

analysis programs, as it has been practical from past experi-

ence [8].

A thermal-circuit developed in the way described above is

fully represented by its topological and algebraic matrices

and its behavior can be expressed by a system of differential

equations. The model can be used to simulate the combined

processes of conduction, convection and radiation in the zone,

under specific environmental conditions. Node voltages and

Nomenclature

A area (m2)

cp specific heat capacity (J/kg K)

C thermal capacitance (J/K)

d thickness of layer (m)

h heat transfer coefficient (W/m2 K)

k thermal conductivity (W/m K)

QL heating/cooling unit loads (W)

Qrad radiation heat load (W)

Qsol solar radiation load (W)

R thermal resistance (K/W)

t time (s)

T temperature (8C)

Tmax maximum temperature during the solar hours

(8C)

Tmin minimum temperature after the solar hours

(8C)

Vz zone volume (m3)

Greek letters

as solar absorptivity

e emissivity

r density (kg/m3)

Subscripts

e exterior surface

i interior surface

o outside

sa sol–air

v ventilation, infiltration

x type of material

Fig. 1. (a) One- and (b) three-dimensional representations of a wall-

section; (c) combination of two adjacent sections in the x-axis.

390 K.J. Kontoleon, D.K. Bikas / Energy and Buildings 34 (2002) 389–399

branch currents correspond to temperatures and heat-flows,

respectively. In the present formulation, instead of setting up

the state equations, we employ a system of algebraic equa-

tions by appropriately modeling the circuit capacitors with

resistances in series with time-varying voltage sources. The

dynamic solution of thermal-circuits with capacitive ele-

ments is formulated by considering the voltage–current

relationships across the capacitive elements at small time

increments, Dt. From the equation relating a capacitance’s

current i(t) and voltage e(t)

iðtÞ ¼ CdeðtÞ

dt(1)

or

iðtnÞC

¼ deðtÞdt

��t¼tn

(2)

The derivative de(t)/dtjt¼tn, as shown in Fig. 2(a), is approxi-

mated by De(tn)/Dt. Thus, Eq. (2) becomes

iðtnÞC

� DeðtnÞDt

¼ eðtnÞ � eðtn � DtÞDt

(3)

and

iðtnÞ �eðtnÞ � eðtn � DtÞ

½Dt=C ¼ eðtnÞR

� �� eðtn � DtÞ

R

� �(4)

The above gives the capacitor’s voltage–current relationship

at time tn. This, as shown in Fig. 2(b) can be modeled with a

resistance with value Dt/C in series with a voltage source

with value eðtn � DtÞ, i.e. the voltage difference across the

capacitor at the previous time-step. Errors due to replacing

the exact derivatives by approximate differences cannot be

totally eliminated but they can significantly be reduced by

decreasing the time-step.

Having replaced all capacitive elements with their equiva-

lent circuits, the thermo-electrical network is purely resistive

and simulates the thermal system behavior at a particular

time-point, spaced from the previous solution time-point by

Dt. Thus, at each time-step, a set of algebraic equations is

valid and its solution gives the heat-flows (branch currents)

and temperatures at the various nodes (node voltages). A

general solution of such a network can be formulated by

defining a standard general branch, as shown in Fig. 3. Note

that, in the most general case, a branch may have a series

voltage source (temperature) and a current source (heat-

flow). For instance, a section of a wall as modeled in Fig. 1(a)

will comprise three branches (the thermal resistance

branches will have zero voltage sources). Using this general

branch definition, by simple matrix manipulations the nodal

solution equation in matrix form is obtained as [13,14]

follows:

eN;t ¼ ½ATGðtÞA�1AT½IðtÞ � GEðtÞ (5)

with eN, t representing the nodal solution vector at time t,

G(t) a diagonal matrix with the conductances at time t and

I(t), E(t) the current and voltage vectors, respectively.

Matrix A (and its transpose, AT ) is a topological matrix

(branch–node matrix) describing the connection of branches

to the nodes of the network (its elements are 0, 1 or –1).

3. Description of the thermal zone model

In this study, we consider a zone of a building with one

external wall. The zone is a square room 8 m 8 m and with

its height at 3 m. As shown in Fig. 4, the external wall has a

glazed opening, while the other three interior walls are

adjacent to other zones. The building is situated at latitude

408N, and the exterior wall of the room is facing south. All

walls have a formation, typical in Mediterranean climate,

consisting of three layers: masonry–insulation–masonry

(MIM). Common brick of 0.09 m thickness constitutes

the wall masonry and a 0.05 m board of expanded poly-

styrene is used for insulation. Thus, the total thickness in all

walls is 0.23 m. The horizontal slabs (floor and ceiling) are

from reinforced concrete and have a thickness 0.12 m. ThreeFig. 2. Capacitor charging during Dt (a) and capacitor model (b).

Fig. 3. General branch of the thermal-circuit.

K.J. Kontoleon, D.K. Bikas / Energy and Buildings 34 (2002) 389–399 391

cases are considered for their insulation (the thickness is

0.03 m): (a) no insulation (NI), (b) exterior face insulation

(EI) and (c) interior face insulation (II).

For the glazed openings, three types of glazing have been

considered: double-glazing (DG), double-glazing with low-ecoating on the interior surface (DG-e) and double-glazing

with low-e coating and a reflective film (DGR-e). Double-

glazing is most common in buildings with glazed openings.

As known, glazings with low-e coating contribute by redu-

cing the heat loss in winter and the heat gain by radiation in

summer. The purpose of glazing with reflective film is to

avoid infrared solar radiation penetration. All glass layers

have a thickness of 0.0032 m and the air-space between

them is 0.0064 m.

In order to study the effect of glazed area on the indoor

temperatures of the zone during the day, the GOP is defined

(for the south wall) as:

GOP ¼ Agl

Aw þ Agl

100 (6)

where Aw, Agl are the wall and glazed areas of the south

surface (AS). As GOP varies, so does the solar heat gain and

the thermal mass of the south wall which contributes to the

total thermal mass of the zone. The indoor environment is

also affected by infiltration and ventilation; air changes rates

(ACH) for winter and summer are taken equal to 0.5 and 1,

respectively.

3.1. Lumped parameter zone thermal model

The zone thermal-circuit model, shown in Fig. 5, makes

provision for four structural heat-flow paths, that refer to the

south wall (w), its glazing surface (gl), the interior walls (iw)

and the two horizontal slabs (fc). Through these paths,

transient conduction is modeled in one-dimension and

transverse heat-flows are assumed negligible. The heat-flow

paths comprise a discrete set of elements using the three-

node representation. Their thermal capacitances are lumped

in these three nodes. Each node corresponds to one of the

materials of the formation (e.g. MIM for walls, glass–air–

glass for the glazing). Hence, all these paths have a total of

12 nodes and 28 branches (16 with thermal resistances and

12 with thermal capacitances). The thermal resistances and

capacitances Rx, Cx (subscript x denotes the type of material,

Fig. 4. Plan and perspective of the zone.

Fig. 5. Thermal-circuit model for the zone.


i.e. br, ins, gl, a and c for brick, insulation, glazing, air and

concrete, respectively) depend on GOP and are calculated

by using their properties. For each type of material, it is

Rx ¼dx

kxAx

(7)

Cx ¼ rxcp;xdxAx (8)

and Ax represents the material surface area as a function of

GOP.

All the above four major paths, Pi (i ¼ 1–4), coincide at a

separate node, the air-node, through interior convective

resistances. The thermal capacitance of the air (Cair) is also

connected to this node. The temperature at the air node, Tair,

characterizes the interior zone space. The interior surface

convective resistances, Ri,w, Ri,gl, Ri,iw, Ri,fc, depend on GOP

as well as on the temperatures developed at their end-nodes,

to which they are connected. As shown in Fig. 6, at each

time-step during the solution procedure, their values are

adjusted iteratively in order to correspond to the tempera-

tures obtained at their end-nodes (boundaries). The itera-

tions terminate when their values, at the beginning and end,

are matching (convergence). Taking into account GOP and

the aspect ratio of the south wall glazing geometry (in the

present study, it is 8:3), the dependence of interior convec-

tive resistances from the temperatures at their end-nodes can

be easily expressed [6,12].

The radiation effects from all the interior zone surfaces

(Ax), which are proportional to emissivity (ex), are taken into

account by introducing four temperature dependent heat

sources, Qrad,x (current sources in Fig. 5), one for each

heat-flow path Pi. In addition, the penetrating solar radiation

at the interior of the glazing surface, is modeled with a time

dependent heat source Qsol. The QL source in Fig. 5 repre-

sents the heating/cooling unit, which is controlled by a

thermostat. The thermostat has a pair of set-points (Tupper,

Tlower), each one for heating and cooling, respectively. In

winter, when the indoor temperature is below the lower

limit, heating is provided until the indoor temperature

reaches the upper limit. The unit restarts its operation when

the indoor temperature falls below the lower limit. For

cooling, the unit operates when the indoor temperature is

higher than the upper limit, until the indoor temperature falls

below the lower limit.

Infiltration, ventilation and environmental control, as seen

in Fig. 5, are taken into account though Rv.

Rv ¼ 1

Vzraircp;airacs(9)

where Vz is the zone-volume and acs is the rate of air

changes per second.

For the external south wall and glazed opening, the forcing

functions Tsa,x(t), in Fig. 5 include the effect of solar radiation

on outside air temperature; Qsol is the incident solar irradia-

tion, as,x the solar absorptivity of the exterior surface material

x, ho the outer surface heat transfer coefficient, due to the

combined convection and radiation, and To the outside ambi-

ent-air temperature. The variation of sol–air temperature is

Tsa;xðtÞ ¼ ToðtÞ þas;xQsolðtÞ

ho;x(10)

The outside temperature is assumed to follow a sinusoidal

variation.

ToðtÞ ¼ Tav þ 12jTo-max � To-minj sin ot � 1

2p

� �(11)

where Tav represents the average outside temperature during

a day period (24 h). Note that the rotational velocity is

o ¼ 2pf , with f the radial frequency (f ¼ 1/86,400 s); To-

min, To-max represent the minimum and maximum outside

temperatures during the day.

3.2. Environmental conditions

In winter, heating is mainly required and cooling is rarely

needed, only when extended glazed surfaces exist. On theFig. 6. Flow chart of the solution procedure.


opposite, summer imposes an unwanted heat load and

cooling is regularly required because of overheating. The

above requirements cover fairly well the other seasons

where mostly heating or cooling is required, or vice versa.

Especially for south walls, the solar heat gain is large for

winter and supplements heat losses, while in summer the

solar gain is relatively small restricting the undesirable gain.

Besides the selection of south orientation for an external

wall which is the most desirable, the optimum GOP and the

type of glazing on heating/cooling demands depend on the

particular climatic conditions and the insulation of walls and

horizontal surfaces. The hourly variation values of solar

incident radiation, shown in Fig. 7(a), are taken for 21

January and July. These correspond to average days with

no clouds and to a particular location for a wall with south

orientation. The fraction of incident solar radiation that

enters through the glazing represents the solar heat gain

coefficient. The solar reflectance of the ground is assumed to

be 0.20 and the wall surfaces are taken to be light-colored

(as ¼ 0:40). The ambient air temperature in winter season,

for a typical day is between 0 and 10 8C, while in summer

temperatures range between 21 and 30 8C (meteorological

data). The ambient-air temperature, as shown in Fig. 7(b),

is assumed to emerge a sinusoidal variation during a day

period. The sol–air temperatures for both the south wall and

the glazed surfaces have been calculated using Eq. (10). At

each time-step, during the solution procedure, the outdoor

temperature constitutes the exterior forcing function affect-

ing the indoor ambience for the particular season.

4. Zone environment without a power plant

For winter and summer, we assume the zone without a

power plant and with the initial indoor temperature at 21 8C.

The selection of the initial indoor temperature aims at

assessing the zone thermal behavior during the day under

loaded conditions for the thermal-mass (external/internal

walls and horizontal slabs). The initial indoor temperature is

the starting temperature (at time-point t ¼ 0 during the

solution procedure), which in our simulation corresponds

to 3:00 a.m. The rate of air changes (ACH) for ventilation

and infiltration in winter and summer is assumed to be 0.5

and 1.0, respectively. The presumed values for ACH can

be higher in a zone with frequent opening of doors and

windows.

4.1. Indoor temperatures in winter

First, we consider the thermal zone without heating or

cooling. The GOP varies from 0 to 100% for the three types

of glazing (DG, DG-e, DGR-e) and for the three types of

horizontal slab insulation (NI, EI, II), as described in Section

3. Results concerning the maximum indoor temperature

during the solar hours, Tmax, and the minimum indoor

temperature after solar hours, Tmin, are discussed in the

following sections. The minimum and the maximum indoor

temperatures, when no insulation is present in the horizontal

slab surfaces (NI), are shown in Fig. 8(a). As expected, as

GOP increases, Tmax also increases, mainly due to the effect

of solar radiation. The variation of Tmin with GOP is

comparatively small. For all types of glazing, the minimum

day temperature after the solar hours shows a slight decrease

with the increase of GOP. Also for all GOP values, the DG-eglazing, compared to DG, achieves higher Tmin and Tmax. On

the other hand, the DGR-e glazing blocks a large amount of

solar penetrating radiation and Tmin, Tmax are lower for all

GOP values, compared to DG and DG-e glazing types. For

no glazing, Tmin is 6.42 8C and Tmax is 10.21 8C; thus, the

temperature swing is 3.79 8C. For GOP ¼ 100%, Tmin, Tmax

and the magnitude of the temperature swing are, respec-

tively: (a) 6.32, 20.53, 14.21 8C for DG; (b) 6.77, 20.96,

14.19 8C for DG-e and (c) 6.27, 16.76, 10.49 8C for DGR-e.Next are presented results concerning the influence of the

slab insulation on the zone indoor temperatures. Computer

results with slabs having insulation in their outer surfaces

and for DG-e glazing are given in Fig. 8(b). As GOP

increases, Tmax during the day rises from 15.59 to

26.53 8C. The variation of Tmin with GOP is small and its

range is within 12.87–14.41 8C. The increase of the tem-

perature swing with GOP is from 2.72 8C (for GOP ¼ 0%)

to 12.12 8C (for GOP ¼ 100%).

Finally, computer results for the II case and for DG-eglazing are given in Fig. 8(c). These show the impact of

outside temperature and solar radiation on the indoor envir-

onment. This formation is ideal for buildings requiring non-

periodic heating. As GOP increases, Tmax during the dayFig. 7. Meteorological data in winter and summer (south orientation): (a)

incident solar radiation; (b) ambient-air temperatures.


increases from 12.82 to 31.47 8C. As before, the variation of

Tmin with GOP is comparatively small and its value is kept

within 9.52–10.77 8C. The temperature swing increases with

GOP and its range is within 3.3 8C (for GOP ¼ 0%) to

20.7 8C (for GOP ¼ 100%). In overall, the following gen-

eral remarks can be made from the above discussed graphs:

� the increase of GOP for the DG-e type leads to higher

Tmin, Tmax, and temperature swing;

� without glazing, the EI case gives maximum Tmin and

Tmax (compared to the NI and II cases) as it keeps a low

indoor temperature swing;

� for GOP > 40%,the highest Tmax during the solar hours is

achieved for the II case;

� in all cases, the highest minimum indoor temperature after

the solar hours is obtained for the EI case;

� the DG-e glazing has the best performance, from the point

of view of Tmin, Tmax and temperature swing, during the

day. Overheating (T i > 25:5 8C) occurs when GOP is

above 70% and for the II case;

� in winter, the DGR-e glazing deteriorates the indoor

environment for all investigated cases.

4.2. Indoor temperatures in summer

Results for the zone thermal behavior in summer

(T i ¼ 21 8C), without floor/ceiling insulation (NI), are

shown in Fig. 8(d). As GOP increases, the penetrating solar

radiation progressively leads to overheating while the var-

iation of the minimum indoor temperature with GOP is

comparatively small. As seen in Fig. 8(d), the maximum

temperature during the solar hours without glazing

(GOP ¼ 0%) is 25.65 8C. For DG glazing, as GOP increases

the maximum temperature during solar hours rises to

30.24 8C (GOP ¼ 100%). The corresponding maximum

temperatures for the DG-e and DGR-e types are 29.90

and 28.21 8C, respectively (the DG and DG-e graphs are

fairly close to one another). As it can be seen, the maximum

indoor temperature during solar hours can be kept at 27.5 8Cwith the DG and DG-e but with a percentage of glazed

Fig. 8. Variation of Tmax and Tmin during the day vs. GOP in winter with (a) NI, (b) EI and (c) II; in summer with (d) NI, (e) EI and (f) II.


openings not exceeding 60%. By changing to the DGR-etype, this percentage can become as high as 80%.

The minimum day temperature after solar hours for DG,

shows a small increase with GOP and it increases from

23.98 8C (GOP ¼ 0%) to 24.57 8C (GOP ¼ 100%). On the

other hand, the DG-e gives a slightly higher Tmin compared

to that of DG. For GOP ¼ 100%, Tmin after solar hours is

24.71 8C. For the case of DGR-e, the reflective film restricts

the solar penetrating radiation and Tmin is 24.43 8C. Thus,

whereas the indoor temperature swing without glazing

is 25:65 � 23:98 ¼ 1:67 8C with DG, DG-e and DGR-e,the corresponding swings are 5.67, 5.19 and 3.78 8C(GOP ¼ 100%). For the same glazed areas, the DGR-e type

has a better performance, allowing lower Tmin, Tmax and

temperature swing values.

The influence of the floor/ceiling exterior face insulation

(EI) on the indoor environment is shown in Fig. 8(e). The EI

case delays the zone heating and the indoor ambience is

cooler. As in the previous case, the increase of GOP pro-

gressively leads to the overheating of the zone. The variation

of Tmin with GOP is comparatively small. From Fig. 8(e),

it can be seen that Tmax without glazing, during the solar

hours, is 23.09 8C. For double-glazing (DG), the maximum

temperature during solar hours rises to 28.67 8C (GOP ¼100%). The maximum temperatures for the DG-e and DGR-

e types are 28.22 and 26.35 8C, respectively and correspond

to GOP ¼ 100%. Thus, the maximum indoor temperature

during solar hours can be kept at 27.5 8C with the double-

glazing but with a percentage of glazing at 80%. With the

DG-e, this percentage can be risen to 90%, while for the

DGR-e, Tmax never exceeds 27.5 8C.

With DG glazing, the minimum day temperature after

solar hours, presents a small increase with GOP and its range

is in the interval 22.87 8C (GOP ¼ 0%) to 24.85 8C(GOP ¼ 100%). In contrast to the case of no insulation,

the DG-e gives a slightly lower Tmin compared to that of DG.

For GOP ¼ 100% the minimum temperature after solar

hours is 24.83 8C. For the case of DGR-e, the reflective

film gives a Tmin at 24.22 8C. In overall, the indoor tem-

perature swing without glazing is 0.22 8C and with DG, DG-

e and DGR-e the corresponding values are 3.82, 3.39 and

2.13 8C (GOP ¼ 100%).

Results corresponding to interior face insulation of floor/

ceiling (II), for the three types of glazing are given in

Fig. 8(f). The increase of GOP causes overheating while

the variation of the minimum indoor temperature is small.

Without glazing (GOP ¼ 0%), the maximum temperature

during the solar hours is 24.26 8C. This temperature for DG

glazing, as GOP increases, rises to 33.09 8C. The corre-

sponding Tmax for DG-e and DGR-e are 32.7 and 29.71 8C,

respectively. As can be seen, with the DG glazing the maxi-

mum indoor temperature during solar hours can be kept at

27.5 8C with a GOP not exceeding 40%. This percentage can

become 45 and 65%, respectively with DG-e and DGR-e.With DG glazing, the minimum day temperature after

solar hours, shows a small increase with GOP as it changes

from 23.56 8C (GOP ¼ 0%) to 25.16 8C (GOP ¼ 100%).

With DG-e glazing a slightly higher Tmin is achieved com-

pared to that of DG (with GOP ¼ 100% this temperature is

25.45 8C) while with the DGR-e glazing Tmin becomes

24.81 8C. Consequently, the indoor temperature swing with-

out glazing is 24:26 � 23:56 ¼ 0:7 8C and with DG, DG-eand DGR-e, the corresponding swings are 7.93, 7.25 and

4.9 8C (GOP ¼ 100%).

From the above discussion, we can extract the following

general remarks for the effect of the type of glazing, GOP

and horizontal slab (floor/ceiling) insulation on the zone

environment (summer):

� Large glazed openings with DGR-e can be used without

causing overheating. The extent of the openings depends

on the existence and the position of insulation (floor/

ceiling).

� The lower maximum indoor temperature during solar

hours corresponds to DGR-e and EI case.

� When large glazed openings are desirable, the II case

should be avoided as it causes overheating.

� Without glazing, the EI case gives the lowest Tmin and

Tmax.

5. Zone energy consumption

The power load demands in buildings constitute the most

important criterion for structure decisions, in order to

achieve a desirable indoor ambience with low energy con-

sumption. To satisfy the above condition, the thermal model

discussed earlier is used in a parametric study involving

GOP, glazing type and horizontal slab (floor/ceiling) insula-

tion (GOP is varied in steps of 10%). The load demands

during a day period are computed for winter and summer

using the meteorological data given in Section 3.2. In this

study, we assume a power plant capacity of 7.5 kW for

heating and cooling and an initial indoor zone temperature

T i ¼ 21 8C. In winter, the set-points of the thermostat of the

heating/cooling unit are set at 18–24 and 24.5–25.5 8C, for

heating and cooling, respectively. Thus, the unit operates for

heating when the indoor temperature falls below 18 8C and

for cooling when this temperature exceeds 25.5 8C. In

summer, where cooling is required, the settings are at 21–

25.5 8C. The total computer runs needed for calculating

the energy demands in this parametric study are 198 (11

GOP 3glazing types 3insulation positions 2seasons)

and have been carried out with a time-step of 60 s in a day

period.

5.1. Daily demands in winter

First, we present results concerning the duration of the

power plant operation during the day, in order to provide an

indoor temperature for the zone within the selected set-

points of the thermostat, as a function of GOP. This is shown


in Fig. 9(a) and (b) for two types of glazing (DG-e, DGR-e)and for three cases of floor/ceiling insulation (NI, EI, II). The

white colored bar graphs in Fig. 9(a) illustrate operation with

DG-e glazing and NI case with the set-points of the thermo-

stat as discussed earlier (18–24 8C). As can be seen from

the graphs in Fig. 9(a), in both cases heating is required. As

GOP increases the operation time decreases (18.5 h for

GOP ¼ 100%) and the energy consumption becomes lower.

Considering the EI case with DG-e glazing, the light-grey

colored bar graphs (Fig. 9(a)), show that the operation time

is minimized for GOP ¼ 70% and is 5.61 h. Recall that for

EI case and DG-e glazing, in a passive zone (see Fig. 8(b))

overheating is observed for GOP > 90%. When heating is

provided, as it is expected, overheating comes at a lower

GOP, and cooling is required. This increases the operation

time of the heating/cooling unit and results in higher energy

demands. Similar results in Fig. 9(a) are obtained for the II

case and DG-e glazing (dark-colored bar graphs); but in this

case, the optimum GOP is 50% leading to the minimum

operation time, which is 6.78 h. The effect of the use of a

reflective film, i.e. DGR-e, for the NI, EI and II cases is

illustrated in Fig. 9(b). The optimum GOP values for NI, EI

and II are 100, 100 and 80% and the corresponding operation

times are 19.83, 6.67 and 7.22 h, respectively. As expected,

the reflective film for heating seasons gives worst results

compared with those of DG-e glazing. The placing of

insulation in the outer surfaces of the horizontal slabs

(floor/ceiling) is preferable.

The energy consumption for DG-e glazing and with ex-

terior or interior insulation is shown in Fig. 9(c) and (d). The

minimum energy consumption for the case of exterior face

insulation is 70% and its value is 42.08 kWh. For GOP above

70%, cooling is required (due to overheating) and as a

consequence the energy consumption is increasing. For the

case of interior face insulation, Fig. 9(d) shows that the

optimum value of GOP is 50% and the energy consumption

amounts to 50.85 kWh. Again for larger glazing areas, over-

heating occurs and the energy consumption is increasing.

5.2. Daily demands in summer

The duration of the power plant operation for two types of

glazing (DG-e, DGR-e) and for three cases of floor/ceiling

insulation (NI, EI, II) is shown in Fig. 10(a) and (b). Thus,

Fig. 10(a) shows the effect of the use of DG-e, for the NI, EI

and II structures. As expected, without glazing and insula-

tion minimum operation time is obtained which is 0.33 h.

For the case of EI with GOP < 60% and that of II with

GOP < 40% cooling is not required. As GOP increases

above the previous limits, the operation time of the unit

becomes higher. For the present set-points of the thermostat

and for EI with GOP ¼ 60% this time is about 0.44 h. The

operation period for the II case and for GOP ¼ 40% is

1.11 h. The use of DGR-e, for the NI, EI and II cases is

illustrated in Fig. 10(b). For NI with GOP < 20%, EI with

GOP < 80% and II with GOP < 40% cooling is not

required. In contrast to winter, the reflective film gives better

results compared with those of DG-e and allows larger

glazing extensions. As before, the placing of insulation in

the outer surfaces (floor/ceiling) is preferable.

Fig. 9. Operation time of power plant vs. GOP in winter for (a) DG-e glazing and (b) DGR-e glazing. Energy consumption in winter for DG-e glazing with (c)

EI and (d) II.


The energy consumption for the case of DG-e glazing and

with exterior or interior floor/ceiling insulation is shown in

Fig. 10(c) and (d). As GOP increases above 40% for the EI

case and above 20% for II case, the energy consumption is

increasing. Similarly, results are obtained in Fig. 10(e) and

(f), for the case of DGR-e with EI and II cases; as GOP

increases above 60% for EI case, and above 20% for II case,

the cooling loads are increasing. For the same percentage of

glazed openings, the cooling consumption for EI case and

with a reflective film is less than that of II case. A compar-

ison between the graphs corresponding to the two different

types of glazing shows that in summer DGR-e is preferable.

6. Discussion and conclusions

In overall, the main objective of this paper was to model

and analyze a zone with south orientation in order to

determine the influence of GOP and the type of glazing

on the indoor temperatures and energy efficiency, in winter

and summer.

The thermal-circuit presented has been shown to be very

suitable for the above modeling as it (a) made possible to

take into account the non-linear variation of convection

resistances and radiation sources with temperatures; (b)

allowed the parametric study with respect to GOP, various

types of glazing and interior/exterior horizontal slab insula-

tion; (c) enabled the inclusion of a temperature controlled

device (thermostat) to maintain the zone temperature within

desirable limits.

The analysis of the loaded thermal zone in winter revealed

that in buildings with double-glazing and insulation at the

interior of the horizontal surfaces, overheating is observed

when GOP exceeds 70%. By changing the position of

insulation to the outer surface, overheating is almost

avoided. In summer, overheating can be avoided with

Fig. 10. Operation time of power plant vs. GOP in summer for (a) DG-e glazing and (b) DGR-e glazing. Energy consumption in summer for DG-e glazing

with (c) EI and (d) II; for DGR-e glazing with (e) EI and (d) II.


GOP < 60% and exterior insulation in the horizontal sur-

faces, unless the DGR-e type of glazing is used; in this case,

overheating occurs for GOP > 80%.

From an energy consumption point of view, it has been

shown that in winter (with insulation in the outer face of the

slabs and double-glazing with low-e coating) the optimum

GOP which minimizes the energy consumption is 70%,

while in summer it drops to 40% with DG-e glazing and

to 60% with DGR-e glazing. Thus, for average days in other

seasons it is reasonable to expect that the optimum GOP lies

somewhere between the above limits.

The specific results given earlier and the above discussion

made it clear that overheating can be avoided and energy

savings can be obtained with the proper selection of GOP as

well as the type of glazing and position of slab insulation. It

is intended to use this zone model together with statistical

meteorological data for all months of the year for the

purpose of obtaining the optimum GOP that minimizes

the annual energy consumption.

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Modeling the influence of glazed openings percentage and type of glazing on the thermal zone...

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