Download Heat capacity in relation to the Danish building regulations

Heat capacity in relation to the Danish building regulations
Lars Olsen, MSc, PhD,
Danish Technological Institute, Department of Building Technology;
[email protected]
KEYWORDS: Storage of heat, heat capacity, overheating, calculations.
SUMMARY:
To fulfil the requirements in the Danish building regulations for new buildings it is necessary to have a limited
heating demand. The heating demand is calculated on the basis of a number of energy related parameters. One
of these is the heat capacity of the building. In the present study three different methods for determination of the
heat capacity of the building have been assessed: Tabulated values in connection with the Danish calculation
method, a simplified CEN method and the active heat capacity. To estimate the active heat capacity an analysis
has been made where surfaces with different materials are exposed to a diurnal variation of the room
temperature. The heat which is transmitted into the surface during a 12 hour period with positive heat flux, and
stored in the material, is called the ability to store heat.
Examples are shown of how it is possible to calculate the heat capacity for different materials. It is demonstrated
how the heat capacity for the single surfaces can be added in order to calculate the heat capacity of a whole
building. The result expressed as the heat capacity per m² heated floor area, is used as one of the input values in
the Danish calculation programme for assessment of the energy demand of buildings. This study indicates that it
can normally not be expected that a detailed calculation will provide a larger heat capacity than when the
Danish tabulated values are used. This is the case for both lightweight and solid buildings. There might be a
need for assessment of the Danish tabulated values to check whether the level the heat capacity is appropriate.
1. Introduction
In the Danish building regulations, which were introduced in 2006, a calculation of the heating and cooling
demand is required (Aggerholm S. and Grau K. (2005)).
It is possible to utilize the thermal mass in solid constructions to reduce the variation of the room temperatures
and thereby create a more uniform indoor climate and to reduce the requirements for heating and cooling.
Previously only demands on heating in the cold period were required. Today there are requirements on both
heating and cooling. In few years it is expected that new requirements will be introduced which will reduce the
energy consumption. This will further encourage to the utilisation of thermal mass for reduction of the heating
and cooling demand and for reductions of the temperature variations in buildings. A study (Olsen L. and Hansen
M. (2007)) on some examples with different thermal capacities of buildings shows that this parameter can
provide an influence on the heating demand of the size of 4% to 13%.
1.1 Objective
On this background it is the objective of this paper to:
•
Perform calculations, which make it possible to quantify the effect of the utilisation of the thermal
mass for accumulation of heat in the surfaces of buildings.
•
Analyse the energy and comfort related performance of the different choices of building materials.
The calculation principle which corresponds to the new building regulations is applied.
•
Show examples on how the material data can be used in connection with the new building
regulations.
•
Show how it is possible to calculate the heat accumulation in an actual construction.
2. Calculations
In order to investigate the effect of different materials’ influence on the thermal indoor climate, calculations are
performed of the heat accumulation achieved when heat is supplied or dissipated at the interior building surfaces
(Olsen L. and Hansen M. (2007)).
Below in table 1 a number of typical data for different materials is shown (Dansk Standard (2005), Dansk
Standard. (2001)). The material lightweight concrete is used for concrete with aggregate of expanded clay.
TABLE 1: Material characteristics used in the calculations.
No. Material
Density
Thermal
conductivity
Thermal
capacity
Thermal
capacity per
volume
Thermal
effusivity
ρ
λ
cp
cp·ρ
D
W/mK
J/(kg·K)
MJ/(m ·K)
3
kg/m
1
Concrete
2
Lightweight
concrete
Masonry
3
4
5
6
7
8
Lightweight
concrete
Gypsum
plasterboard with
paper liners
Autoclaved
aerated concrete
Lightweight
concrete
Wood
3
2
½
J/(m ·K·s )
2400
2.1
1000
2.40
2245
1800
0.8
1000
1.80
1200
1800
0.62
840
1.51
968
1200
0.4
1000
1.20
693
900
0.25
1000
0.90
474
700
0.19
1000
0.70
365
600
0.17
1000
0.60
319
500
0.13
1600
0.80
322
The calculations of the accumulation of heat are done with the programme Heat2 (Bloomberg T. and Claesson J.
(2003)). The heat accumulation is calculated with the influence of a sinusoidal fluctuation of the air temperature
with an amplitude of ±1 K. The materials are assumed to be applied in the following thicknesses: 2.5 cm, 5 cm
and 10 cm. The exposure is assumed to be from one side while the other surface is adiabatic. This adiabatic
surface corresponds to an insulated side of a well insulated wall or that the wall has an equal two-sided exposure,
and the thickness corresponds to the half of the wall thickness.
2.1 Calculation of the heat accumulation
Below in FIG. 1 and 2 examples on the calculated temperatures and heat flows in the materials are shown
(positive heat flow, when the heat flow is supplied to the material).
Surface temperature
Temperatures and heat flow
0.60
6
0.40
4
0.20
2
0.00
0
-0.20
-2
-0.40
-4
-0.60
-6
-0.80
-8
Temperature
2
Heat flow, (W/m )
0.80
10 Air temperature
Temperature 10 cm depth
8 Heat flow
1.00
-1.00
-10
0
4
8
12
Hour
16
20
24
FIG. 1: Example of surface temperature, air temperature, temperature in the depth of 10 cm and the heat flow at
the surface for a concrete wall (material no. 1), thickness of the wall 10 cm.
Surface temperature
Temperatures and heat flow
0.60
6
0.40
4
0.20
2
0.00
0
-0.20
-2
-0.40
-4
-0.60
-6
-0.80
-8
Temperature
2
Heat flow, (W/m )
0.80
10 Air temperature
Temperature 10 cm depth
8 Heat flow
1.00
-1.00
-10
0
4
8
12
Hour
16
20
24
FIG. 2: Example of surface temperature, air temperature, temperature in the depth of 10 cm and the heat flow at
the surface of a solid wood wall (material no. 8), thickness of the wall 10 cm.
In FIG. 1 an example with a 10 cm thick concrete wall is shown. The curves show the temperature and heat
flow, when the air temperature (blue curve) varies ±1 K. The calculations show that this results in a surface
temperature (purple curve), which varies ±0.4 K. The maximum of the air temperature is assumed to be at hour
12. The maximum of the surface temperature is calculated to be 3-4 hours later. The temperature in the depth of
10 cm from the surface (red curve) varies with nearly the same size of temperature fluctuations as at the surface.
The maximum temperature occurs with a delay of approx. 5-6 hours compared to the maximum of the air
temperature.
The heat flow at the surface (green curve) varies proportionally with the temperature difference between the air
temperature and the surface temperature. The size of the heat flow can be seen at the right side scale in FIG. 1.
The maximum value of the heat flow occurs 1-2 hours after the maximum of the air temperature is obtained.
These results are compared with the conditions of a wall of wood (FIG. 2). In this case the maximum surface
temperature fluctuation is ±0.75 K. The temperature in a depth of 10 cm thickness varies with a fluctuation of
approx. ±0.35 K. The heat flow is less than the flow obtained with the other walls due to the lower thermal
conductivity and the smaller heat capacity per volume.
In TABLE 2 below a summation of the flow during the 12 hours, where the air temperature is larger than the
surface temperature (positive heat flow), is shown. The sum is shown in the table as the calculated heat
accumulation per surface area exposed to a sinusoidal temperature variation. It corresponds to the amount of heat
transferred into the material in the period with positive heat flow.
In the table the thermal capacity per surface area with the different thicknesses of the material is also shown.
This size is calculated as: cp·ρ·t [Wh/(m²·K)], where t is the thickness of the material.
The calculated heat accumulation depends on the amplitude (temperature variation). It is assumed that the
difference between the maximum and minimum air temperature is 2 K. If the temperature of the material follows
this temperature variation exactly, there will be a 100% utilization of the thermal capacity. In practice the
temperature in the material will fluctuate less due to the surface resistances and the thermal conductivity of the
material. The temperature variation in the material corresponds to the amount of heat accumulated in the
material. The size of the accumulated heat is shown in TABLE 2.
The accumulated heat can be related to the maximum possible amount of heat at a certain temperature
fluctuation of the whole material. The relation between these sizes can be defined as a utilization of the thermal
capacity. It is also possible to use the term active thermal capacity, which is the actual thermal capacity
multiplied by the utilisation of the thermal capacity.
The temperature variation which corresponds to the sinusoidal fluctuation of ± 1 K is therefore 2 K.
The utilisation of the thermal capacity is shown in TABLE 2. The table shows that at a thickness of the materials
of 2.5 cm the utilisation is between 86 and 96% of the thermal capacity for all the materials. Correspondingly
between 64 and 89% of the thermal capacity is utilized with a thickness of the materials of 5 cm and with a
thickness of the materials of 10 cm is between 37 and 56% of the thermal heat capacity utilized.
The utilisation of the thermal capacity is less for concrete than for materials with a smaller density. The reason
can be explained by the reduction of the amount of heat transferred due to the surface resistance and the thermal
conductivity of the material.
In practice it is not of great importance that the utilisation of the thermal capacity is less for concrete than for
other materials with lower density. It is the size of the heat accumulation per surface area which is the most
important parameter.
The unutilized thermal capacity can in principle be utilized if the temperature variations have a longer time
period than assumed in the present calculations, e.g. weekly variations. That means, if periods of days with a
large internal gain of heat are followed by periods with smaller internal gains, a larger part of the thermal
capacity will be able to participate in the heat accumulation.
Alternatively the unutilized heat capacity can be utilized if there is an active storage of heat in the constructions,
e.g. due to embedded pipes and the like.
The utilization of the thermal capacity must from an overall point of view be considered to be more dependent
on the thickness of the material than the characteristics of the material. Therefore the heat accumulation per
surface area must be regarded as the most important parameter to consider, when the performance in relation to
heat accumulation of a construction is evaluated.
In FIG. 3 the heat accumulation is shown in dependence of the effusivity and thickness of the materials. It
appears that the heat accumulation is increased as a function of the effusivity and the thickness of the material.
For a certain thickness it appears that the slope of the curves is largest for small values of the effusivity and
smallest for large values of the effusivity. The only exception is wood which in the thickness of 5–10 cm gives a
minor deviation in comparison with the other materials.
The curves in FIG. 3 can be utilized to estimate the heat accumulation for other materials than the investigated, if
the effusivity has been calculated.
Heat accumulation
50
2
Heat accumulation (Wh/m K)
45
40
35
30
0.100 m
25
0.050 m
l
0.025 m
20
15
10
5
0
0
500
1000
1500
2000
2
2500
½
Thermal effusivity (J/(m ·K·s ))
FIG. 3: Calculated heat accumulation in relation to effusivity and thickness of the material.
TABLE 2: Thermal capacity per surface area, calculated heat accumulation per surface area and utilisation of the thermal capacity.
The calculated heat accumulation is estimated with a variation of the air temperature with a period length of 24 hours and an amplitude of ± 1K.
No. Material
Density
Thermal capacity per surface area
[Wh/(K·m²)]
Calculated heat accumulation per
surface area [Wh/m²K] with sinusoidal
variation (± 1 K)
Utilisation of the thermal
capacity [%]
ρ
Thickness of the material
Thickness of the material
Thickness of the material
3
kg/m
0.025 m
0.050 m
0.100 m
0.025 m
0.050 m
0.100 m
0.025 m
0.050 m
0.100 m
1
Concrete
2400
16.7
33.3
66.7
28.6
42.7
48.8
86
64
37
2
Lightweight concrete
1800
12.5
25.0
50.0
22.8
35.3
40.4
91
71
40
3
Masonry
1800
10.5
21.0
42.0
19.6
31.7
36.8
93
76
44
4
1200
8.3
16.7
33.3
15.8
26.6
30.9
95
80
46
900
6.3
12.5
25.0
12.0
20.9
24.5
96
83
49
6
Lightweight concrete
Gypsum plasterboard
with paper liners
Autoclaved aerated
concrete
700
4.9
9.7
19.4
9.5
16.8
20.5
98
87
53
7
Lightweight concrete
600
4.2
8.3
16.7
8.2
14.8
18.6
98
89
56
8
Wood
500
5.6
11.1
22.2
10.6
17.5
17.8
96
79
40
5
8
3. Thermal capacity of a building
In calculations according to the Danish building regulations it is recommended to specify the building in one of
four categories of thermal capacity for a building (Aggerholm S. and Grau K. (2005)). The categories are
ranging from an extra light weight building to an extra heavy weight building. The thermal capacity of the
building per floor area ranges from values of 40 Wh/(K·m2) to 160 Wh/(K·m2).
In the European standards (Dansk Standard (2004)) a simplified method is given for the estimation of the
thermal capacity of surfaces and buildings. This method is not described in details here, but provides an
approximate method to obtain the thermal capacity for each single surface.
An example is calculated where the internal surface area is estimated for of the different constructions. The
surface area of the different constructions is correlated to the gross floor area. In TABLE 3 an example of how it
is possible to calculate the total heat capacity and the total active heat capacity is shown.
TABLE 3: Example of calculation of total heat capacity and total active heat capacity for a building.
Construction
Surfacearea in
relation to
the floor
area
Material
thickness
Heat
capacity
per
surface
area
Heat
capacity
per floor
area
Wh/(K·m²) Wh/(K·m²)
m
Active heat
capacity per
surface
area
Active
heat
capacity
per floor
area
Wh/(K·m²)
Wh/(K·m²)
Roof, concrete
Floor,
tiles/concrete
Partition walls
concrete
External walls,
concrete
0.90
0.10
66.7
60.0
24.4
22.0
0.90
0.10
66.7
60.0
24.4
22.0
0.90
0.09
60.0
54.0
22.2
20.0
0.29
0.10
66.7
19.3
24.4
7.1
Sum
2.99
193.4
71.0
In this example the total heat capacity per floor area is estimated to be 193 Wh/(K·m2). The active heat capacity
per floor area is estimated to be 71 Wh/(K·m2). This value can be compared with the tabulated value applied in
the Danish calculation rules of 160 Wh/(K·m2).
Calculations with other materials demonstrate a similar difference between the calculated total active heat
capacity for a building and the values obtained using the Danish tabular values. (Olsen L. and Hansen M.
(2007)).
4. Conclusions
Following conclusions can be drawn from this study:
•
A large part of the heat capacity of heavy weight solid constructions can be utilized for heat
accumulation.
•
The part of the material closest to the surfaces takes more active part in the accumulation than the
parts of the constructions with a larger distance to the interior surfaces.
•
The heat capacity of the building has a major influence on the thermal performance of a building
for both heating and cooling.
•
It is demonstrated, how it is possible to calculate the heat capacity of a certain building.
•
It can not be expected to obtain a larger heat capacity of a building by doing detailed calculations
instead of using the Danish tabulated values.
•
It seems that there is a need of revising the Danish tabulated values for heat capacities in buildings.
5. References
Aggerholm S. and Grau K. (2005). By og Byg Anvisning 213, Bygningers energibehov. Beregningsvejledning.
(ver. 1.06.03), Statens Byggeforskningsinstitut 2005.
Bloomberg T. and Claesson J. (2003). Heat 2. version 6.0, T, www.buildingphysics.com
Dansk Standard (2001). Byggematerialer og produkter - Hygrotermiske egenskaber - Tabeller med
designværdier, DS/EN 12524:2001.
Dansk Standard (2004). Termisk ydeevne for bygninger - Beregning af energiforbrug til rumopvarmning. DS/EN
ISO 13790:2004.
Dansk Standard (2005). Beregning af bygningers varmetab, DS 418, 6. udgave 2002-04-03, inkl. DS 418/Till. 1
2005-12-21.
Olsen L. and Hansen M. (2007). Varmeakkumulering i beton, Arbejdsrapport fra Miljøstyrelsen, Nr. 19, 2007.