Architectural solutions to increase the energy efficiency of buildings/Architekturos sprendiniai, didinantys energini pastatu efektyvuma.
Parasonis, Josifas ; Keizikas, Andrius ; Endriukaityte, Audrone 等
1. Introduction
Efficient energy resource utilisation during the lifecycle of a
building is in part determined by the use of rational architectural and
layout measures at the time of planning the building volume. Givoni
(1981) mentions that the ability of a building to save energy--aside
from thermodynamic and heat retention qualities of materials--depends on
its shape, orientation, layout of transparent envelopes, size, measures
of protection from the sun, and the facade colour. Parasonis and
Keizikas (2010) note that manipulation of the shape of the building
alters its energy use value, even though the physical characteristics of
the envelopes remain unchanged (assessed according to the building
technical regulation STR 2.01.09:2005 (2005)). That means that this
factor influences the energy demand of buildings.
Energy efficiency is one of the most essential aspects of the
sustainability of buildings. The energy efficiency potential of
buildings, which depends on the chosen architectural and layout
solutions, can be assessed using various building energy efficiency
methodologies, including national ones such as STR 2.01.09:2005 (2005)
under EN 15217:2007 (2007); international ones such as the
"passive" home certification system (Schnieders 2003); the
LEED, DGNB, and BREEAM rating systems, and others (Ruckert et al.
2010a). According to the EBPD strategy, by the year 2020, their
requirements will have to approach the nearly zero energy building
standard (Directive 2010/31/EU 2010; Marszal et al. 2011). For this
reason, the search for measures that allow for savings of materials,
energy, and financial resources in the long-term outlook of the
lifecycle of buildings is a relevant problem.
These goals are pursued by implementing the LONGLIFE energy
efficient multiunit residential housing project for climatic conditions
of the Baltic States according to the Baltic Sea Region Programme
2007-2013 (Ruckert et al. 2010b), with Vilnius Gediminas Technical
University as one of the project partners representing Lithuania. During
implementation of the project, most of the attention is devoted to
saving natural energy resources and financial resources throughout all
of the stages of the building lifecycle. It is planned that the annual
energy demand of a LONGLIFE building will not exceed 40 kWh per unit of
heated area, not including the energy used by domestic electric
appliances. This type of multiunit building will draw 30% of its energy
needs from renewable resources in 2012, nearly 100% excluding the energy
used by domestic appliances by 2020, and all energy including that used
by domestic appliances by 2050 (Ruckert et al. 2010a).
Within the framework of the aforementioned project, the paper
presents the influence of the studied architectural and layout measures
(compactness, building shape, and transparent and opaque external
envelope combinations) on energy efficiency of a building. Besides,
measures seeking to minimise energy loss, where applicable, as well as
maximise its gains (based on the land lot and the conditions of the
local environment) under Lithuanian climatic conditions are proposed.
2. The influence of architectural and layout solutions on the
energy balance of a building
Compactness--an ability of a building volume to fit as much useful
area into the external envelope (the totality of external walls,
windows, roof and lower heated floor areas) as possible--is one of
architectural and layout characteristics of a building.
During the construction and demolition stages, the utility of
compactness is direct, as it determines quantitative needs of
construction materials and thus the energy needs for their extraction,
processing, transporting, construction, demolition, and recycling.
Besides, buildings that have a smaller external envelope area but fit
the same heated area will have less wasted energy, which is relevant
during the operation stage.
In scientific sources, compactness is assessed and its limit state
(the most compact result of a building) is determined in various ways.
To express compactness, Aksoy and Inalli (2006) use the Shape Factor
(SF), which is equal to the proportion of a building's length to
its width. Bostancioglu (2010) uses the ratio of external wall area to
floor area (EWA/FA). Both A/S ratio, used by Gonzalo and Habermann
(2002), and A/V ratio, applied by Hegger et al. (2008), determine the
proportion of the area of a building envelope to its volume. This ratio
is described by Depecker et al. (2001), who refers to it as the shape
coefficient. Ourghi et al. (2007) and Tuhus-Dubrow and Krarti (2010)
propose using the relative compactness (RC) coefficient, which reflects
the ratio between the shape coefficient of a designed building (A/V) and
the minimal shape coefficient of a rectangular building (reference
building) with an equal volume [(A/V).sub.ref] (where A represents the
area of the external envelope and V represents the volume of a building)
and shows the deviation of the shape of a building from the optimal
compactness result:
RC = [(A/V).sub.building]/[(A/V).sub.ref] =
[A.sub.ref]/[A.sub.building]. (1)
However, buildings with identical shapes and volumes can differ in
both their layout solutions and the number of storeys, thereby
containing different useful (heated) areas. RC does not identify that
within the same casing, a building with a greater number of square
metres will be characterised by greater rationality and superior energy
efficiency.
We propose several improvements to the Eq. (1): rather than using
A/V, it would be much more appropriate to express compactness by the A/S
ratio with the area of the external envelope of a building (A) and the
useful (heated) area (S), showing how efficiently geometry of the
building is utilised. We propose that the non-dimensional A/S ratio can
be referred to as the concept of "geometric efficiency" (GE).
In comparison with A/V ratio, GE values in Fig. 1 demonstrate that
the best results are achieved with more compact and larger volumes.
With a significantly larger area, non-compact buildings achieve GE
values that are analogous to those of compact buildings. This means that
both compact and non-compact buildings can have the same GE values. For
this reason, when comparing buildings, we propose using the modified RC
ratio, which is RGE:
RGE = (A/S)/[(A/S).sub.ref] = GE/[GE.sub.ref] (2)
where: [GE.sub.ref] = [(A/S).sub.ref] is the limit (reference)
expression of geometric efficiency that is the closest to a cubic
building (reference building) that accommodates a given area; RGE shows
how far GE of a designed building deviates from the [GE.sub.ref] value
of the reference building.
3. Limit states of proportions of a building
In this section, a method is proposed for determining the limit
states of proportions of a building in search of the most energy
efficient solution for the volume of a building, considering the local
climatic conditions.
The benchmark [GE.sub.ref]--which is the limit state of a building
with the smallest external envelope area--is determined by solving the
envelope surface area optimisation problem (Zilinskas 2005). In our
case, we have the total heated area of the building S and the desired
floor height h (multiplication of which would result in the volume V).
For the purpose of calculations, the assumption was made that the design
of the building is cube-shaped, as sides of equal length cover the
smallest area. Fig. 2 presents a simplified reference building model.
Mathematically, the external envelope area minimisation problem is
expressed as follows:
[min.sub.X]A(X), X = [[x.sub.i], i = 1,2,3}, [x.sub.i] > 0. (3)
Vector X = ([x.sub.i], i = 1, 2, 3} represents dimensions of the
building: width, length, and height. The objective function (envelope
area) of the problem looks like this:
A(X) = 2[x.sub.1] + 2[x.sub.1][x.sub.2] + 2[x.sub.2][x.sub.3], (4)
while the permissible range V (the building volume, known size) is
expressed in the following way:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
[FIGURE 2 OMITTED]
The minimisation of the external envelope area can be applied to
volumes of various shapes, for example a cylinder or regular polygons.
According to Tuhus-Dubrow and Krarti (2010), compact rectangular and
regular polygon-shaped building volumes have optimal solutions under all
climatic conditions. Their geometric efficiency value can be greater
than that of a cube, but volumes of non-rectangular and curvilinear
surface buildings have drawbacks in practical application. Thus, as a
basis for the establishment of geometric efficiency, a limitary cubic
volume is accepted as a reference shape.
Compactness is not the only volume/layout measure influencing
energy needs. AlAnzi et al. (2009) indicates that the influence of a
shape is important in the relationship between the area of windows and
their solar transmittance abilities. This proposition is supported by
Wang et al. (2006), Jedrzejuk and Marks (2002), Caldas and Norford
(2002), which present algorithms for finding the optimal polygon shape
of a building based on criteria of losses, gains, transparent and opaque
external envelope area combinations, orientation, and climatic
conditions. This proposition can be tested by determining the limitary
building volume solution that retains the most gains and comparing it to
the limit state of the reference building, given a fixed ratio of window
and wall areas within the facades.
During the heating season, the flow of energy in opaque envelope
elements moves from the facility to the exterior, while their function
is to minimise this flow. Meanwhile, in transparent envelopes, the
energy exchange process is bidirectional: windows both lose heat due to
conduction and provide a possibility of reclaiming solar energy from the
environment. When window energy gains begin exceeding heat transmittance
losses, a greater window area provides the potential to reclaim more
solar energy and decrease heating energy demand.
To maximise gains, the opposite problem is to be solved--the
maximisation of the external envelope through which the greatest
quantity of solar energy is reclaimed. Here, the facade orientation,
gains, quantity, and thermal properties of transparent and opaque
envelopes are expressed through the facade influence coefficient
[EF.sub.1], which is introduced into the envelope maximisation problem.
The general expression of the problem looks like this:
[max.sub.X] AF (X), X = [[x.sub.i], i = 1, 2, 3}, [x.sub.i] > 0.
(6)
Vector X = ([x.sub.i], i = 1, 2, 3} represents dimensions of the
building: width, length and height. The objective function of the task
AF (the facade area) looks like this:
AF(X) = 2[x.sub.1][x.sub.3] ([EF.sub.1] + [EF.sub.3]) +
2[x.sub.2][x.sub.3] ([EF.sub.2] + [EF.sub.4]), (7)
where: [EF.sub.1] and [EF.sub.3] as well as [EF.sub.2] and
[EF.sub.4] are the influence coefficients of the opposite facades of a
rectangular building, reflecting the maximum values of their gains
according to their orientation.
The permissible range of the problem V (volume) remains analogous
to the one expressed in Eq. (5).
The establishment of [EF.sub.i], where i indicates the orientation
direction, relies on the energy balance maximisation of the facades
according to their orientation max [EF.sub.i], where:
[EF.sub.i] = [Q.sup.wall.sub.i] x [AC.sup.wall.sub.i] +
[Q.sup.window.sub.i] x [AC.sup.window.sub.i], i = 1...8. (8)
For equality, the following constraints are applied:
[AC.sup.wall.sub.i] [member of] [0;l]; [AC.sup.window.sub.i]
[member of] [0;1]; [AC.sup.wall.sub.i] + [AC.sup.window.sub.i] = 1, (9)
where: [Q.sub.i] represents the energy balance of a facade element
oriented towards direction i during the heating season; [AC.sub.i]
represents the area coefficient, indicating the part of the total facade
covered with transparent or opaque elements.
For an accurate comparison of maximised and minimised volume limit
states, identical EF coefficients must be applied to facades oriented
towards a given direction. Calculated under these conditions, the energy
efficiency of buildings will show the rationality of deviation of the
volume from the reference proportions.
To save energy and material resources, it is useful to compare the
external envelope minimisation with maximisation possibilities in the
context of energy losses experienced during every stage of the lifecycle
of a building. That would help avoiding inaccuracies related to the
nature of energy losses predominant in various locations. For example,
in northern regions energy resources are used to heat buildings, while
in southern regions they are devoted to cooling. That is also reflected
in the volumetric solutions of buildings. Ourghi et al. (2007) shows
that a compact shape of a building (similar to the reference building)
in southern regions is more efficient. The most suitable type for
Lithuanian climatic conditions becomes clear after performing
calculations according to the presented methodology.
4. Case study
4.1. Determination of the reference building
Based on climatic conditions predominant in Lithuania, a multiunit
residential building with a planned heated area S of 900 [m.sup.2]
(which includes the area occupied by internal walls but not the area
occupied by external envelope elements) is being considered.
When the height of a storey h is equal to 3.2 m (from the floor of
one storey to the floor of the next storey), the building volume V is
equal to 2880 [m.sup.3]. For this volume, the geometric efficiency
[GE.sub.ref] of the reference building [House.sub.ref] is calculated. To
solve the optimisation task, the Microsoft Office Excel what-if analysis
Solver tool (which finds the optimal value of a target cell by changing
values in cells applied to calculate the target cell) is used. The given
result is [GE.sub.ref] = 1.353 and the optimal number of floors n of
[House.sub.ref] is equal to 4.
4.2. The climate data and characteristics of envelope elements
Comparing buildings of different compactness, it is necessary to
analyse the potential of the transparent and opaque elements of the
external envelope, which determine their efficiency, both admitting
solar gains and limiting heat losses, depending on the local climatic
conditions. In search for the most efficient internal solution, which is
subject to the orientation of a building, this potential determines the
proportion of rational quantities of walls and windows.
RSN 156-94 "Construction Climatology" (1995) provides the
most data for the vicinity of Kaunas, which geographically corresponds
to the centre of Lithuania. The climate data of this city are used in
subsequent calculations and are presented in Table 1.
In this study, thermal characteristics of walls and windows are
used, values of which range from the minimum requirements spelled out in
Lithuanian regulations STR 2.05.01:2005 (2005) to the maximum declared
values of envelope elements available on the market. These are presented
in Table 2.
Below (Figs 3 and 4), graphic representation of heat gain and loss
balances for external envelope elements with various orientations are
presented. These are determined based on STR 2.09.04:2008 "Capacity
of the Building Heating System. Heat Needed for Heating Purposes"
(2008). The total balance of each element during the heating season
subject to their orientations is presented in Table 3.
During the warm part of the year (differently than during the
heating season) the internal temperature of buildings is not regulated.
Thus, heat losses through the building envelopes are not evaluated
during this period of time.
These calculations are based on assumptions that the installation
of external envelope elements was performed so as to avoid leaks and
linear thermal bridges. These losses are not included in the balance
calculations. It is also assumed that windows are not going to be opened
during the heating season; it is intended that a mechanical ventilation
system with heat recovery will help avoiding natural ventilation losses.
However, conditioning systems in multi-storey apartment houses are not
considered necessary during summertime if external shading systems are
applied to openings and the cooling of internal spaces is performed by
natural ventilation as needed. Climatic data confirm that the
temperature during the hottest month in Kaunas is 17.7 [degrees]C and
the absolute temperature maximum does not reach 35 degrees (RSN 156-94
1995). This means that it is possible to avoid both the expenditure for
installation and maintenance of conditioning systems and the loss of
energy and other related resources during the operation stage of the
building.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
The data presented in Table 3 provide a possibility of choosing a
quantity- and quality-wise efficient combination of transparent and
opaque envelope elements for the operation stage of a building, subject
to their orientation. The results confirm the following: under
Lithuanian climatic conditions, a window meeting the minimum normative
requirements (window-5) facing south demonstrates better energy balance
during the heating season than the most efficient wall solution
(wall-4); the most efficient window solution (window-8) in all other
directions except for north demonstrates a better energy balance during
the heating season than the best wall solution (wall-4); and the most
efficient window solution (window-8) in every direction is more
efficient than the wall solution meeting the minimum normative thermal
requirements (wall-1).
4.3. Determination of the most efficient shape of a building
On this basis, the search for the building shape solution that
reclaims the most energy during the operation stage of a building is
performed. To that end, the most efficient external elements--window
(window-8) and wall (wall-4)--are used, while in the first case the
facades are turned toward the cardinal directions (S-E-N-W) and in the
second case--toward the intercardinal directions (SE-NENW-SW). Because
constraints on the number of floors can be applied to a multiunit
residential building (e.g. a land lot has a limitation in maximal
building height, such as n = 4), as part of the study, two building
volume searches are conducted, of which one plans for this constraint.
Seeking for a study that is closer to realistic conditions,
additional constraints are imposed on external envelopes of the building
volume that correspond to requirements of structure installation and
normative facility insulation (STR2.02.01:2004 (2004)): the total
transparent area of the building envelope is set to be no less than 1/6
of the total area of the heated building; the total area of windows is
allowed to vary between 10-70% compared to the area of the entire
facade, and the minimum length of the edges of the building is limited
to 9.5 metres.
These data allow delieating values of the facade weight coefficient
[EF.sub.i] required for external envelope maximisation when oriented
toward different points of the compass. When the window efficiency is
greater than that of the wall, it is granted the maximum limitary area
intended for windows; when the wall efficiency within a facade is
greater, the area of this envelope component is maximised accordingly,
with the aforementioned conditions satisfied. The EF values are
presented in Table 4.
To determine the limits of the building volume dimensions that have
the potential to attract the maximum quantity of solar energy gains, the
what-if analysis with Microsoft Office Excel Solver tool is used. Based
on the constraints presented and the data from Table 4, it determined
proportions of the building both with unlimited height (House 1) and
with a height of n = 4 (House 2). The achieved limitary building
proportions are the same in both cases, i.e. when oriented toward
S-E-N-W as well as SE-NE-NW-SW. The results in comparison with the
reference building ([House.sub.ref]) are presented in Table 5.
Energy balances influenced by building shape and external envelope
components are presented in Table 6. To facilitate comparison, analogous
distributions of transparent and opaque envelopes in the facades are
applied to [House.sub.ref]:
Under Lithuanian climatic conditions, in comparison to
[House.sub.ref], the potential gains of the building oriented toward the
cardinal directions (House 1) are 13984.97 - 9139.58 = 4845.39 kWh or
5.4 kWh/([m.sup.2] year) greater; while those of House 2 are 3632.15 kWh
or 4 kWh/([m.sup.2] year) greater. Buildings oriented toward the
intercardinal directions have somewhat less of this potential.
The calculation results confirm that the ability of a building to
reclaim a greater quantity of solar energy during the heating season
depends on its shape, the physical characteristics of its external
envelope elements, and its orientation. In order to determine whether
the House 1 and House 2 gains during the operation stage will offset the
11% and 6.4% increase (that is reflected by RGE in Table 5) in materials
for external envelope and energy needed to attain, transport, and
utilise them, the total energy balance of the building lifecycle
(including the resource extraction, transport, building construction,
operation, and demolition stages) must be determined. Such calculations
require an additional study, which is planned to be the next stage of
the work of authors.
5. Discussions
In this paper, it has been determined that a less compact building
has a greater potential to reclaim solar energy during the heating
season than a compact one, provided the characteristics of transparent
facade elements are used rationally. The results of the study allow
considering that in time, as the thermal characteristics of the elements
improve and their production technologies are perfected, this can
significantly compensate for additional energy use (due to the larger
area of external envelope and related installation costs) during the
construction stage.
The maximisation of the area of the external envelope of a building
is to be sought provided sufficient efficiency is proven for the entire
operation stage. The calculations have demonstrated that this method of
determining a building shape can be justified when the designs take full
advantage of the potential of transparent elements.
The minimal amount of glass in a facade is regulated by hygiene
norms based on insulation requirements, while the maximum can result in
not only large energy gains during the heating season but also facility
overheating during the warm period. In order to avoid possible
discomfort that would require installation of an air conditioning system
and additional energy consumption during the operation stage, it is
useful to consider installing effective external measures against the
sun, which could also serve as decorative elements of a building and
contribute to the variety of architecture.
Regulations pertaining to a land lot and its surroundings that
cover building height, density, orientation, and other requirements, can
limit possible architectural and layout solutions. However, the measures
scrutinised in this paper allow finding a solution in the context of
such limitations and take the maximum advantage of the shape and
external envelope characteristics as well as minimise energy resource
needs during various stages of the building lifecycle. For example,
compactness is sought for where solar gains are lacking.
Viewed in a different light, the research data can be useful in
developing new residential locations. By anticipating the size,
proportions, and orientation of a residential building, energy and other
resource needs during construction and operation stages can be
forecasted, which is useful for implementation of the EBPD strategy
(Directive 2010/31/EU 2010).
In residential building design, questions of compactness are closer
related to guidelines that strive for a maximum output for minimum
input, rather than limits imposed on the variety of architectural
solutions. This argument is confirmed by the graphs presented in Fig. 5,
based on a studied multiunit building. Various proportions for
rectangular buildings with an area of 900 [m.sup.2] (graph on the left)
and their corresponding GE values (graph on the right) are presented.
Fig. 5 also shows that the spectrum of these values falls within various
limits of deviation from [GE.sub.ref] (i.e., of reference building with
4 storeys and dimensions [x.sub.1] = [x.sub.2] = 15 m):
[FIGURE 5 OMITTED]
The limits of deviation (5%, 10%, 20%) from [GE.sub.ref] value
delineated in the right part of Fig. 5 are an RGE representation
([RGE.sub.n] = 1.05; 1.10; 1.20). They show that the [GE.sub.ref]
solution is the best one in terms of compactness, but it is not the only
good one if the deviation is acceptable: RGE can be a standardised
indicator (showing permissible deviation), the determination of which
during the pre-design stage can govern the preparation of architectural
and layout solutions with predictable construction material quantities
needed and corresponding heat losses during the operation stage of a
building.
In order to use RGE, the [GE.sub.ref] of the reference building has
to be known in each case. To avoid inaccuracies and simplify the use of
these indicators in normative documents and recommendations, tables of
calculated [GE.sub.ref] values can be supplied. An example of such table
is provided below (Table 7), where the mean storey height is equal to
3.2 m. The values presented are for buildings with internal area values
(S) that fall within limits of 50-2500 [m.sup.2].
All of this leads us to believe that by manipulating compactness of
a building and characteristics of external envelope elements, it is
possible to not only find the maximum energy efficiency result of the
building based on the environment and land lot conditions but also
standardise the usage limits of these measures, which would allow a
superior building energy efficiency result to be achieved.
6. Conclusions
It is worth expressing the base indicator of compactness using the
A/S ratio with the area of the external envelope of a building (A) and
the useful (heated) area (S), as this indicates how efficiently a
building's geometry is used, which the A/V ratio does not reflect.
In this case, we can refer to the A/S non-dimensional ratio as
"Geometric Efficiency" (GE).
The study has demonstrated that the geometric efficiency of
buildings can vary within especially wide limits, which results in a
difference in resource needs of up to several percent during the
implementation stage of a project.
Relative Geometric Efficiency (RGE), which is equal to
GE/[GE.sub.ref], is proposed to assess the compactness of a building.
RGE indicates the level by which geometric efficiency (GE) of a designed
building deviates from its reference (optimal) [GE.sub.ref] value.
It was determined that under Lithuanian climatic conditions during
the heating season and depending on orientation of the facades, the
suggested recommendations regarding application of transparent and
opaque external wall areas make it possible to markedly reduce the
energy demand of a building.
Calculations made according to the presented methodology have
demonstrated that depending on its shape and assuming an identical
percentage of glassed area during the heating season, gains for a 900
[m.sup.2] building can vary up to 53% or 5.4 kWh/[m.sup.2]. In this
case, compact buildings have the potential to save resources during the
construction stage of a project, while less compact buildings have an
opportunity to reclaim more renewable energy during the operation stage
(by orienting the largest facades in a southern dir.). In order to avoid
possible overheating of facilities due to solar gains, in this case it
is recommended to standardise the requirement to install suitable
external protective measures.
doi.org/10.3846/13923730.2011.652983
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Josifas Parasonis (1), Andrius Keizikas (2), Audrone Endriukaityte
(3), Diana Kalibatiene (4)
Vilnius Gediminas Technical University, Saul?tekio al. 11, LT-10223
Vilnius, Lithuania
E-mails: (1) josifas.parasonis@vgtu.lt; (2)
andrius.keizikas@vgtu.lt (corresponding author); (3)
audrone.endriukaityte@vgtu.lt; (4) diana.kalibatiene@vgtu.lt
Received 10 Jun. 2011; accepted 17 Oct. 2011
Josifas PARASONIS. Prof., Dr Habil, Head of Department of
Architectural Engineering at Vilnius Gediminas Technical University,
Lithuania. Member of CIB Committee W086 "Building Pathology",
actual member of International Informatization Academy (Canada) and
Independent Academy of Sciences of Israel, member of Board of Advisers
at The American Biographical Institute. His research interests include
reliability of structures and buildings; thermal renovation of
buildings.
Andrius KEIZIKAS. A PhD student and researcher at the Department of
Architectural Engineering, Vilnius Gediminas Technical University,
Lithuania. His research interests include interdisciplinary researches
on architecture and sustainability, particularly the influence of
architectural measures on energy efficiency of buildings.
Audrone ENDRIUKAITYTE. Dr, Marketing Director at private company
Paroc UAB, a lecturer at the Department of Architectural Engineering,
Vilnius Gediminas Technical University, Lithuania. Her research
interests include building structures and thermal processes in
buildings.
Diana KALIBATIENE. Doc, Dr at the Department of Information Systems
and researcher at the Information Systems Research Laboratory of Vilnius
Gediminas Technical University, Lithuania. She is a member of the
European Committee and Lithuanian Government supported SOCRATES/ERASMUS
Thematic Network projects "Doctoral Education in Computing"
(ETN DEC) and "Teaching, Research, Innovation in Computing
Education" (ETN TRICE). Her research interests include development
of business rule and ontology based information systems, conceptual data
modelling and formal specification, data and knowledge engineering. She
is the co-author of 35 scientific papers.
Table 1. Climate. Mean monthly outside air temperature and daily solar
radiation flux density for Kaunas, Noreikiskes (RSN 156-94 (1995))
Jan Feb Mar Apr
1 Mean -5.2 -4.3 -0.3 6
temperature,
[degrees]C
Daily 2 South 42.2 72.8 123.7 119.2
flux 3 South-west 35.2 64.1 112 113.3
density, 4 West 20.6 44.7 84.5 93.5
W/[m.sup.2]: 5 North-west 15.7 33.3 59.7 70.1
6 North 15.6 32.4 52.7 56.9
7 North-east 15.7 33.3 59.3 70.8
8 East 19.9 42.7 81.7 97.9
9 South-east 34 61.1 109.7 118.4
May Jun Jul Aug Sep Oct Nov
1 12.8 16.2 16.9 16.4 11.9 7.1 1.8
Daily 132 136.9 127.5 127.7 117.2 71.6 31.4
flux 135 146.1 133 128.6 105.4 37 25.5
density, 123 142.1 127.5 109.3 78.9 38 14.7
W/[m.sup.2]: 97 117.4 105.9 85.4 54.8 25.6 10.7
84 97.8 88.7 67.9 45.3 23.7 10.5
105 121.3 109.1 87.3 54.7 25.8 10.6
134 150 134 113.9 81.8 39.8 14.8
139 152.7 137.3 128.6 107.3 61.6 24.9
Dec
1 -2.3
Daily 28.7
flux 23.5
density, 12.7
W/[m.sup.2]: 9.5
9.5
9.5
12.5
22.9
Table 2. Characteristics of different envelope elements
Envelope Wall Window
element
1 2 3 4 5 6 7 8
Heat 0.2 0.16 0.12 0.1 1.6 1.35 0.94 0.73
transfer
coef.,
W/[m.sup.2]K
Solar heat 0 0 0 0 0.61 0.61 0.49 0.49
gain coef.
Table 3. Heating season energy balance (kWh) per area of
1[m.sup.2] of envelope elements oriented toward various directions
Envelope Direction
element
South, East, North, West,
[Q.sub.1] [Q.sub.2] [Q.sub.3] [Q.sub.4]
1. (wall-1) -19.92 -19.92 -20.91 -19.92
2. (wall-2) -15.93 -15.93 -16.72 -15.93
3. (wall-3) -11.94 -11.94 -12.54 -11.94
4. (wall-4) -9.95 -9.95 -10.46 -9.95
5. (window-5) 14.15 -49.81 -96.09 -50.05
6. (window-6) 39.03 -24.93 -69.96 -25.17
7. (window-7) 45.73 -5.63 -41.1 -5.83
8. (window-8) 66.65 15.26 -19.15 15.07
Envelope Direction
element
South-east, North-east, North-west, South-west,
[Q.sub.5] [Q.sub.6] [Q.sub.7] [Q.sub.8]
1. (wall-1) -19.92 -20.91 -20.91 -19.92
2. (wall-2) -15.93 -16.72 -16.72 -15.93
3. (wall-3) -11.94 -12.54 -12.54 -11.94
4. (wall-4) -9.95 -10.46 -10.46 -9.95
5. (window-5) -6.05 -79.72 -79.87 -14.09
6. (window-6) 18.84 -54.83 -54.96 9.84
7. (window-7) 29.51 -29.67 -29.79 23.06
8. (window-8) 50.42 -8.76 -8.87 43.95
Table 4. A representation of [EF.sub.i] influence coefficients
South East
Area Balance Area Balance
coeff. [Q.sub.1] coeff. [Q.sub.2]
Wall-4 0.3 -9.95 0.3 -9.95
Window-8 0.7 66.65 0.7 15.26
[EF.sub.i] 43.67 7.697
South-east North-east
Area Balance Area Balance
coeff. [Q.sub.5] coeff. [Q.sub.6]
Wall-4 0.3 -9.95 0.3 -10.46
Window-8 0.7 50.42 0.7 -8.76
[EF.sub.i] 32.309 -9.27
North West
Area Balance Area Balance
coeff. [Q.sub.3] coeff. [Q.sub.4]
Wall-4 0.9 -10.46 0.3 -9.95
Window-8 0.1 -19.15 0.7 15.07
E[F.sub.i] -11.329 7.564
North-west South-west
Area Balance Area Balance
coeff. [Q.sub.7] coeff. [Q.sub.8]
Wall-4 0.3 -10.46 0.3 -9.95
Window-8 0.7 -8.87 0.7 43.95
E[F.sub.i] -9.347 27.78
Table 5. Parameters of the most efficient house shape to absorb
solar gains during the heating season in comparison with
[House.sub.ref]
[x.sub.1] [x.sub.2] [x.sub.3 ] n Envelope surface
areas, [m.sup.2]
South * or
South-east *
House ref. 15 15 12.8 4 192
House 1 10.5 9.5 28.8 9 302.4
House 2 23.7 9.5 12.8 4 302.4
Envelope surface areas, [m.sup.2]
East or North or West or Roof Ground
North-east North-west South-west
House ref. 192 192 192 225 225
House 1 273.6 302.4 273.6 100 100
House 2 121.6 302.4 121.6 225 225
Envelope GE RGE
surface
areas,
[m.sup.2]
Total
House ref. 1218 1.35 1
House 1 1352 1.50 1.11
House 2 1298 1.44 1.06
* indicates orientation of the main facade
[x.sub.1]--length; [x.sub.2]--width; [x.sub.3]--height;
h--floor height; n--number of floors
Table 6. Heating season energy balance per vertical components
of building envelopes oriented toward S-E-N-W; SE-NE-NW-SW
House Envelope Southern facade Eastern facade
S-E- component
N-W
Area, Balance, Area, Balance,
[m.sup.2] kWh [m.sup.2] kWh
Ref. Wall 57.6 -573.12 57.6 -573.12
Window 134.4 8957.76 134.4 2050.944
1 Wall 91.09 -906.35 82.08 -816.70
Window 212.35 14153.13 191.52 2922.60
2 Wall 91.09 -906.35 36.48 -362.98
Window 212.35 14153.13 121.6 1855.62
House Envelope South-east wall North-east wall
SE-NE- component
NW-SW
Area, Balance, Area, Balance,
[m.sup.2] kWh [m.sup.2] kWh
Ref. Wall 57.60 -573.12 57.60 -602.50
Window 134.40 6776.45 134.40 -1177.34
1 Wall 91.09 -906.35 82.08 -858.56
Window 212.35 10706.69 191.52 -1677.72
2 Wall 91.09 -906.35 36.48 -381.58
Window 212.35 10706.69 121.60 -1065.22
House Northern facade Western facade Total
S-E- component
N-W area,
[m.sup.2]
Area, Balance, Area, Balance,
[m.sup.2] kWh [m.sup.2] kWh
Ref. 172.8 -1807.49 57.6 -573.12 345.60
19.2 -367.68 134.4 2025.408 422.40
1 273.06 -2856.21 82.08 -816.70 528.08
30.34 -581.01 191.52 2886.21 625.71
2 273.06 -2856.21 36.48 -362.98 436.88
30.34 -581.01 121.6 1832.51 485.87
House North-west wall South-west wall Total
SE-NE- component
NW-SW area,
[m.sup.2]
Area, Balance, Area, Balance,
[m.sup.2] kWh [m.sup.2] kWh
Ref. 57.60 -602.50 57.60 -573.12 230.40
134.40 -1192.13 134.40 5906.88 537.60
1 91.09 -952.80 82.08 -816.70 346.34
212.35 -1883.54 191.52 8417.30 807.74
2 91.09 -952.80 36.48 -362.98 255.14
212.35 -1883.54 121.60 5344.32 667.90
House Total %
S-E- gains,
N-W kWh
Ref. 9139.58 10
1 13984.97 15
2 12771.73 14
House Total %
SE-NE- gains,
NW-SW kWh
Ref. 7962.62 10
1 12028.33 15
2 10498.54 13
Table 7. Geometric characteristics of reference buildings
(storey height h = 3.2 m)
Area, [GE.sub. n Side Area, [GE.sub. n
[m.sup.2] ref] length, [m.sup.2] ref]
m
50 3.56 2 5 600 1.55 4
75 3.09 2 6.12 700 1.47 4
100 2.81 2 7.07 800 1.41 4
125 2.62 2 7.91 900 1.35 4
150 2.48 3 7.07 1000 1.30 5
175 2.34 3 7.64 1200 1.23 5
200 2.23 3 8.16 1400 1.16 5
250 2.07 3 9.13 1600 1.12 5
300 1.95 3 10.0 1800 1.07 6
350 1.85 3 10.80 2000 1.03 6
400 1.77 3 11.55 2250 0.99 6
450 1.71 4 10.61 2500 0.96 6
500 1.64 4 11.18 ...
Area, Side
[m.sup.2] length,
m
50 12.25
75 13.23
100 14.14
125 15
150 14.14
175 15.49
200 16.73
250 17.89
300 17.32
350 18.26
400 19.36
450 20.41
500
Fig. 1. A/V ratio and GE values of various orthogonal volumes
of different sizes, shapes and number of levels
Dimensions: 3/3/3 9/9/9 9/9/9 15/15/15 12/12/30
length/width/
height, m
Number of 1 2 3 5 10
levels (n)
External 54 486 486 1350 1728
envelope
area (A),
[m.sup.2]
Internal 9 162 243 1125 1440
(heated)
area (S),
[m.sup.2]
Internal 27 729 729 3375 4320
volume (V),
[m.sup.3]
A/V ratio, 1/m 2 0.667 0.667 0.4 0.4
Geometric 6 3 2 1.2 1.2
efficiency
(GE=A/S)
Dimensions: 12/12/30 33.54/33.54/3
length/width/
height, m
Number of 11 1
levels (n)
External 1728 2652.5
envelope
area (A),
[m.sup.2]
Internal 1584 1125
(heated)
area (S),
[m.sup.2]
Internal 4320 3374.8
volume (V),
[m.sup.3]
A/V ratio, 1/m 0.4 0.786
Geometric 1.09 2.36
efficiency
(GE=A/S)
