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Numerical solution of TIM-PCM solar thermal storage system with ESP-r
D. Heim & P. Klemm
Department of Building Physics and Building Materials, Technical University of Lodz, Poland
ABSTRACT: This paper details the addition of the special – phase change material function to the ESP-r energy simulation program. Passive building elements with PCM were modelled using the concept of the special
materials technique. Phase change materials were introduced to ESP-r as means of modelling active building
elements, i.e. those building elements which change their thermophysical properties in response to some external excitation. The control volume effective heat capacity method is proposed to carry out thermal simulations of building structures containing PCMs. The TIM-PCM intelligent building facade was proposed as a
latent heat solar energy storage system. A numerical simulation for a triple zone building, based on real climatic data for Warsaw, is conducted to predict the TIM-PCM wall behavior and the influence of that structure
on the diurnal latent heat storage effect. The results show the latent heat storage effect on the storage performance of the TIM-PCM intelligent facade system.
1 INTRODUCTION
Nowadays many building designers would like to
apply a modern, low energy technology and find out
its advantages, before the design process is finished.
It requires using advanced numerical techniques to
simulate thermal behaviour of modern, technologically advanced building elements like solar collectors, photovoltaics, thermochromic glazing, heat
pipes, phase change materials, etc. Many of them are
known as the intelligent building facade and, in general, are either passive or active solar elements.
1.1 Passive solar systems
Sunspace, greenhouse or solar wall is commonly
used in a building as passive solar systems. They can
successfully collect, store and distribute solar energy
not only in southern and moderate climates but also
in the northern latitudes. However, in the region of
harsh climate conditions thermal efficiency of the
passive systems is not so satisfactory. Traditional
passive elements operate properly only during transition periods - the start and end of the heating seasons. Then the solar heat gains during a day equal
the heating energy requirements during a night. At
these periods the gains mentioned above appear almost every day, relatively regularly, and the heat capacity of traditional building materials is sufficient
for diurnal heat storage systems. Nevertheless, in
winter, low external air temperature causes exces-
sive heat losses into the external environment. Also
the solar heat gains are low and occur periodically.
Due to the factors mentioned above two kinds of
problems are encountered. The first one constitutes
to the lack of satisfactory proportions between the
solar heat gains and conduction heat losses. The second concerns the inadequate thermal mass for long
term storage.
On the basis of the problems already described it
is reasonable to employ particular, additional strategies which improve solar systems efficiency. The
strategies are usually those which aim at reducing
heat losses and increasing storage abilities.
Mitchell & Beckman (1989) gave an example
analysis of theoretical limits for storage energy in a
building. The limit of maximum energy uses supposes that gains are used only when there are building losses; that is when the ambient temperature is
lower than that of the building space. During time
periods when the gains exceed the losses, the excess
of the gains over the losses is not useful and is given
back to the environment. This situation concerns the
building with zero thermal storage capacity. The
limit of minimum energy uses assumes that gains
can be used any time. If the losses are greater than
gains, the gains offset the auxiliary energy requirement. If the gains exceed losses, the excess is stored
for use at any time during the period. This situation
would occur in a building with a large enough mass
to store energy over a long period (like one month).
1.2 Transparent insulation materials
The majority of traditional transparent partitions like
glass, polycarbonate, polyethylene, etc. is regarded
as having insufficient value of heat conduction coefficient. However, improving these features leads at
the same time to deteriorating direct solar transmi ttance, which consequently decreases solar radiation
heat gains. Therefore, using an additional layer of
Transparent Insulation Material (TIM) is fully reasonable in advanced, high efficient solar systems.
The general construction of TIM partitioned consists of an outer glass cover for weather protection, a
shading device and translucent capillary structure
(Braun et al. 1992). The shading device is necessary
to prevent overheating in summer and to regulate
energy gains during the transition periods. However,
in the middle of winter, the absorber temperature
does not exceed 30°C (Heim & Klemm 2002) and
no blinds - shutter control is required. For TIM elements with an air gap between the absorber and the
capillary material a plastic film or a thin glass pane
covers the rear TIM face. In a modular construction
these components are held together by a frame. The
frame can be mounted onto the black painted wall.
1.3 Phase change materials
Most solar energy storage is accomplished by sensible heating of either water or rocks with no phase or
chemical changes taking place within the system.
Nevertheless, storage for long periods requires a
fairly large volume of a rock bed or a water tank,
which at times is neither practical nor available.
Thermophysical properties of the building materials used in solar storage systems have strong influence on their thermal efficiency. In passive solar
technology, heat capacity of construction elements is
one of the prime features. Traditional storage systems, such as a rock-bed, a massive wall etc., not
only use exclusively sensible heat capacity but also
give rise to several problems including high cost,
excessive mass and undesirable temperature fluctuations. If, however, traditional building constructions
are combined with Phase Change Material (PCM),
additional latent heat of the phase change is used to
increase thermal capacity of the material. Additionally, the phase change is usually almost isothermal,
thus providing an excellent means of temperature
control.
The utilization of PCMs in active and passive
solar buildings has been a subject of considerable
interest since their first reported application in the
1940s (Lane 1983). In building passive systems,
pure organic or inorganic PCMs can be impregnated
in traditional construction materials, such as gypsum, concrete or ceramic. Thermal performances of
different types of organic or inorganic chemical
compounds were analysed in the past (Abhat 1983,
Hawes et al. 1993, Romanowska & Jablonski 1995).
The results show that organic materials, such as paraffins or fatty acids, are usually thermally more stable and easier to encapsulate than inorganic ones,
such as salt hydrates.
1.4 PCM – ceramic composites
For the purposes of this work, PCM-ceramic composites made of clay with cellulose addition and
fatty acids were considered. Base ceramic material
was characterized by 30% of porosity, obtained by
utilization of the wastes of the paper industry. Fatty
acids were introduced into the porous of ceramic increasing its thermal capacity.
Some laboratory measurements of ceramic compound with fatty acids were undertaken using Differential Scanning Calorimeter (Romanowska et al.
1998). The results showed that it is possible to obtain heightened heat accumulation composite with
almost isothermal change of phases. The PCM considered here are self-nucleating and exhibit no overheating and overcooling effect. The heat of phase
change obtained from laboratory measurements was
about 20kJ/kg, which is an average value for PCMcomposites and over twenty times higher as far as
ordinary ceramics is concerned.
2 THERMAL SIMULATION OF TIM
Thermal simulation of dynamic building behavior
under the changeable climatic conditions is perceived as essential to access precisely the efficiency
of employing TIM. Up till now, many simulation
programs have been developed on the basis of advanced mathematical models for calculations the energy transport in TIM systems. The most popular of
them are HAUSSIM, TRANSYS and ESP-r.
HAUSSIM based on the mathematical model proposed by Hollands et al. (1984) which is able to numerically solve the non-stationary temperature response of TIM wall. Within TRANSYS a special
module was created to model the TIM due to the different properties, (Platzer 1992).
The ESP-r (Environmental Systems Performance
– r for the European Reference Program) is another
simulation program based on the mathematical
model proposed by Clarke (2001). It is capable of
modeling the energy and fluid flows within a combined building and plant systems. ESP-r uses an advanced numerical method to integrate the various
equation types which can be used to represent heat
and mass balances within a building. At present,
however, ESP-r does not contain a specific module
or specific algorithms to model TIM explicitly. Although ESP-r cannot effectively deal with the temperature dependent thermal conductivity, the solar
radiation, transmission and multi-reflection through
the TIM honeycomb structure, there are four possible ways of modeling TIM wall within ESP-r
(Strachan & Johnstone 1994). For the purpose of this
work the “ air gap as an extra zone” approach has
been chosen. A proposal model of TIM wall within
ESP-r was formed as parts of the PASSYS program
(Jensen 1993). Experiments were to be conducted in
some of the PASSYS test sites in Belgium, Italy,
German and Holland. The objective was to carry out
the measurements under different climatic conditions in order to evaluate the performance of such
solar components.
3 MODELLING PCM STRUCTURES
Theoretical (Drake et al. 1987, Peippo et al. 1991,
Heim & Klemm 2001) and experimental (Heim et al.
2001, Athienitis et al. 1997) analyses of the optimal
transition temperature and latent heat capacity of
PCM were conducted successfully. However, a
building scale numerical simulation of phase-change
phenomena in thermal behavior of materials is necessary to estimate the diurnal latent heat storage effect and to ascertain savings in energy consumption.
Storage effects in PCMs should be analysed in the
context of the climate and the construction and operation of the building altogether. However, the
phase transition is not taken into consideration in
several building simulation programs adjusted to
solving heat transfer problems. Thus, the main objective of this paper was to modify the existing
simulation program ESP-r (Clarke 2001) in order to
include phase-change phenomena which would
make it possible to model and simulate advanced
active or passive building elements with PCMs, for
instance intelligent building facades.
According to the control volume and the effective
heat capacity method, the effect of the phase transition is added to the energy balance equation by the
materials properties substitution. Effective capacity
is a highly non-linear function of temperature within
the phase change temperature range; it can be substituted, however, by a simpler linear relationship.
For instance, a similar approach was proposed, for
the thermal simulation of PCM single components in
(Drake 1987, Jokisalo et al. 2000), and for water
freezing and solidification in (Gawin 1993).
3.1 Mathematical model
Differential equations of transient heat conduction
for variable thermophysical properties and conduction heat flux only are given by:
[
( )]
∂
ñ(T ) h (T ) = ∇. ë(T ) ∇T r ,t + g( r ,t)
∂T
(1)
where T = temperature, ρ = density, h = enthalpy, λ
= conductivity, g = heat generation rate. When
∂ñ
∂h ∂h ∂T
∂T
≈ 0 and
=
= C eff ( T )
∂T
∂T ∂T ∂t
∂t
equation (1) becomes:
ñ( T ) C eff ( T )
[
( )
T r,t
=
∂T
(2)
( )]
= ∇. ë( T ) ∇T r,t + g( r ,t)
where Ceff = effective heat capacity.
For the non-linear problem (in the phase change
temperature range) defined by equation (2), the
Goodman transform (Samarskii & Vabishchevivh
1995) can be used to remove the temperature dependent, effective heat capacity Ceff, outside the differential operator by defining a new dependent variable by:
Cl
υ = ∫ C eff ( T ) dT
Cs
where Cs = heat capacity in solid phase, Cl = heat
capacity in liquid phase.
Equation (2) can thus be rearranged as:
∂T ∂υ
=
∂υ ∂t
∂T


∇ υ  + g( r ,t)
= ∇.  ë( T )
∂υ


ñ( T ) C eff ( T )
(3)
3.2 Numerical model
The control volume approach, because of the simplicity of formulation and physical elegance (Clarke
2001), is adapted to describe physical elements of
the model (zones and networks). This method also
allows the adoption of variable thermophysical
properties (Nakhi 1995). The geometry and fabric of
coupled polyhedral zones, connected to one another
through associated network which describe energy
sub-systems, such as air, fluid and moisture flow and
plants, are defined by their number. The complete
model of the building comprises zones and networks
together with internal conditions (occupancy characteristics and control strategies) and external conditions (climate).
The control volume formulation is obtained by
integrating associated partial differential equation
(2) over small polyhedron control volume V, applying the mean value theorem and divergence theorem,
with homogeneous material and uniform boundary
at each surface. Equation (2) thus becomes:
( )
( ) ( ) ∂∂Tt = −λ (T ) ∂∂nT
ñ T C eff T V T
s
s
()
+ V T g (4)
where T – average temperature and g – heat generation rate over control volume, ns – outward drawn
normal unit vector.
3.3 Implementation to ESP-r
Behaviour of passive building elements with PCM
was modelled using the concept of special materials
technique (Kelly 1998). Special materials were introduced to ESP-r as means of modelling active
building elements, i.e. those building elements,
which change their thermophysical properties in response to some external excitation. Special materials
functions apply to a particular node within a multilayer construction. The node defined as a special
material - phase change material node represents the
layer whose physical properties are temperature dependent. This temperature dependence is in accordance with thermophysical properties defined in
special material databases. Variable thermophysical
properties simulation requires the storage and transfer of properties’ values being estimated at each time
step.
4 PROBLEM DEFINITION
Heim & Klemm (2002) showed a positive impact of
transparent insulation on the thermal performance of
the building opaque partition. However, overheating
effect was also reported and, therefore, some traditional techniques were used to lower the temperature
and reduce its fluctuation. Unfortunately, many of
these techniques were not sufficient enough and
caused unexpected problems.
It encouraged the authors to take up a challenge
to create and analyse a new partially transparent,
partially opaque, solar heat storage system. The honeycomb structure of TIM was chosen for an outer,
translucent thermal insulation system. PCM-ceramic
compounds were used as a latent heat storage massive wall.
4.1 TIM-PCM wall
For decades of investigations different forms of intelligent facades have been proposed and analyzed.
Telkes (1978) proposed improving the thermal capacity of Trombe wall by application of PCM. A
great deal of research work with semi-translucent
TIM-PCM wall system was done by Manz et al.
(1997).
With a view of effective gaining, long-term storage and easy distribution of solar energy TIM-PCM
intelligent facade was proposed (Fig. 1). The collector-storage is divided into two opaque and transparent parts. The outer part is completely transparent
and consists of external glass, air gap and 10cm of
TIM with a polycarbonate layer. The internal parti-
tion built from 25cm of PCM-ceramic composite
with cement plasters on its both sides. From the air
gap side the opaque is covered with the high absorptivity (α=0.90) finishing lining. The additional zone
represents the air gap between the TIM and the massive wall. This was done so as convection within the
air gap could be simulated and also so as the correct
temperature dependent air gap resistances could be
used dependent of solar insolation on the outside
surface of the TIM.
Figure 1. Cross-section through TIM-PCM wall.
A hypothetical PCM-ceramic composite with a
heat of fusion of 20kJ/kg (corresponding to a 30% of
fatty acids mixtures impregnated the porous of ceramic) was taken into consideration. The melting
temperatures Tm were set to 20°C and solidification
Ts to 21°C, in order to conduct the desired simulation. Thermophysical properties of TIM layers taken
for calculations come from macro scale, laboratory
measurements done within the framework of
PASSYS program (Jensen 1993).
4.2 Triple zone model
The triple zone, naturally ventilated building with
two direct gains rooms, insulated transparently was
modeled within ESP-r to conduct the numerical
analysis. The perspective view presented in Figure 2
shows the scheme of ventilation network, windows
and TIM-PCM walls, which was applied as a southern external partition for the east and the west passive rooms. Both zones, 4×5×2.5m each, are separated by centrally placed, buffer zone. TIM-PCM
wall was applied on the south elevation. The area of
each intelligent facade equals 10m2 and covers the
whole south elevation. Therefore, the windows of
both rooms had to be defined on the east and west
side respectively. Thermophysical properties of partitions and magnitude of airflow were defined according to the European standards and existing rules.
The heat transfer coefficient for all external, opaque
partitions is set to 0.30W/m2K, and for windows
1.3W/m2K.
5 NUMERICAL RESULTS
Due to the Control Volume Method used in the ESPr program, every multi-layer construction is built of
several layers of homogenous material. Each single
layer is described in space by three nodes. They are
placed in the geometrical center point and on the
boundaries.
5.1 One day - test analysis
Figure 2. Schematic, prospective view of geometry and air
flows in analyzed triple zone building.
4.3 Operations and boundary conditions
The boundary conditions on the external sides of the
zones were defined due to the one-hour characteristic of the weather. The real climatic data for Warsaw
– Poland (52ºN) was used for the simulation. A twoweek period in January 1982 was selected. The first
week has an average character for temperature and
direct solar radiation. The second week represented
relatively low value of solar radiation and slight
amount of energy is expected to be absorbed. History of ambient temperature and direct solar radiation for a selected period is presented in Figure 3.
For others, the internal partition of the boundary
conditions for temperature was defined as an isothermal. The wind speed and direction determined
infiltration flow through the gaps and openings. The
magnitudes of components guaranteed the airflow of
the order of 1ac/h. The equipment, light and occupant casual gains were neglected so as not to affect
the results of the calculations. Continuous heating
with the ideal control set on 20°C was defined for
the whole heating season.
Figure 3. History of ambient temperature and direct solar radiation for analyzed period.
Firstly, the numerical simulation was conducted for
a selected, one-day period to confirm the correctness
of the method. The selected day was chosen from
the winter period to show the effect of storage and
released the solar energy one by one. The temperature histories of the absorptive surface for PCMceramic composite and an ordinary ceramic massive
wall are presented in Figure 4. Additional latent heat
of phase change considerably reduces the surface
temperature fluctuation. Additionally, the results
show the overloaded effect for PCM-composite after
eight hours. It produces the slightly rise in temperature.
Figure 4. History of absorptive surface temperature for PCMceramic composite (PCM) and ordinary ceramic (no PCM)
storage wall.
5.2 Two weeks analysis
The histories of the PCM-composite layer (PCM)
and ordinary ceramic (no PCM) temperature were
calculated within a selected two-week period as
show in Figure 3. The temperature of three nodes
representing analyzed homogenous layer is presented.
The temperature history the depicted in Figure 5
concerns the nodes situated on the external absorber
side. This node is highly exposed to daily temperature fluctuation. During the majority of the first
week this part of construction is overloaded during a
day and is unable to store more solar energy. However, additional latent heat storage allows to reduce
daily temperature fluctuation at that point about 3K
from 28-29°C to 25-26°C. During a night, the heat is
released and the node temperature is keeping over
20°C all the time. The more considerable temperature fluctuation is reported for the ordinary material,
where the node temperature varies between 29°C (at
sunny day) and 18°C (at night).
Figure 5. History of external node temperature for PCMceramic composite (PCM) and ordinary ceramic (no PCM)
storage wall.
Figure 8. History of central node temperature for PCM-ceramic
composite (PCM) and ordinary ceramic (no PCM) storage
wall.
The reduction of temperature fluctuation is easy
to notice comparing temperature frequency distribution (Fig. 6 & 7). For PCM more than 80% of the
temperature records its value is in the phase change
temperature range between Tm=20°C and Ts =21°C.
Figure 9. History of internal node temperature for PCMceramic composite (PCM) and ordinary ceramic (no PCM)
storage wall
Figure 6. External node’s resultant temperature frequency distribution for ordinary ceramic storage wall.
Figure 10. History of surface temperature for PCM-ceramic
composite (PCM) with latent heat of phase change 20kJ/kg and
ordinary ceramic (no PCM) storage wall.
Figure 7. External node’s resultant temperature frequency distribution for PCM-ceramic composite storage wall.
The latent heat of phase change facilitates thermal
conditions in other parts of the PCM-construction.
During winter periods the central node temperature
is sustained on the level of 20°C corresponding to
the composite melting temperature (Fig. 8).
Similar stable thermal conditions are detected on
the internal (room’s) side of TIM-ceramic partition
(Fig. 9). Through the implementation of latent heat
storage the inner surface of the wall is not easily affected by changeable external and internal conditions.
Figure 11. History of surface temperature for PCM-ceramic
composite (PCM) with latent heat of phase change 40kJ/kg and
ordinary ceramic (no PCM) storage wall.
REFERENCES
Figure 12. History of surface temperature for PCM-ceramic
composite (PCM) with latent heat of phase change 60kJ/kg and
ordinary ceramic (no PCM) storage wall.
Additionally, to show the influence of increasing
latent heat capacity the further two cases were analyzed. The results of the absorber’s surface temperature were calculated for the following cases.
Figure 10 refers to PCM-composite with latent heat
of phase change equals 20kJ/kg. The next one, Figure 11, depicts the composite with the same value of
melting (Tm=20°C) and solidification (Ts =21°C)
temperature but twice higher value of the heat of fusion is set to 40kJ/kg. The third composite (Fig. 12)
has also the same range of phase change temperature
though three times higher latent heat amounting
60kJ/kg. The influence of increasing latent heat capacity on the surface temperature history remains insignificant. Twice and three times increasing latent
heat capacity reduces daily the absorber’s surface
temperature fluctuation for approximately 1K and
4K respectively.
6 CONCLUSIONS AND FUTURE WORK
This study is the first step in the integration of transparently insulated, latent heat storage systems within
a building structure. The initial model implemented
in ESP-r to calculate the effect of phase change
works properly but further development and verification are planed. The obtained results show the effect of latent heat storage on the thermal behavior of
the building’s external partition TIM-PCM intelligent facade. This effect caused considerable reducing the day and night temperature fluctuation. The
PCM-ceramic composite designed for passive solar
heating works properly under January weather conditions. However, to design the appropriate composite material for passive heating during winter and
cooling in summer, the wider analyses using multicriterion optimization are planed. The behavior of
the material composite corresponds to the experimental measurements; further macro-scale experiments, however, are necessary to validate the model.
Additionally, a more accurate description of the
PCM structure with variable density and conductivity will be analyzed in the future.
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This study was partly prepared during the author's
postgraduate studentship at the Strathclyde University, Glasgow, Scotland. Special thanks go to Professor J. A. Clarke from the Department of Mechanical Engineering, as well as the other members
of the ESRU group, for their kind support and valuable advice.
This work was financed by the State Committee
for Scientific Research from funds in 2002 – 2003 as
a research project no. 5 T07E 021 23.

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