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TRANSCRIPT
Building Physics
EXTERIOR CLIMATE THERMAL COMFORT HEAT AIR EXCHANGE ENERGY DAYLIGHT
Heinrich Manz
Translated by Carolyn Gorczyca Thürlimann
Lucerne University of Applied Sciences and Arts
School of Engineering and Architecture
Author
Prof. Heinrich Manz, Ph.D. Lucerne University of Applied Sciences and Arts School of Engineering and Architecture Technikumstrasse 21 CH-6048 Horw Tel. +41 41 349 3915 [email protected] 1. edition, 2014
Sustainable development means development that meets the needs of the present without compromising the ability of future generations to meet their own needs. „Brundtland Commission“, World Commission on Environment and Development (WCED) of the United Nations (UN), 1987
Content
INTRODUCTION 12
1 HEAT TRANSFER 14
1.1 Conduction 14 1.1.1 Heat Equation (Fourier’s Differential Equation) 14 1.1.2 One-Dimensional, Steady-State Heat Conduction 16 1.1.3 Multi-Dimensional, Steady-State Heat Conduction 17 1.1.4 One-Dimensional, Non-Steady-State Heat Conduction 19
1.2 Convection 19 1.2.1 Forced and Free Convection 19 1.2.2 Convection on Surfaces 20 1.2.3 Convection in Cavities 21
1.3 Thermal Radiation 23 1.3.1 Laws and Characteristics 23 1.3.2 Radiation Exchange between Surfaces 27
1.4 Design Values for the Total Heat Transfer on Surfaces 29
Literature 30
2 EXTERIOR CLIMATE 32
2.1 Solar Radiation 32 2.1.1 Solar Radiation Source 32 2.1.2 Influence of the Atmosphere 33 2.1.3 Direct Radiation on Tilted Surfaces 35 2.1.4 Global Irradiance 39
2.2 Air Temperatures 43
2.3 Soil Temperatures 45
2.4 Wind 45
2.5 Climate Fluctuations and Changes 46
2.6 Impacts on the Building Envelope 47 2.6.1 External Heat Transfer Coefficient 47 2.6.2 Surface Temperature Reduction Due to Infrared Radiation 47 2.6.3 Service Life of Exterior Building Elements 48
Problems 49
Literature 49
3 THERMAL COMFORT 52
3.1 Human and Interior Space 52
3.2 Heat Balance of Humans 53
3.3 Requirements for Thermal Comfort 56
3.4 Detailed Comfort Analysis 58 3.4.1 Global Comfort Criteria 58 3.4.2 Local Comfort Criteria 60
3.5 Cold downdraft 62
3.6 Comfort Measurements 64
3.7 Adaptive Comfort 64
3.8 Implications 65
Problems 65
Literature 66
4 STEADY-STATE THERMAL TRANSMISSION 70
4.1 Standard Cross Section 70
4.2 Thermal Bridges 75
4.3 Cavities in Window Frames etc. 79
Problems 80
Literature 87
5 NON-STEADY-STATE THERMAL TRANSMISSION 90
5.1 Non-Steady-State Heat Propagation in a Material Layer 90 5.1.1 Heat Equation and Illustration 90 5.1.2 Thermal Diffusivity and Thermal Effusivity 91 5.1.3 Inertia of Walls: Charge and Discharge Performance 93
5.2 Reaction of a Material Layer to Periodic Changes 95 5.2.1 Material Layer with a Finite Thickness: Amplitude Damping und Phase Shift 95 5.2.2 Semi-Infinite Material Layers: Penetration Depth 96 5.2.3 Effective Thickness for Heat Storage 99
5.3 Non-Steady-State Properties of Opaque External Walls 100
5.4 Structural Consequences 104
Problems 105
Literature 106
6 TRANSPARENT BUILDING ELEMENTS 108
6.1 Classification and Characteristics 108
6.2 Optical Properties of Glazings 110
6.3 Thermal Properties of Glazings 114
6.4 Energy Fluxes Through Windows 119
6.5 Solar Shading Devices 119
Problems 122
Literature 123
7 AIR EXCHANGE 126
7.1 Wind Pressure on the Building Surface 127
7.2 Thermally Induced Pressure Differences 131
7.3 Airflow Through Leakages 133
7.4 Indoor Air Quality 136
7.5 Airtightness of the Building Envelope 137
7.6 Mechanical Ventilation with Heat Recovery 139
7.7 Passive Cooling by Night-time Ventilation 141
Problems 142
Literature 144
8 NON-STEADY-STATE BEHAVIOR OF A ROOM 146
8.1 Energy flows in a room 146
8.2 Energy Balance in a Room 148
8.3 Time Constant and Gain/Loss-Ratio 148
8.4 Building Simulation 152
8.5 Building Simulation Example: Office Room in Summer 153
8.6 Structural Consequences 156
Problems 156
Literature 157
9 ENERGY AND SUSTAINABILITY 160
9.1 Energy and Sustainability Challenges 160
9.2 Heating Energy Demand 165 9.2.1 Balancing the Energy Flow in a Building 165 9.2.2 Heating Degree Days 167
9.3 Protection Against Overheating in Summer 168
9.4 Renewable Energy 169
9.5 Total Energy Expenditure During a Life Cycle 172
9.6 Energy Demand per Floor Area and Energy Standards 174
9.7 Strategies for Low-Energy Buildings 178
9.8 Existing Building Stock and Refurbishment 179
9.9 Climate Change and Energy Demand 180
9.10 Summary 181
Problems 182
Literature 182
10 DAYLIGHT 186
10.1 Solar Radiation and Spectral Luminous Efficiency of the Human Eye 186
10.2 Fundamental Photometric Terms and Relationships 187 10.2.1 Luminous Flux Φ 187 10.2.2 Illuminance E 189 10.2.3 Luminous Intensity I 190 10.2.4 Photometric Inverse-Square Law 191 10.2.5 Luminance L 192 10.2.6 Overview 192
10.3 Luminance Distribution of the Sky 193
10.4 Transmittance Factors of the Building Envelope 194
10.5 Daylight Factor 195 10.5.1 Components of Daylight Factor 195 10.5.2 Sky Component TH 197 10.5.3 Externally Reflected Component TV 197 10.5.4 Internally Reflected Component TR 198 10.5.5 Example to Calculating the Daylight Factor 200
10.6 Influence of Fenestration 205
10.7 Rules for Good Daylighting 207
10.8 Daylight Planning 208
Problems 210
Literature 213
APPENDIX 215
A WEATHER DATA 216
B PROPERTIES OF BUILDING MATERIALS 223
Symbols
a Thermal diffusivity m2/s
a Air leakage coefficient m3/(h⋅m⋅Pa2/3)
A Area m2
b Thermal effusivity J/(m2⋅K⋅s1/2)
c Specific heat J/(kg⋅K)
C Specific heat per area J/(m2⋅K)
d Thickness m
E Energy demand per floor area MJ/(m2⋅a) or kWh/(m2⋅a)
g Total solar energy transmittance -
g Acceleration of gravity, g = 9.81 m/s2 m/s2
h Heat transfer coefficient (surface) W/(m2⋅K)
H Global heat loss coefficient W/(m2⋅K)
I Solar irradiance W/m2
n Air change rate 1/h
p Pressure Pa
∆p Pressure difference Pa
P Power W
q Heat per area J/m2
q Heat flux W/m2
Q Heat (in standards also used as ‘heat per area’) J (or J/m2)
Q Heat flow W
R Thermal resistance m2K/W
t Time s
T Temperature K
T Time period s
U Thermal transmittance W/(m2⋅K)
v Velocity m/s
V Volume m3
V Air flow rate m3/h
x,y,z Coordinates (in space) m
α Absorptance -
ε Phase shift h
ε Emissivity -
h Efficiency or utilization factor -
θ Temperature °C
∆θ Temperature difference °C or K
λ Thermal conductivity W/(m⋅K)
λ Wave length m
Λ Heat transfer coefficient (overall) W/(m2⋅K)
ν Amplitude damping -
ρ Reflectance -
ρ Density kg/m3
s Stefan-Boltzmann constant, s = 5.67·10-8 W/(m2⋅K4)
s Penetration depth m
τ Transmittance -
τ Time constant s or h
χ Point thermal transmittance W/K
ψ Linear thermal transmittance W/(m⋅K)
Subscripts
a Air
c Convection
e External or exterior
f Frame
g Glazing
i Internal or interior
r Radiation
s Surface
se Surface external
si Surface internal
v Visible
w Window
Symbols Chapter 10 (Daylight)
A Area m2
E Illuminance lx
I Luminous intensity cd
L Luminance cd/m2
K Luminous efficacy lm/W
TLQ Daylight factor -
V Spectral luminous efficiency (human eye) -
λ Wavelength m or nm
τ Transmittance -
Vτ Visible light transmittance -
Φ Luminous flux lm
Φλ Spectral luminous flux lm/nm
Φeλ Spectral radiative flux W/nm
Ω Solid angle sr
Introduction Today a great deal of energy is expended to ensure comfortable conditions in the interior space of buildings. In Switzerland 47% of the total energy demand is generated to operate buildings: heat-ing (35.1%), hot water (5.5%), lighting (3.4%), ventilation and increasingly also cooling (2.7%) (Source: Swiss Federal Office of Energy, 2008). Also in the European Union the building sector with 40 % of the energy needs represents the largest energy consumer.
Linked with energy use, especially from fossil fuels, are problems such as pollution, climate change and the shortage of resources that against the backdrop of the rising world population are becom-ing increasingly more important.
With sensible design of buildings, especially of the building envelope, the energy demand can to-day be reduced with reasonable effort by a factor of 5 to 10 compared with older construction. Ad-ditionally, in such well-designed structures also the comfort, especially the thermal comfort, is con-siderably better.
An understanding for the interplay with the outdoor climate and the different energy fluxes in the building – as well as the conditions for thermal comfort – is imperative to being able to design, con-struct and plan energy efficient buildings.
Chapter 1
Heat transfer
Heat Transfer 14
1 Heat Transfer With many problems in the natural sciences and technology it is essential to understand and to quantify heat transport. Heat flow arises because of temperature differences in which the heat flows from a location of higher temperature to a location of lower temperature. In buildings, espe-cially in the building envelope, large temperature gradients are often present that induce heat flow (Chapters 4 to 8). The understanding of the mechanisms of heat transfer is also important regard-ing the thermal comfort of people in interior spaces (Chapter 3) and the energy balance of build-ings (Chapter 9). The most important laws of heat transport will therefore be introduced in this chapter. Heat is transported by different means. A distinction is made between three fundamental modes of heat transport: conduction, convection (fluid flow) and radiation. Table 1.1 shows in which mediums these transport modes can occur. As regards radiation the thermal radiation ex-change between solid surfaces is of particular importance in building physics.
Heat Transport Mode Medium
Conduction
Convection
Radiation
solid, liquid, gas
liquid, gas
solid, liquid, gas, vacuum
(→ system: solid-gas)
Table 1: Heat transport mechanisms
By conduction heat is transported in a material through the mechanical propagation from atomic and molecular vibrations (collisions). With this no mass transport arises. For example, an iron rod heated on one side conducts the heat to the colder side. By convection heat is transported through motion processes (fluid flow); i.e. mass transport takes place. Warm wind, for example, transports heat in the atmosphere. By thermal radiation thermal energy is transported through electromagnet-ic radiation. This transport process does not require a medium; i.e. it can also take place in a vacu-um. Examples are solar radiation or heat radiation of hot cooktops.
1.1 Conduction
1.1.1 Heat Equation (Fourier’s Differential Equation)
In a homogeneous medium a cuboid is considered with side lengths of ∆x, ∆y and ∆z (Fig. 1.1). In the medium there is a temperature difference. For the sake of clarity only the heat flow in the x-direction is drawn in Figure 1.1. According to Fourier's law of thermal conduction (Jean Baptiste Joseph Fourier, 1768-1830), the heat flux in the x-direction is:
∂∂
−= 2mW
xTqx λ
λ thermal conductivity W/(m·K)
T temperature K
The thermal conductivity is a material property. The value of the heat flux is higher the larger the thermal conductivity of the material is and the larger the local change in temperature is. The nega-tive sign indicates that the heat flows from a location of higher temperature to a location of lower temperature. The heat flux in the y- and z-direction can be determined analogously.
Heat Transfer 15
Fig. 1.1: Geometry to the derivation of the heat equation
The first law of thermodynamics, the conservation of energy, is now applied to the control volume in Figure 1.1. A balance is established consisting of the heat flow through the surfaces and the change of stored heat in the volume element.
tTc
zT
zyT
yxT
x ∂∂ρ
∂∂λ
∂∂
∂∂λ
∂∂
∂∂λ
∂∂
=
+
+
ρ density kg/m3
c specific heat capacity J/(kg·K)
t time s
x,y,z coordinates m
With a constant thermal conductivity λ arises
++= 2
2
2
2
2
2
zT
yT
xT
ctT
∂∂
∂∂
∂∂
ρλ
∂∂
This equation is referred to as heat equation or Fourier’s differential equation and describes the spatial and temporal temperature distribution. The value λ/(ρ⋅c) is denoted thermal diffusivity and is a measure of the speed of temperature equalization in a medium.
=
sm
ca
2
ρλ
Additionally, the initial conditions belong to the heat equation, given by the temperature distribution at time t = 0, as well as the boundary conditions. The boundary conditions can be in different forms. So, for example, the temperature or a certain heat flux can be given at the boundary of the solution domain.
Table 1.1 gives numerical values for the thermal conductivity, density, specific heat capacity and the thermal diffusivity of three different materials. The thermal conductivity of good conducting metals is up to four magnitudes above those of heat insulation materials. In the following three special cases of the heat equation will be discussed.
Heat Transfer 16
Material λ (W/m·K) ρ (kg/m3) c (J/kg·K) a (m2/s)
copper
wood (spruce)
mineral wool
380
0.14
0.04
8900
500
80
380
2200
600
11236·10-8
13·10-8
83·10-8
Tab. 1.1: Thermal conductivity λ, density ρ, specific heat c and thermal diffusivity a of different materials.
1.1.2 One-Dimensional, Steady-State Heat Conduction
The simplest heat conduction problem is the case of one-dimensional, steady-state (= time-independent) heat conduction in a homogeneous layer (Fig. 1.2). The heat equation reduces to
02
2
=xT
∂∂
xCC)x(TCxT
⋅+=→=→ 121∂∂
This implies that a linear temperature profile occurs in the layer.
Fig. 1.2: Temperature profile in a homogeneous wall
With the boundary conditions
T(x = 0) = T0 = C2
as well as Fourier's law of thermal conduction
1CqxT
=−=λ∂
∂
the temperature profile is given by:
xqT)x(T ⋅−=λ
0
The heat flux through the layer amounts to:
( ) ( )10101 TTR
TTd
q −=−=λ
T1 denotes the temperature of the backside of the layer. The value R = d/λ is referred to as the thermal resistance.
The temperature profile in a multi-layered wall is shown in Figure 1.3.
Heat Transfer 17
Fig. 1.3: Temperature profile in a multi-layered wall (itot = 2)
The multi-layered wall can be considered as a series of thermal resistances. For a wall with i layers the total thermal resistance Rtot is given as follows:
∑∑ ==i i
i
iitot
dRRλ
The heat flux q through the multi-layered wall amounts to:
( )toti
tot
TTR
q −= 01
totiTT −0 denotes the difference of the surface temperatures between all layers. The temperature change in the i-th layer is
( )toti
tot
ii TT
RRT −= 0∆
The temperature number i is
( )∑ −−=i
itot
ii tot
TTRRTT 00
The temperature Ti can also be easily determined graphically, since in a temperature vs. thermal resistance diagram the temperature profile can be described by a straight line.
1.1.3 Multi-Dimensional, Steady-State Heat Conduction
In Section 1.1.2 the one-dimensional steady-state heat flow through a wall was examined. In these cases the temperatures depend only on one coordinate, the coordinate x perpendicular to the lay-er. This applies to a plane, infinitely long and high wall only. When this assumption is not applica-ble then more dimensions need to be taken into consideration.
Assuming steady-state conditions the so-called Laplace equation arises from the heat equation.
02
2
2
2
2
2
=++zT
yT
xT
∂∂
∂∂
∂∂
In the three-dimensional case the temperature T depends on three coordinates x, y and z:
T = T(x,y,z)
The heat flux q can be regarded as a vector with the three components xq , yq and zq .
Heat Transfer 18
zyx ezTe
yTe
xTT gradq
⋅⋅−⋅⋅−⋅⋅−=⋅−=
∂∂λ
∂∂λ
∂∂λλ
zTq
yTq
xTq zyx ∂
∂λ∂∂λ
∂∂λ ⋅−=⋅−=⋅−=
The components of the heat flux vectors are illustrated in Figure 1.4.
Fig. 1.4: Components of the heat flux vectors in the two-dimensional (left) and in the three-dimensional case (right)
For plane problems is T = T(x,y). These temperature field can be represented by lines with con-stant temperature (= isotherms). The heat flux vector is always perpendicular to an isotherm. The orthogonal trajectory to the isotherm indicates therefore the path of heat flow (= heat flow line or adiabat)(Fig. 1.5). An illustration of the two-dimensional heat conduction situation is illustrated in Fig. 1.6. By analogy with a topographic map the isotherms can be interpreted as contour lines (constant elevation) and the heat flow lines as the lines, which follow the highest gradient. Two-dimensional heat conduction situations will be handled with examples in Section 4.2.
Fig.1.5: Isotherms (T = constant) and heat flow lines.
For some special boundary conditions analytical solutions of the Laplace equation exist. But in building physics numerical methods are much more important to the solution of multi-dimensional heat conduction problems.
Heat Transfer 19
Fig. 1.6: Illustration of isotherms and heat flow lines
1.1.4 One-Dimensional, Non-Steady-State Heat Conduction
For one-dimensional, non-steady-state heat conduction the heat equation can be written as fol-lows:
2
2
xTa
tT
∂∂
∂∂
=
Only a few analytical solutions exist for this case. In building physics, therefore, also here the nu-merical methods are more important. In Chapter 5 this equation will be discussed by means of an illustrative model.
1.2 Convection
1.2.1 Forced and Free Convection
Convection refers to the transfer of heat by the movement of molecules within liquids and gases. With this type of heat transfer, mass is transported. In building physics the heat transfer medium is usually air. One can distinguish between free and forced convection. Free convection, or natural convection, occurs in liquids or gases if the temperature distribution on the boundary surfaces pro-duces no stable layers. The fluid movement is initiated by density variations due to temperature dif-ferences. In an indoor environment free convection can e.g. occur with warm radiators or cold win-dow surfaces. In the case of forced convection the cause of fluid flow is an externally imposed pressure difference, e.g. from the wind or a fan. The fluid flow can in both cases be laminar (order-ly flow with “parallel” streamlines) or turbulent (chaotic flow). The type of flow – laminar or turbulent – influences the heat transfer.
The processes of convective heat transfer are complicated. The most important parameters to the convective heat flow are:
- physical properties of the fluid (e.g. air)
- temperature difference ∆T btw. wall surface and fluid
Heat Transfer 20
- fluid velocity v
- type of fluid flow (laminar or turbulent → Reynolds number Re)
- surface roughness
- heat flow direction (horizontal, vertical up or down)
- geometry
Empirical formulas based on measurements are often used. In this section some useful formulas will be introduced.
1.2.2 Convection on Surfaces
Firstly, we will consider the heat transfer on inner and exterior surfaces (walls, ceilings, floors). The heat flux that is caused by convection on a surface amounts to:
( )
⋅=−⋅= 2m
WThTThq csac ∆
hc denotes the heat transfer coefficient (surface) for convection. Ta is the air temperature at a given distance from the surface and Ts is the surface temperature.
For the case of free convection the heat transfer coefficient with horizontal heat flow (interior wall) can be approximately described with
⋅=
KmWT.hc 2
3311 ∆
and with vertical heat flow (floors and ceilings of room interiors) with
⋅=
KmWT.hc 2
3521 ∆
Figure 1.7 illustrates the two equations.
Figure 1.7: Convective heat transfer coefficient as a function of the temperature difference at an interior surface [1.1].
In the case of forced convection, like with a wind-blown exterior wall, the heat transfer coefficient can be specified by
3521 T.hc ∆⋅=
3311 T.hc ∆⋅=
Heat transfer coefficient
hc (W/(m2K))
Temperature difference ∆T
Heat Transfer 21
⋅⋅=
KmWTv.h
..
c 2
7080
2731267
Figure 1.8 shows this graphically and additionally illustrates the influence of the surface roughness.
Fig. 1.8: Convective heat transfer coefficient on exterior surfaces [1.1]
1.2.3 Convection in Cavities
Figure 1.9 shows a narrow, vertical cavity with isothermal sidewalls at different temperatures. The fluid heats up on the warm surface, expands and rises up due to the lower density. On the cold surface it cools down and sinks so that a closed movement results.
Fig. 1.9: Convection in a narrow, vertical cavity (H >> L) with isothermal sidewalls at different temperatures (Th > Tk).
For example, it is of interest in glazings or in solar collector cavities, whether fluid flow is initiated. In these cases the convection increases the thermal losses and, therefore, is not desirable.
We consider the case of narrow, vertical cavity with H >> L. Three dimensionless characteristic values; the Nusselt, Rayleigh and Prandtl numbers; are fundamental to the characterization of the problem:
7080
2731267
..
cTv.h
⋅⋅=
Heat transfer coefficient
hc (W/(m2K))
Wind speed (m/s or km/h)
Heat Transfer 22
)(LhNu −⋅
=λ
)(a
LTgRa −⋅
⋅⋅⋅=
ν∆β 3
)(a
Pr −=ν
h heat transfer coefficient
L cavity width
λ thermal conductivity of fluid
g acceleration of gravity, g = 9.81 m/s2
β volumetric thermal expansion coefficient
∆T temperature difference between the walls
ν kinematic viscosity
a thermal diffusivity
Fig. 1.10: Convection in narrow cavities: Nusselt number as a function of Rayleigh number [1.2].
The heat flux through the cavity, caused by convection and conduction, can be expressed with the Nusselt number as follows:
LTNuq ∆λ ⋅
⋅=
For Nu = 1 the heat transport is only by conduction. Figure 1.10 shows the Nusselt number as a function of the Rayleigh number for Pr = 0.72 (air). The graph shows that the convection is initiated at a critical Rayleigh number Racrit. The inclination of the cavity to the horizontal plane is plotted as a curve parameter.
According to [1.3] for narrow horizontal (C = 0.16, n = 0.28) and vertical (C = 0.035, n = 0.38) cavi-ties the following can be applied:
nRaCNu ⋅=
Heat Transfer 23
1.3 Thermal Radiation
1.3.1 Laws and Characteristics
If heat is transmitted in the form of electromagnetic radiation one speaks of thermal radiation. Eve-ry body with a temperature above absolute zero (T > 0 K) emits thermal radiation. The electromag-netic radiation is classified, for example, as ultraviolet, visible or infrared according to the wave-length (Fig. 1.11). Radiation with a wavelength between 0.38 und 0.78 µm is visible to the human eye.
Fig. 1.11: Electromagnetic spectrum
The correlation between the propagation velocity c (the speed of light), wavelength λ and frequen-cy ν is:
νλ ⋅==ncc 0
c0 denotes the speed of light in a vacuum (c0 = 2.998·108 m/s). The speed of light c is proportion-ately smaller for mediums with a refractive index n > 1 (glass n ≈ 1.5). The frequency is independ-ent of the medium.
Thermal radiation can also be regarded as the flow of photons. A single photon contains the ener-gy
E = h·ν
h denotes Planck’s constant (h = 6.626·10-34 J·s).
When radiation strikes a surface it is either reflected, absorbed or transmitted. The conservation of energy requires that the sum of the reflectance ρ, absorptance α and transmittance τ is equal to 1:
ρ + α + τ = 1
In the case of an opaque (= nontransparent) body (τ = 0) the equation reduces to
ρ + α = 1
For an ideal black body αs = 1 and ρs = 0. That signifies that all of the incident radiation is ab-sorbed. The values ρ, α and τ are particularly dependent on the angle of incidence and the wave-length of the radiation. To exemplify a wavelength dependent reflectance, Fig. 1.12 shows ρ(λ) for different plaster layers. It shows that surfaces that appear white to the human eye must not neces-sarily be highly reflective also for radiation with longer wavelengths.
Heat Transfer 24
Fig. 1.12: Spectral reflectance of different colored plaster-surfaces [1.4]
The surface roughness determines the spatial distribution of the reflected radiation. If the extent of roughness is large in comparison to the wavelength of the radiation, the surface reflects diffuse ra-diation. With reflection for very smooth surfaces the angle of reflection is equal to the incidence angle.
Fig. 1.13: Direct (left) and diffuse reflection (right) on surface
A black body with a temperature T emits energy according to Planck’s law (Max Planck, 1858–1947):
−
⋅⋅
=125
1
)T
Cexp(
Cdqd s
λλλ
C1 = 3.74·10-16 W·m2
C2 = 0.01439 m·K
The wavelength, with which the emitted power spectral density is maximal, can be calculated with Wien’s displacement law (Wilhelm Wien, 1864-1928):
λmax·T = 2.898·10-3 m·K
With Wien’s displacement law and using the surface temperature of the sun (T ≈ 6000 K) one ob-tains λmax = 0.5 µm, and using a room temperature (T ≈ 300 K) a λmax = 10 µm. Figure 1.14 shows the spectral distribution of radiation from black bodies. In addition the points of maximum emission are plotted. Figure 1.15 shows the normalized spectral distribution of radiation from black bodies.
β1 β2 β1
o
Heat Transfer 25
Fig. 1.14: Spectral distribution of radiation from black bodies at different temperatures
Fig. 1.15: Normalized spectral distribution of radiation from black bodies
The total emitted power density from a black surface can be obtained by integration of Planck’s equation:
4
0
Tddqdq s
s ⋅=⋅= ∫∞
=
sλλλ
This equation is named Stefan-Boltzmann law (Josef Stefan, 1835-1893 and Ludwig Boltzmann, 1844-1906). s denotes the Stefan-Boltzmann constant (s = 5.67·10-8 W/(m2K4)). This law states that the power emitted is directly proportional to the fourth power of the surface temperature of a body.
Heat Transfer 26
For gray bodies ε(λ) = constant < 1 applies and it can be written:
4Tqq s ⋅⋅=⋅= sεε
Kirchhoff’s law of thermal radiation (Gustav Robert Kirchhoff, 1824-1887) states, that with a certain wavelength and temperature the emissivity is equal to the absorptance of a body:
α(λ,T) = ε(λ,T)
Fig. 1.16: Spectral emissivities of materials [1.5]
solar IR (T = 300 K)
α (-) τ (-) ε (-) smooth concrete lime-sand brick synthetic plaster, white mineral plaster, gray fir wood untreated brick facing, red aluminum anodized aluminum chrome-plated aluminum with Ni, black Corten steel, raw material Corten steel, weathered float glass 6 mm solar control glass Calorex-A2 (Schott) insulating glass Comfort (Glaverbel) glass with SiO2/Au(10 nm)/SiO2 glass with TiO2/Ag(20 nm)/TiO2 glass with Cu(10 nm)/ SiO2(50 nm)
0.55 0.60 0.36 0.65 0.44 0.54 0.33 0.33 0.87 0.86 0.86 0.12 0.41 0.34 0.32 0.40 0.34
0 0 0 0 0 0 0 0 0 0 0 0.80 0.36 0.54 0.35 0.21 0.36
0.96 0.96 0.97 0.97 0.92 0.93 0.92 0.07 0.10 0.51 0.92 0.91 0.11 0.12 0.10 0.03 0.05
Table 1.2: Solar absorptance α, solar transmittance τ and emissivity ε (T = 300 K) of building materials in the infrared range (IR) [1.6]
Wavelength λ (µm)
Heat Transfer 27
Absorptance and emissivity can be very different for different wavelengths. An example for this are selective absorbers of solar collectors: high absorptance in the wavelength range of solar radiation with λ < 3 µm, low emissivity for thermal radiation with λ > 3 µm. Figure 1.16 shows qualitatively the wavelength dependent emission properties of materials and Table 1.2 gives some numerical values for solar absorptance, solar transmittance and emissivity of building materials.
As an application example, Figure 1.17 shows the radiation balance of a building surface. I and IIR denote the intensities of solar and infrared radiation. In addition, not shown in the figure, energy fluxes occur by thermal conduction in the wall and due to convective losses of the surface to the exterior.
Fig. 1.17: Radiation balance of a building surface
1.3.2 Radiation Exchange between Surfaces
As an example of radiation exchange between surfaces, the case of two planes of infinite length and width will be considered here. The plane surfaces are at temperatures T1 and T2, respectively. It is assumed that both planes are opaque and have wavelength independent emissivities ε1 and ε2, respectively. This situation is similar to those in a glazing cavity or the cavity of a solar collector in the range of infrared radiation. The emitted heat flux E1 from plane number 1 can be calculated as follows:
4111 TE ⋅⋅= sε
Fig. 1.18: Radiative heat transfer between two parallel planes
From this radiative flow a part is absorbed by plane number 2, the remaining part is reflected and strikes plane number 1 and so on. Figure 1.18 shows the back and forth reflected radiation pro-duced due to emission by plane number 1.
The absorbed energy in plane number 2 can be added up as follows:
1212122
21212121221 E....EEEq nn ⋅⋅⋅++⋅⋅⋅+⋅⋅⋅+⋅=→ ρραρραρραα
Ts ε·s·Ts
4
ε·IIR
α·I
Heat Transfer 28
This geometric series can be summarized using the relationship:
xx
n
n
−=⋅∑
∞
= 10
γγ
This leads to:
21
1221 1 ρρ
α⋅−
⋅=→
Eq
Analogous is:
21
2112 1 ρρ
α⋅−
⋅=→
Eq
The net energy flux from plane number 1 to plane number 2 amounts to:
21
2112
21
21
21
12122112 111 ρρ
ααρρ
αρρ
α⋅−
⋅−⋅=
⋅−⋅
−⋅−
⋅=−= →→
EEEEqqq
With the definitions for E1 and E2, respectively, and Kirchhoff’s law
ρ = 1 – α = 1 – ε
it leads to:
( )111
21
42
41
12
−+
−=
εε
s TTq
For the case of black, parallel planes (ε1 = ε2 = 1) it results in:
( )42
4112 TTq −= s
With not too large temperature differences the radiation transport can be approximately linearized:
( )3
212112 2
4
+
⋅=−⋅≈TTKwithTTKq s
K denotes the transport coefficient for radiation.
It can also be described as:
( )111
21
124
24
11212
−+=−⋅=
εε
sCwithTTCq
C12 denotes the so-called radiation exchange factor, which is determined by the geometry and emission characteristics of the surface.
Not always does the total emitted radiation of a body strike another, as in the case of parallel planes. With the so-called view factor or solid angle factor F, the heat flow due to radiation be-tween two surfaces in arbitrary spatial positions to one another can be calculated:
( )42
41
211221
1212112 111
TTFF))((
FAQ −⋅⋅⋅−−−
⋅⋅⋅⋅=
εεεεs
Heat Transfer 29
For the view factor F12 and F21 it gives:
122
121
21221
112
1 2
1
FAAF
dAdAs
coscosA
FA A
⋅=
⋅⋅⋅
π= ∫ ∫
ββ
The view factors contain the spatial geometry and are tabulated for different cases (refer to e.g. [1.7,1.8]). For parallel planes it gives F12 = F21 = 1.
Fig. 1.19: Radiation exchange between two surfaces
1.4 Design Values for the Total Heat Transfer on Surfaces
The specified design values for thermal resistance and heat transfer coefficients in Table 1.3 are suitable for many calculations, especially for verifications according to SIA 180 [1.9] regarding heat and moisture protection. These values include the heat transfer due to convection as well as radia-tion.
application case location thermal resistance R = 1/h
heat transfer coefficient h R = 1/h h
energy calculations interior exterior building element in ground
0.13 (m2K)/W 7.7 W/(m2K) 0.04 (m2K)/W 25 W/(m2K) 0 (m2K)/W
calculation for moisture pro-tection
exterior climate building element in ground interior, top room-half interior, lower room-half windows and doors
0.04 (m2K)/W 25 W/(m2K) 0 (m2K)/W 0.25 (m2K)/W 4 W/(m2K) 0.35 (m2K)/W 2.9 W/(m2K) 0.15 (m2K)/W 6.7 W/(m2K)
Note: The values for the interior sides consider building edges; with covered locations without air circulation, e.g. behind furniture, higher thermal resistances can yet occur.
Table 1.3: Design values for thermal resistances and heat transfer coefficients according to SIA 180 [1.9].
Heat Transfer 30
Literature
[1.1] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[1.2] Duffie, J. A., Beckman, W. A., Solar Engineering of Thermal Processes, John Wiley & Sons, New York, 1991
[1.3] EN 673, Glass in building: Determination of Thermal Transmittance (U value): Calculation Method, European Committee for Standardization, Brussels, 1997
[1.4] Sagelsdorff, R., Frank, T., element 29: Wärmeschutz und Energie im Hochbau, Schweize-rische Ziegelindustrie, Zürich, 1990
[1.5] Hauri, H. H., Zürcher, C., Moderne Bauphysik, Verlag der Fachvereine, Zürich, 1984
[1.6] Zürcher, C., Strahlungsvorgänge an Gebäudeoberflächen (Teil 1), 2. Schweizerisches Sta-tus-Seminar Wärmeschutz-Forschung im Hochbau, Zürich, 1982
[1.7] Siegel, R., Howell, J. R., Lohrengel, J., Wärmeübertragung durch Strahlung (3 Bände), Springer-Verlag, Berlin, 1988
[1.8] VDI-Wärmeatlas, Verlag des Vereins Deutscher Ingenieure, Düsseldorf, 1984
[1.9] SIA Norm 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Architekten-Verein, Zürich, 1999
[1.10] Grigull., U., Sandner, H., Wärmeleitung, Springer-Verlag, Berlin, 1990
[1.11] Merker, G.P., Konvektive Wärmeübertragung, Springer-Verlag, Berlin, 1987
[1.12] Pitts, D. R., Sissom, E. L., Heat Transfer, Schaum's outline series, McGraw-Hill, New York, 1977
Chapter 2
Exterior Climate
Exterior Climate 32
2 Exterior Climate The climatic conditions outside of a building are important in many respects. They influence the re-quired power and energy to heat and cool, but also they basically determine the interior climate, particularly in an unheated or uncooled building. The air exchange that naturally occurs in an inte-rior room will also be influenced by local wind conditions. The amount of daylight that can be used in building interiors depends on the solar radiation supplied. All these topics will be handled in the following sections. The exterior climate additionally causes thermal and hygric loads to the building construction.
The most important climate parameters in building physics are: solar radiation, infrared radiation (atmosphere, environment), temperature, humidity (see Building Physics III) and wind. Weather patterns exhibit basically three different components: yearly and daily periodicity as well as a dis-tinct random component. For building planning one therefore mostly uses weather data based on an average value over many years (e.g. 10 years or more).
In Switzerland, climate data has been systematically recorded since 1864 by the national weather service (Meteoschweiz). In the early 1980s an automatic measuring network (ANETZ), consisting of 72 stations, was put into operation. A large number of weather parameters are measured in 10-minute intervals. The data is compiled into datasets, e.g. available as hourly average values or as monthly average values over many years. Also weather data records from more than 7000 stations all over the world, representing typical years, can be utilized by planners with the commercial data-base software Meteonorm [2.1]. Long-term monthly average values from Swiss climate data are also available in various SIA standards [2.2, 2.3].
In view of the trend in buildings that calls for little operating energy, knowledge of local climatic conditions becomes increasingly significant for building planning. The exterior climate dictates the outer boundary conditions of the building envelope; the intended use, and accordingly the require-ments regarding thermal comfort, determines the inner boundary conditions (see Chapter 3).
2.1 Solar Radiation
2.1.1 Solar Radiation Source
On a human time scale the sun is an inexhaustible energy source. The nuclear fusion processes in its interior take place at extremely high temperatures of approximately 2·107 K. Energy released by these processes is transported through radiation and convection to the outer layers and from there, emitted into outer space. The gaseous surface of the sun can be approximated as a black body with a surface temperature TS of 5760 K. The radiation emitted has the same intensity in all direc-tions (isotropic). The radiative power of the sun can be calculated as follows (Stefan-Boltzmann law):
4S
2SS Tr4P ⋅⋅⋅= sπ
rS designates the sun’s radius and s the Stefan-Boltzmann constant (s = 5.67·10-8 Wm-2·K-4).
Figure 2.1 gives data on the geometry and temperature of the sun and Earth. The diagram is not shown to scale. If the Earth would have the size of a pea, the sun would in proportion be a sphere with a diameter of 1 m. The distance between these two celestial bodies in this model would be 108 m.
With the Earth’s radius rE and a distance from the Earth to the sun R the irradiation on Earth PE can be calculated as follows:
4S2
2E2
SE TRrrP ⋅⋅⋅⋅= sπ
Exterior Climate 33
By means of satellite measurements the average solar irradiance can be determined outside the Earth’s atmosphere. This so-called solar constant is subject to a variation in the range of ± 3% due to the elliptical orbit of the Earth.
Solar constant: I0 = 1367 W/m2
Fig. 2.1: Geometric relationships (not shown to scale) between the sun und Earth
The total extraterrestrial irradiation PE on the Earth is 1.7·1017 W (extraterrestrial = outside the at-mosphere). From this 1.5·1018 kWh solar energy reaches the Earth’s envelope per year. The global energy demand lies many magnitudes below this value (Tab. 2.1). However, it must be added that only about half of this radiation energy strikes the Earth’s surface; only about 30% of the Earth’s surface consists of land and also not all of this remaining surface is available solely for energy utili-zation.
Table 2.2 shows the breakdown of the extraterrestrial irradiation into three different wavelength in-tervals. In terms of energy, just under half of this radiation is visible. Given by the sun’s outer sur-face temperature (T ≈ 5760 K) the maximum irradiance is at a wavelength of about 0.5 µm, i.e. in the visible range (Wien’s displacement law).
Extraterrestrial Solar Energy (kWh/a)
Energy Demand 2004 (kWh/a)
World
Switzerland
1.5·1018
4.1·1013
11·1013
2.4·1011
Tab. 2.1: Extraterrestrial irradiation und energy demand
Ultraviolet Radiation (UV)
Visible Radiation (VIS)
Infrared Radiation (IR)
Wavelength interval 0.30 – 0.38 µm 0.38 – 0.78 µm 0.78 – 3 µm
Percentage of energy 7% 47% 46%
Tab. 2.2: Spectral distribution of extraterrestrial solar radiation
2.1.2 Influence of the Atmosphere
The short-wave radiation that is emitted from the sun, with a wavelength between 0.3 und 3 µm, cannot strike the Earth’s surface unhindered. In the atmosphere the incident radiation is partially scattered (i.e., the photons’ course changes) and partially absorbed (i.e., converted to heat).
rS = 0.695·109 m
rE = 6.37·106 m
Photosphere (T ≈ 5760 K)
Core (T ≈ 2·107 K)
Convection zone (T ≈ 130’000 K)
R = 1.496·1011 m ± 1.7%
Sun
Earth
Exterior Climate 34
Figure 2.2 shows the energy flows of the Earth-atmosphere system. To maintain a steady state, the power emitted from the Earth into space has to be equal to the power the Earth receives from the sun. This radiation exchange determines the prevailing temperature on the Earth’s surface, which is of course of vital importance for life on Earth. Due to the temperature on Earth, the maxi-mum intensity of emitted long-wave radiation occurs at a wavelength of about 10 µm (Wien’s dis-placement law).
Fig. 2.2: Energy flows of the Earth-atmosphere system [2.4]. The solar radiation received is set at 100%. Weather patterns essentially happen in the troposphere, the approximately 10 km thick bot-
tom layer.
The spectral distribution of short-wave solar radiation that reaches the Earth’s surface, in compari-son to long-wave radiation from the atmosphere, is shown in Figure 2.3. The clouds influence the spectral distribution of the long-wave radiation.
Fig. 2.3: Spectral distribution of short-wave solar radiation and long-wave atmospheric counterra-diation [2.5]
The effect of absorption and scattering in the Earth’s atmosphere on the spectral distribution of the solar radiation is shown in Figure 2.4. Ozone (O3), water vapor (H2O) and carbon dioxide (CO2) are the most important atmospheric gases responsible for absorption. Each gas exhibits a charac-teristic absorption band. Depending on the ratio between the wavelength and the size of the scat-
Exterior Climate 35
tered particles (gas molecules or aerosols, i.e. small particles like dust or water droplets), different scattering mechanisms occur. Solar radiation is therefore attenuated due to absorption and scatter-ing by crossing the Earth’s atmosphere.
Fig. 2.4: Spectral distribution of extraterrestrial und terrestrial solar radiation and indications of wavelength dependent attenuation mechanisms in the atmosphere [2.6]
Depending on the path length of the solar radiation in the atmosphere (incidence angle) the solar spectrum will change. In building physics however, if a spectral calculation is needed, a constant solar spectrum will generally be used. A typical spectrum for middle geographic latitudes (Zurich 47°) is given in Table 2.3. The spectrum is discretized into 20 wavelength intervals with the same energy content and is well suited for spectral numerical calculations.
Tab. 2.3: Typical spectral distribution of terrestrial irradiation (AM 2), divided into wavelength inter-vals of equal energy [2.7].
2.1.3 Direct Radiation on Tilted Surfaces
In this chapter the parameters, which determine the incidence angle of solar radiation on a tilted surface on Earth will be presented. All formula are valid for the direct (beam) radiation only – i.e. the radiation that by crossing the Earth’s atmosphere is not scattered – and are based on the rela-tive movement of the Earth and sun i.e. on the spatial geometry [2.8].
Exterior Climate 36
As a reminder, in Figure 2.5 a couple of geometrical relationships are presented. The orbit of the Earth around the sun lies in a plane perpendicular to the plane of the paper. The Earth rotates once every 24 hours around its own axis, which is inclined 23.45° from its plane of orbit. This incli-nation is the cause for the seasons. The geographic latitude φ of a location on the Earth’s surface is the angle between the plane of the equator and a line through this location and the Earth’s cen-ter. The circle of longitude λ, or meridian, passes though both poles. The circle of longitude through the Greenwich observatory in London was set with a value λ = 0°.
Fig. 2.5: Inclination of the Earth’s axis in relation to the plane of orbit and the definition of the longi-tudes and latitudes
In Figure 2.6 an inclined surface is shown, e.g. an exterior wall of a building, and the direct radia-tion that falls on it. The formulas to calculate the position of the sun and the angle of incidence as well as the symbols used are listed below.
Solar declination δ :
)(sin. °
+
⋅⋅=365
n2843604523δ
Equation of time z (refer to Fig. 2.7):
( ) ( ) ( ) ( ) ( ) ( ) )(sin.cos.sin.cos.sin.cos. ht30050t30010t21570t20520t1220t0080z ⋅−⋅−⋅−⋅−⋅−⋅=
whereby 365360nt ⋅=
Incidence angle θ :
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) )(sinsinsincoscoscossinsincos
coscoscoscoscossincossincossinsincos−⋅⋅⋅+⋅⋅⋅⋅+⋅⋅⋅+⋅⋅⋅−⋅⋅=
ωγβδωγβφδωβφδγβφδβφδθ
WW
W
Elevation angle of the sun ϕS:
( ) ( ) ( ) ( ) ( ) ( ) )(coscoscossinsinsin −⋅⋅+⋅= ωφδφδϕS
Azimuth angle of the sun γS:
Exterior Climate 37
( ) ( ) ( )( ) )(
cossincossin −
⋅=
SS ϕ
ωδγ
β Inclination angle of the wall; horizontal = 0°, vertical = 90° ° δ Solar declination, angle of the sun at mid-day over the equator plane -23.45° ≤ δ ≤ 23.45° ° θ Incidence angle in relation to a perpendicular of the wall surface ° λ0 Geographic longitude of the reference meridian (Zurich λ0 = -15°) ° λ Geographic longitude of location (Zürich λ = -8.57°) ° γ Azimuth angle between sun and wall γ = γs - γw ° γw Azimuth angle of the wall; South = 0, East positive, West negative ° γs Azimuth angle of the sun ° φ Geographic latitude of location; -90° ≤ φ ≤ 90° (Zurich φ = 47.38°) ° ω Hour angle; ω = 15⋅(12 - tS); mornings ω > 0; noon ω = 0; afternoon ω < 0 ° ϕS Elevation angle of the sun ° n Day of the year; 1 ≤ n ≤ 365 - tS Solar time; tS = t0+ z + t*( λ0 - λ)/15 with t* = 1 h h t0 Local time h z Time difference, see equation of time h
Fig. 2.6: Definitions of the angles for the calculation of the incidence angle
Figure 2.9 shows the position of the sun (elevation angle ϕS and azimuth angle γS) in the course of a year for an observer in Switzerland (φ = 47° und λ = -8°). The sun reaches its highest position on June 22, the lowest on December 21. In summer the days are longer than the nights, in winter the reverse applies. Twice a year, on March 21 and on September 23, day and night are equally long.
Exterior Climate 38
Fig. 2.7: Equation of time
Fig. 2.8: Projection of the sun’s orbit on a hemisphere for a location at latitude φ
Fig. 2.9: Solar position diagram for φ = 47° and λ = -8° (Switzerland)
For the calculation of a cast shadow (Fig. 2.10), e.g. from a roof overhang or a balcony, the shad-ing angle ε is required:
Elev
atio
n an
gle
ϕ S (°
)
Azimuth angle γS (°)
z (m
in)
Day number n
Equinox (21.3/23.9.) N
W S
Zenith
Summer
Winter φ
Axis of the Earth
Exterior Climate 39
( )( )WS
S
γγϕε−
=cos
tan)tan(
Fig. 2.10: Angle for the calculation of a cast shadow
2.1.4 Global Irradiance
The total irradiance that strikes a particular surface is referred to as the global irradiance:
Global irradiance = Direct (or beam) irradiance + Diffuse irradiance
The global irradiance on a horizontal (Index h) surface is composed of the direct irradiance (Index b = beam), i.e. the radiation that comes directly from the sun, as well as the diffuse irradiance from the sky, i.e. the radiation that is scattered at least once as it passes through the Earth’s atmos-phere. Thus:
Ig,h = Ib,h + Id,h (W/m2)
For the diffuse irradiance it is often assumed that approximately the same amount of energy is ir-radiated from all directions of the sky’s hemisphere (isotropic irradiation).
Solar radiation strikes a surface tilted by an angle β (Fig. 2.11). The global irradiance on a tilted surface Ig (β) is made up of the contribution of the direct irradiance, the diffuse irradiance from the sky and the global irradiance that is reflected off the ground in the direction of the surface. The tilt-ed surface with an angle β faces only one part of the sky. The portion of the hemisphere that the surface faces amounts to (1+cos(β))/2 and is referred to as the view factor or the solid angle factor. The difference to 1 results in (1-cos(β))/2 and equates to the view factor that is formed by the ground. The ground reflection ρ lies mostly in the range from 0.2 to 0.4. With snow cover the ground reflection amounts to about 0.7. The global irradiance on an inclined surface can be calcu-lated as follows:
hghdbg I2
1I2
1II ,,)cos()cos()()( ⋅
−⋅+⋅
++=
βρβββ
For vertical surfaces (β = 90°) it becomes:
hghdvdvg I21I
21II ,,,, ⋅⋅+⋅+= ρ
Exterior Climate 40
Fig. 2.11: Direct and diffuse radiation striking a surface with a tilt angle of β.
Depending on conditions in the atmosphere, particularly the extent of cloud cover, the percentage of diffuse to global irradiance will vary considerably. Figure 2.12 gives typical values for this. On the Swiss Plateau about half of solar energy is irradiated as diffuse radiation in average.
Fig. 2.12: Influence of weather conditions on the global irradiance and the percentage of diffuse ir-radiance
In Figure 2.13 the solar irradiance in the course of a day for different surface orientations is given.
Figures 2.14 und 2.15 show the monthly global irradiation in a year on surfaces with different orien-tations. These values are based on the average values from measurements taken at 16 stations in Germany. The difference between winter and summer is striking. Collectors for active solar sys-tems are often positioned at an angle that approximately corresponds to the latitude of the location. In the northern hemisphere the south facade is especially suitable to passive use of solar energy for heating. In comparison to other facade orientations, the irradiation is high in winter and some-what low (overheating control) in summer. Clearly, the least solar energy is irradiated on the north facade.
β
Direct radiation
Diffuse radiation from the sky
Diffuse radiation from the ground
Exterior Climate 41
Fig. 2.13: Global irradiance on surfaces with different orientations in July (50° northern latitude, big city atmosphere) [2.9]
Fig. 2.14: Global irradiation on southern oriented surfaces with different tilt angles [2.10]
Fig. 2.15: Influence of the orientation of a vertical surface on the irradiated solar energy [2.10]
Exterior Climate 42
Fig. 2.16: Worldwide distribution of global solar irradiation [2.11]
Exterior Climate 43
For different locations on Earth there are major differences in the annual amount of irradiated solar energy (Tab. 2.4, Fig. 2.16). This results in different potentials with regard to solar energy use. However, also in the middle latitudes the irradiated solar energy is sufficient to supply a substantial share of the energy demand in buildings.
Location Irradiation (MJ/m2a) London 3400 Paris 4070 Zurich 4200 Rome 6050 Cairo 7340 Sahara 8460
Tab. 2.4: Annual global irradiation on a horizontal surface for different locations on Earth [2.10]
2.2 Air Temperatures
The air temperature at ground level is the result of the energy flows in the Earth-atmosphere sys-tem (Chap. 1.1.2). Figure 2.17 shows typical values for the air temperature in Zurich according to the time of day and month. The highest temperature is reached in July and the lowest in January. The diurnal cycle exhibits a minimum before sunrise and a maximum in the late afternoon since there is a time delay between maximum solar irradiance and maximum air temperature due to the heat storage capacity of the soil.
Fig. 2.17: Typical air temperature in the course of a day for Zurich in different months [2.5]
A condensed presentation of temperatures at a given location is possible by means of cumulative distributions. The data are thereby added up from the smallest value. The cumulative distribution function typically has an S-shaped curve and indicates over how many hours per year the tempera-ture is lower, respectively higher, than a given value (Fig. 2.18).
Exterior Climate 44
Fig. 2.18: Cumulative distribution of the air temperature for nighttime (A) and daytime (B) [2.12]
In Figure 2.19 the monthly mean values of the air temperature is given for Zurich. In the same fig-ure the monthly irradiation is also plotted. The minima of both values occur at a shift in time due to the heat storage capacity of the soil. With about the same solar irradiance in the months of No-vember and January, the air temperature in January is significantly lower than in November.
Fig. 2.19: Annual variation of solar irradiance and air temperature for Zurich (Weather data from [2.3])
Num
ber o
f hou
rs p
er y
ear w
ith
exte
rior t
empe
ratu
res
belo
w θ
(h)
Num
ber o
f hou
rs p
er y
ear w
ith
exte
rior t
empe
ratu
res
abov
e θ
(h)
Temperature θ (°C)
Exterior Climate 45
2.3 Soil Temperatures
Fig. 2.20 shows the penetration of the seasonal temperature fluctuations in the soil. The annual mean value of the surface temperature is 13°C in this case, which is the very same temperature that occurs at greater depths. Due to the storage capacity of the soil the temperature fluctuations that penetrate the ground are delayed (refer to Chap. 5). Thus, for example, the minimum tempera-ture at a depth of 2 m is reached in the month of March. From March through August heat flows in-to the soil and from September through February the soil’s heat is released into the air (→ temper-ature gradient).
Fig. 2.20: Penetration of temperature fluctuations in the soil
2.4 Wind
The atmospheric air pressure is, in relation to building physics, of secondary importance. The air pressure decreases with increasing altitude. In Zurich the average air pressure is approximately 95'000 Pa; fluctuations occur in a range of about ± 3%. These temporal fluctuations occur very slowly in comparison to fluctuations of the wind-induced pressure.
Fig. 2.21: Wind profile at different surface roughnesses [2.13]
Annual mean temperature
Depth (m)
Tem
pera
ture
(°C
) H
eigh
t z (m
)
Exterior Climate 46
With regard to the air exchange in buildings, local wind conditions matter. Wind is characterized by two parameters, wind direction and wind speed (Figures 2.21 und 2.22). They are subject to local and temporal variations. The wind speed as a function of the height above the ground depends on the surface roughness. To calculate a wind profile the following empirical power law is often used:
α
⋅=
GG z
zvzv )( (m/s)
v denotes the wind velocity, z the height above the ground, vG the wind speed at a reference height zG and α the so-called roughness exponent. For built-up areas α = 0.4 approximately applies and α = 0.16 for open areas (Fig. 2.21).
Fig. 2.22: Wind direction and speed at Zurich-Kloten [2.5]
2.5 Climate Fluctuations and Changes
In addition to daily, yearly and random fluctuations, exterior air temperatures show also a certain variability of annual mean values and, additionally, long-term changes (Fig. 2.23).
0
5
10
15
20
1900 1950 2000 2050
Tem
pera
ture
(°C
)
Jahr
Lugano
Zurich
Davos
1983-2003(K/Decade)
1901-2003(K/Decade)
0.7950.117Lugano0.7950.161Geneva0.7760.143Zurich0.6420.165Davos
Geneva
Fig. 2.23: Measured (1901-2003) [2.14] and predicted [2.15] annual mean air temperatures at four locations in Switzerland [2.16]
The gradual warming of the global climate that arises from greenhouse gas emissions, especially from carbon dioxide, is clearly apparent in temperature measurements collected over a number of
Exterior Climate 47
years. In the 20th century, there was a global temperature increase of 0.6 K and an increase of 1.0 to 1.6K in Switzerland. The temperature increase in the last 30 years was particularly pronounced and larger than what was predicted by all climate models. A global temperature increase from 1.4 to 5.8 is expected in the 21st century [2.15]. The degree of the predicted increase varies with each scenario (assumed greenhouse gas emissions) and applied climate model.
Considering the long service life of buildings, in Switzerland typically 80 years, the buildings that we construct today must therefore also function some day in a warmer climate. With higher exterior temperatures, thermal protection in summertime calls for greater attention.
2.6 Impacts on the Building Envelope
2.6.1 External Heat Transfer Coefficient
The thermal interaction between the external surface of the building envelope and the outside envi-ronment depends on both heat transport mechanisms, infrared radiation and convection. The con-vective heat transfer coefficient increases relatively strongly with increasing air velocity. The follow-ing approximate formula can be used:
7080
2731267
..
cTv.h
⋅⋅= (W/m2K)
v Air velocity m/s
T Temperature K
As a function of temperature and emissivity, both the building surface and the environment (ground, neighboring buildings, trees, atmosphere) emit infrared radiation. Under cloudy skies and with fog the radiation temperature of the atmosphere corresponds somewhat to the outside air temperature in the vicinity of the building. The total infrared radiation exchange with the environ-ment can be characterized approximately by a radiative heat transfer coefficient from about 4 to 5 W/m2K.
The following value for the total external heat transfer coefficient applies for heat transmission cal-culations (Chapters 4 und 9, U-value, energy demand) [2.2]:
he = 25 W/m2K (with Re = 1/he = 0.04 m2K/W)
This value contains both the convective and the radiative heat transfer and is based on a con-servative assumption. The external heat transfer coefficient is probably slightly overestimated and thereby also the heat loss through the building element (note: with modern well insulated building elements, the influence of he on the U-value is however very small).
For building elements below ground it is assumed [2.2]: Re = 0.
2.6.2 Surface Temperature Reduction Due to Infrared Radiation
During a night with a cloudless sky a building surface is in a radiation exchange with higher and therefore colder air layers than during a night with an overcast sky. This is because the atmos-phere becomes partially permeable to infrared radiation with wavelengths of about 10 µm and ra-diates back significantly less than what the air temperature in the building vicinity corresponds to (Fig. 2.3). As a result the building surface loses additional heat due to infrared radiation (Fig. 2.24). With good thermal insulation, the heat flow through the wall or glazing is very limited and on a cloudless night the external surface temperature can drop a few Kelvin below the outside tempera-ture. If the dew point temperature is reached, condensation occurs on the external surface. Partic-ularly with well-insulated glazings, this external surface condensation can be observed sometimes
Exterior Climate 48
on a morning after a cold cloudless night. But also with well-insulated facades and roofs this effect arises (→ algae, fungi). If the surface temperature falls below 0°C, frost can even form.
Fig. 2.24: Lowering of the external surface temperature θse on a cloudless night due to increased infrared radiative losses IRq∆ to the sky.
2.6.3 Service Life of Exterior Building Elements
The solar irradiation on a building envelope, also on the Swiss Plateau, can cause quite consider-able variations in the surface temperatures:
— summer: ca. +15°C (night) to +80°C (day, high solar irradiance)
— winter: ca. -10°C (night) to +20°C (day)
The color of the building external surface also plays a strong role in determining the occurring tem-perature, due to the different absorptances for solar radiation (Fig. 2.25).
Fig. 2.25: Influence of the facade color on the occurring surface temperature with solar irradiation
These daily temperature fluctuations — in combination with exposure to water, air contaminants (corrosion), wind and ultraviolet radiation — greatly stress the exterior elements of the building en-velope and thus limit its service life (Tab. 2.5)
θi θsi
θse θe
interior exterior
Overcast night sky
θi θsi
θse θe
interior exterior
∆qIR
Cloudless night sky
.
Exterior Climate 49
Service life (year) paint plaster window metal facade brick facing concrete
5 - 10 30 - 50 20 - 25 ca. 20 20 - 100 30 - 100
Tab. 2.5: Service life of exterior building elements [2.9]
Problems
Problem 1: Shading on a Window
A window is set into a Southwest orientated facade with a recess of 20 cm. What percentage of the window with the dimensions 1.4 m x 1.4 m will be in shade from the wall protrusion in summer (June 23) at 15.30 h (standard time)? What other objects can cast a shadow on a building façade? Name some examples.
Problem 2: Wind Velocity und Solar Irradiance on a High-Rise Building
In Zurich a high-rise building is planned for with a square footprint, a side length s = 30 m and a height h = 120 m with 40 stories each having 900 m2 floor area.
a.) What wind speed can be expected at a height z2 at the top floor, if at a height z1 = 10 m a ve-locity of v1 = 50 km/h is measured? Use the power law below to describe the wind velocity pro-file for your assessment und take a large surface roughness (α = 0.4).
α
⋅=
1
212 z
zvv
b.) How much solar energy will be irradiated on the building envelope – façades N/E/S/W and hor-izontal roof – per year (MJ/a)? Use the weather data for the city of Zurich (see Appendix).
c.) Apply the results from b.) to obtain the irradiated solar energy per square meter floor area.
d.) Assume that a similar building is planned for in the vicinity, in which however the side lengths, height and number of floors n are modified by a factor γ. How do the results for this building differ from those in problem c.)?
Literature [2.1] Meteonorm 6.0 (Edition 2007), Datenbanksoftware, Meteotest, Bern;
http://www.meteonorm.com [2.2] SIA 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Archi-
tekten-Verein, Zürich, 1999 [2.3] SIA 381/2, Klimadaten zu Empfehlung 380/1 «Energie im Hochbau», Schweizerischer In-
genieur- und Architekten-Verein, Zürich, 1991
[2.4] Volz A., Studie über die Auswirkungen von Kohlendioxid-Emissionen auf das Klima, Bericht der KFA Jülich Nr. 1877, 1983
Exterior Climate 50
[2.5] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[2.6] Iqbal M., An Introduction to Solar Radiation, Academic Press, Toronto, 1983
[2.7] Wiebelt J.A., Henderson J.B., Selected Ordinates for Total Solar Radiation Property Eval-uation from Spectral Data, Trans. of the ASME, J. of Heat Transfer, 101(101), 1979
[2.8] Duffie J.A., Beckman W.A., Solar Engineering of Thermal Processes, John Wiley & Sons, New York, 1991
[2.9] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006
[2.10] Goetzberger A., Wittwer V., Sonnenenergie: Thermische Nutzung, Teubner, Stuttgart, 1989
[2.11] Energieatlas GmbH, CH-4142 Münchenstein, 2005; Datenquelle: Meteonorm 4.0, Meteo-test, Bern
[2.12] Baumgartner T., Steinemann U., Geiger W., Meteodaten für die Haustechnik, SIA Doku-mentation D012, 1987
[2.13] Moor H., Physikalische Grundlagen der Gebäudeaerodynamik im Hinblick auf die Berech-nung des Luftaustausches, EMPA Dübendorf, 1987
[2.14] Begert M., Seiz G., Schlegel T., Musa M., Baudraz G., Moesch M., Homogenization of measured time series of climatic parameters in Switzerland and computation of norm val-ues 1961-1990. Final project report NORM90, MeteoSwiss, Zurich, 2003
[2.15] Intergovernmental Panel on Climate Change: http://www.ipcc.ch. Retrieved October 2004.
[2.16] Christenson M., Manz H., Gyalistras D., Climate warming impact on degree-days and build-ing energy demand in Switzerland, Energy Conversion and Management, Vol. 47, 2006, 671-686
Chapter 3
Thermal Comfort
Figure: Infrared Image of a Person
„high“ temperature
„low“ temperature
Thermal Comfort 52
3 Thermal Comfort Whether a person feels comfortable in an indoor environment depends not only on the thermal conditions of the room, but also on the air quality, the acoustics (noise level, reverberation, etc.), visual (availability of natural light, glare, etc.) and additional factors (occupancy rate, furnishings, aesthetics, etc.). The thermal comfort is however an important aspect of total comfort.
People in indoor environments are connected thermally with the building structure. The heat transport processes between a human and the room, as well as the conditions with which people feel satisfied with their sensation to heat, shall thus be presented in the following. Thermal comfort is on the one hand determined by the building envelope, and on the other hand by the HVAC facili-ties. The mechanical equipment can be regarded as supplementary measures to balance out the inadequacy of the building envelope. Because the operation of the mechanical equipment requires energy, the goal must be to design the building envelope to guarantee good comfort with as little mechanical equipment as possible. From this point of view the resulting requirements on the build-ing envelope shall be introduced.
3.1 Human and Interior Space
Since a person is a source of heat in an indoor environment, the air in the immediate vicinity of the human body will be heated. The air consequently expands and a buoyancy flow arises that envel-ops the person. About 60 to 100 m3/h of air is transported above from below. The boundary layer of the rising air (Fig. 3.1) has a thickness of approximately 10 to 15 cm. Comparable updrafts also arise from other heat sources in the room, as for example from a radiator, a computer or a lamp.
Fig. 3.1: Temperature- und air velocity profile at a warm surface
Fig. 3.2: Convective und radiative heat flows between a human and a room
Downdraft
Buoyancy flow
Radiation exchange
Distance x
Temperature θ
Velocity v
Heat flow
Boundary layer
Thermal Comfort 53
At cold surfaces, especially windows in winter, downdrafts (cold sinking air) develop. Humans in an interior find themselves in a “landscape” of boundary layer currents that they themselves influence. These “landscapes” can also be influenced naturally by the momentum of the entering air current; from air inlets of mechanical ventilation systems or from open windows. Additionally, radiative heat exchange takes place between a person and the environment (Fig. 3.2). With an interior tempera-ture of T ≈ 300 K, this radiation exchange occurs in the infrared region with a maximum intensity at a wavelength of about 10 µm (Wien’s displacement law).
3.2 Heat Balance of Humans
Humans belong to the organisms that maintain a constant internal body temperature also with changing temperature in the environment. This results from the body’s own thermoregulatory sys-tem. The so-called core body temperature is about 37°C. The body exterior is subject to large tem-perature variations. Figure 3.3 shows the temperature distribution in the human body.
Fig. 3.3: Temperature distribution in the human body with different ambient conditions [3.1]
The food that humans ingest contains energy that is converted into heat by a biochemical process. This exothermic reaction in the human body is often referred to as metabolism. The rate of this heat production in the human body is notably dependent on the level of physical activity. Table 3.1 shows the metabolic rate in relation to the activity. An adult can, e.g. during a foot race, reach a temporary metabolic rate of more than 800 Watt. The unit met serves as a description of the de-gree of activity (1 met = 58 W/m2 = 104 W/Person = seated, relaxed).
The average heat flux through the body surface of a relaxed seated person is given as:
22 mW58
m81W104
AQq ===
.
The heat flux varies depending on the body part [3.2]:
— head: ca. 115 W/m2 — hand: ca. 75 W/m2 — foot-sole: up to 145 W/m2
Thermal Comfort 54
As already mentioned above, the temperature in the internal body must be kept at a constant tem-perature. It thus follows that the sum of the heat output and enthalpy flow plus the mechanical out-put must be equal to the metabolic output (conservation of energy):
Metabolic output = Heat- and enthalpy flow + Mechanical output
This energy flow balance – somewhat dramatized – could also be called the “equation of life and death”. The mechanical output is generally small in comparison with the other values and can be neglected for the usual indoor activities. The heat flow is a combination of the heat loss of the body through convection to the ambient air, plus a contribution produced through the infrared radiation exchange between a person and the enclosing surfaces (walls including windows, floors and ceil-ings). There where the body is in direct contact with the surroundings e.g. on the floor or if the legs, seat or back are in contact with a chair, the heat can additionally flow by conduction. Enthalpy flow occurs because the evaporation of sweat extracts body heat. The exhalation of moist breath also adds to enthalpy flow (Figures 3.4 und 3.5).
With high ambient temperatures (e.g. in a sauna) or with strong physical labor, not enough energy can be lead away by radiation and convection. Under these conditions heat must be given off pri-marily by evaporation of water (Fig. 3.6); assuming that the air moisture is not too high.
Activity Metabolic rates
met W/m2* W/Person**
Reclining, asleep 0.8 46 83 Seated, relaxed 1.0 58 104 Sedentary activity (office, dwelling, school, laboratory) 1.2 70 126 Standing, relaxed 1.2 70 126 Light activity, standing (shopping, light industry, laboratory) 1.6 93 167 Medium activity, standing (domestic work, machine work) 2.0 116 209 Walking (4 km/h) 2.8 162 292 Heavy activity (heavy industry) 3.0 174 313 Walking (5 km/h) 3.4 197 354 Running (10 km/h) 8.0 464 834 * based on the body surface area ** valid for one person of 1.8 m2 body-surface area (e.g. height 1.7 m, weight 69 kg)
Table 3.1: Heat production with different activities [3.3]
Fig. 3.4: Heat loss from the skin due to radiation, convection, and evaporation [3.1]
Thermal Comfort 55
Fig. 3.5: The heat loss mechanisms of a partially clothed body [3.4]
Fig. 3.6: Heat loss with different ambient temperatures [3.4]
Type of Clothing clo m2K/W
Naked, standing 0.0 0.0 Underpants, bathing suit 0.1 0.015 Typical tropical clothing: underpants, shirt/blouse with short sleeves and open col-lar, shorts, light socks and sandals
0.3 0.045
Light summer clothing: underpants, shirt/blouse with short sleeves and open col-lar, light-weight trousers or skirt, light socks and shoes
0.5 0.08
Light work clothing: underwear, shirt/blouse with short sleeves and open collar, work trousers, socks and shoes
0.7 0.11
House clothing in winter: underwear, shirt/blouse with long sleeves, sweater with long sleeves, trousers or skirt, thick socks and shoes
1.0 0.155
Traditional winter clothing: long-underwear, shirt with long sleeves, suit with trou-sers, jacket and vest or dress, thick socks and shoes
1.5 0.23
Warm winter clothing 3.0 0.45
Table 3.2: Thermal resistances of different clothing ensembles [3.3]
Thermal Comfort 56
Clothing acts as a resistance to both the heat flow and the vapor diffusion flow. The thermal insula-tion values of different clothing ensembles are shown in Table 3.2. A typical clothing ensemble in winter for an interior space is designated as 1 clo, the abbreviation for “cloth”.
Mass 70 kg Volume 70 dm3 Surface area 1.8 m2 Core body temperature 37°C Skin temperature 34°C Inhaled airflow rate 0.5 m3/h Breath rate 16 min-1 Pulse 60 - 80 min-1 H2O-Production 40 g/h CO2-Production 15 - 20 l/min
Table 3.3: Data on the human body
3.3 Requirements for Thermal Comfort
The requirements for thermal comfort, and respectively a persons discomfort in a room, can be di-vided into two areas of influence:
Influence of the room:
— air temperature — surface temperatures of the enclosing areas — air movement (velocity, turbulence intensity, direction) — relative air humidity
Influence of people:
— physical activity (heat production) — clothing (thermal insulation) — physiological condition
Not everyone is sensitive to the same things in the same way. All predictions are therefore statisti-cal. The room conditions that apply as optimal are those that feel comfortable for most of the occu-pants. In the SIA standard 180 [3.3] it is stipulated that 80% of the occupants, provided that they are engaged in normal activity and dressed appropriately for the season, should find the room conditions comfortable. A PPD index establishes a Predicted Percentage of Dissatisfied [3.5]. The SIA standard 180 thereby requires a PPD < 20%. As an approximation, the perceived room temperature, which is designated as the operative room temperature θo, can be calculated as the mean air temperature θa plus the mean radiant tempera-ture rθ , where rθ is assumed as the mean surface temperature of the enclosures (walls, ceiling and floor):
2ra
oθθθ +
= where ∑∑ =
=
⋅⋅=tot
tot
k
1kskkk
1kk
r AA
1 θθ (°C)
Ak area of the k-th enclosure surface m2
θsk temperature of the k-th surface area °C
Thermal Comfort 57
From this relationship it follows that e.g. lower surface temperatures can be compensated by high-er air temperatures. The temperature difference should however not be larger than about 1.5 to 3 K [3.6].
In Figure 3.7 the optimal room temperature as a function of physical activity and clothing can be determined. So, for example, with a sedentary activity and normal daily wear clothing in winter the optimal room temperature θo is at 21.5°C with a tolerance range of ± 2°C. Figure 3.7 also gives the temperature tolerance, within which a PPD < 10% applies. According to [3.3] only a PPD < 20% is required, therefore a range is included in Figure 3.7 to account for comfort losses not covered. In the following chapter these additional comfort parameters will be discussed in greater detail. In Ta-ble 3.4 the comfort requirements specified in [3.3] are displayed.
Fig. 3.7: Optimal operative temperature θo as a function of activity and clothing [2.3]. The shaded areas indicate the temperature range inside which the condition PPD < 10% is fulfilled.
Parameter Winter (clothing 1 clo and activity 1.2 met)
Summer (clothing 0.5 clo and activity 1.2 met)
- room temperature 19°C – 24°C 23.5°C – 26.5°C - air temperature difference (0.1 m to 1.1 m above floor)
< 3 K < 3 K
- floor temperature 19°C – 26°C n/a - max. asymmetry of radiant temperature
- heated ceiling 4 K - cold walls 10 K - warm walls 20 K
- cold walls 10 K - cold ceiling 13 K - warm ceiling 5 K
- air velocity < 0.15 m/s < 0.2 m/s
Table 3.4: Comfort requirements according to [3.3]
Spec
ific
met
abol
ic ra
te (m
et)
Thermal resistance of clothing (clo)
Thermal Comfort 58
3.4 Detailed Comfort Analysis
Based on numerous experiments on subjects, P. Ole Fanger (1934-2006) [3.5, 3.7, 3.8, 3.9, 3.10] developed a model that can predict the thermal comfort of people under the application of physical and physiological quantities, in indoor environments with a moderate climate. Based on a global, steady-state energy balance of the human body, refer to Chapter 3.2, an average vote PMV (Pre-dicted Mean Vote) can thereby be predicted. The predicted percentage of dissatisfied PPD is then treated as a function of the average PMV value. That is, the PMV- and PPD-Indexes describe the hot and cold discomfort of the whole body.
Discomfort can however also result from unwanted cooling or heating of one particular part of the body. One then speaks about local discomfort. Causes for this can be drafts, radiant temperature asymmetry, or high or low floor surface temperatures.
3.4.1 Global Comfort Criteria The predicted mean vote PMV [3.5, 3.7] is dependent on both the influences of the environment (air temperature and surface temperatures, air movement and humidity) and on the person (physi-cal activity, clothing). The PMV is an index that predicts, with the help of a 7-point thermal sensa-tion scale, the mean value of the votes of a large group of persons (Table 3.5).
PMV -3 -2 -1 0 +1 +2 +3
Assessment cold cool slightly cool
neutral slightly warm
warm hot
Table 3.5: Thermal sensation scale after Fanger [3.5]
The predicted mean vote PMV is given by the equation [3.5]:
( ) ( )[ ][ ] ( ) ( )
( )[ ( ) ( )aclccl4
r4
cl
cl8
a5
3M0360
hf273273
f1096334M00140p5867M10711558WM420
pWM996573310053WM0280e3030PMV
θθθθ
θ
−−+−+⋅
⋅−−−−⋅−−−⋅−
−−−⋅⋅−−+⋅=−−
−−
.....
.... .
M metabolic rate, per square meter of body surface area W/m2 W external work (typically W = 0), per square meter of body surface area W/m2 Rcl thermal resistance of clothing m2K/W θa air temperature °C
rθ mean radiant temperature °C p partial water vapor pressure Pa Surface temperature of clothing:
( ) ( ) ( )[ ] ( )aclcclrclclclcl hff.RWM.. θθθθθ −++−+⋅⋅−−−= − 448 273273109630280735 (°C)
Convective heat transfer coefficient:
( )
−= v112382h 250
aclc .,.max .θθ (W/m2K)
v relative air velocity m/s
Ratio of person’s surface area while clothed to while nude:
Thermal Comfort 59
>⋅+
<⋅+=
W/Km.Rfür,R..W/Km.Rfür,R..
fclcl
clclcl 2
2
0780645005107802901001
Mean radiant temperature:
∑=
⋅=totk
1kskPkr F θθ (°C) where ∑
=
=totk
1kPk 1F
FPk radiant view factor between a person P and the surface k - θsk temperature of the k-th surface °C The radiation exchange between a person and the environment is better described with respect to the spatial geometry by means of the view factor (solid angle) than with the mean value of the sur-face temperatures of the enclosing surfaces. Figure 3.8 presents diagrams to determine the view factor FPk between a person and the surrounding surfaces.
Fig. 3.8: View factor between a seated person and a rectangular surface [3.7]
Thermal Comfort 60
The predicted percentage of dissatisfied can be calculated by an empirical formula [3.5]:
( )24 PMV21790PMV033530e95100PPD ⋅+⋅−⋅−= ..
This equation is shown graphically in Figure 3.9. It should be noted that even under optimal envi-ronmental conditions 5% of the people will still be dissatisfied.
Fig. 3.9: Predicted percentage of dissatisfied PPD in relation to the predicted mean vote PMV [3.5]
3.4.2 Local Comfort Criteria
Local discomfort can occur from the following:
— air movement — asymmetrical radiant fluxes — floor temperature
3.4.2.1 Draft
Draft is an unwanted local cooling of the human body by air movement. In addition to air tempera-ture and velocity, the turbulence intensity also influences the sensation to draft. The greater the air velocity is as well as its fluctuations (turbulence), the higher is the convective heat transfer coeffi-cient and with that, the cooling effect of the air on the skin.
The predicted percentage of dissatisfied with respect to draft, i.e., the Draft Rating DR can be cal-culated as follows [3.3, 3.5]:
( ) ( ) ( )143Tuv370050v34DR 620a ... . +⋅⋅⋅−⋅−= θ (%)
if v < 0.05 m/s, then v = 0.05 m/s
if DR > 100%, then DR = 100%
Thermal Comfort 61
Tu local turbulence intensity, ratio of the standard deviation of the local air velocity to the local mean air velocity %
The model to calculate the draft rating is based on studies comprising 150 subjects exposed to air temperatures of 20°C to 26°C, mean air velocities of 0.05 m/s to 0.4 m/s and turbulence intensities of 0% to 70%. The model applies to people performing light, mainly sedentary activity, with a ther-mal sensation for the whole body close to neutral (Fig. 3.10).
In different studies it was also shown that the exposure time, the extent of physical activity as well as the direction of airflow, was significant to the sensation to draft [3.11, 3.12, 3.13, 3.14]. These factors were however not considered in the model described above.
Fig. 3.10: Combination of air velocity and turbulence intensity with a DR < 20% [3.3]
3.4.2.2 Radiant Temperature Asymmetry
An asymmetrical radiation exchange between a person and the environment e.g. caused by cold or warm window surfaces or a heated ceiling, and accordingly a cooled ceiling, can cause discomfort, also if the global energy balance corresponds to a comfortable state.
The asymmetry of the radiant fluxes can be described by the difference of the mean surface tem-peratures of both half spaces:
)( C2r1rr °−= θθθ∆
1rθ Mean surface temperature of half space 1 °C
2rθ Mean surface temperature of half space 2 °C
Figure 3.11 shows the influence of the radiant temperature asymmetry rθ∆ on the satisfaction.
3.4.2.3 Floor Temperature
Too low or too high floor temperatures can also cause local discomfort (Fig. 3.12).
Thermal Comfort 62
Fig. 3.11: Predicted percentage of dissatisfied with radiant temperature asymmetry [3.8]
Fig. 3.12: Influence of the floor temperature on the predicted percentage of dissatisfied with normal shoes for seated and standing persons [3.4]
3.5 Cold downdraft
A cold downdraft occurs at vertical surfaces especially at window glazings in winter because the thermal resistance of the building envelope – and the resulting internal surface temperature – is in general considerably smaller here than on the neighboring opaque elements. This descending air-flow (Fig. 3.13) can cause discomfort. The maximum air velocity as a function of the distance x from the cold vertical surface can be approximated by the following empirical formula determined with an air temperature of 20°C [3.15, 3.16, 3.17]:
H0830v ⋅= θ∆.max x < 0.4 m
H321x
1430v ⋅+
= θ∆.
.max 0.4 m ≤ x ≤ 2 m
H0430v ⋅= θ∆.max x > 2 m
x distance from the cold surface m ∆θ temperature difference between the air and cold surface K H height of the cold surface m
Thermal Comfort 63
The maximum air velocity at the bottom of the cold vertical surface is usually less notable than the maximum velocity in the habitation area (x ≥ 1 m). The temperature difference between the air and the cold surface amounts to
( )eiih
U θθθ∆ −=
Should a specific air velocity not be exceeded for comfort reasons, e.g. vmax < 0.15 m/s, a required thermal transmittance value U can be determined for a given value of glazing height H, distance x, internal heat transfer coefficient hi and interior and exterior temperature, θi and θe. Low thermal transmittance values are not only advantageous from an energy point of view, but they also have a positive effect on thermal comfort due to the small temperature difference between the air and in-ternal surfaces of the building envelope.
Fig. 3.13: Cold downdraft from vertical surfaces
Fig. 3.14: Maximum air velocity from cold downdrafts as a function of distance, temperature differ-ence and height
H
x
Thermal Comfort 64
3.6 Comfort Measurements
With comfort measuring instruments relevant quantities in buildings can be determined by meas-urements. Complaints can be evaluated relatively quickly and objectively as to whether an ade-quate thermal comfort is provided for, or not. Figure 3.15 shows such an instrument with sensors to measure the air temperature, air velocity and turbulence intensity, air humidity as well as the asymmetry of the radiant temperature. The sensor to measure the surface temperature is not shown in this photo. By applying a software as well as the Fanger formulae to the measured data, the PMV, PPD und DR values can be determined.
Fig. 3.15: Sensors for comfort assessments mounted on a tripod
3.7 Adaptive Comfort
Humans have the ability to adapt to the changes in their thermal surroundings in order to reduce a possible discomfort. This can result not only by changing the clothing and the physical activity, but also from cold or hot food and drinks as well as air movement (fan). Recent studies indicate that this ability to adapt plays a role in the sensation of comfort.
Fig. 3.16: Acceptable operative room temperature in naturally ventilated rooms [3.19]
air temperature
air velocity and turbulence intensity
asymmetry of radiant temperature
air humidity
Thermal Comfort 65
Models for adaptive comfort are often based on the assumption that weather conditions co-determine the sensation of comfort [3.18]. Thus the higher the operative room temperature that is still felt as comfortable, the higher is the average outdoor air temperature (Fig. 3.16). For user sat-isfaction, it is mostly beneficial to give the user the possibility to set the interior room climate them-selves, within fixed constraints, e.g. to allow one to open the windows in summer. Surveys have shown that using this approach a larger range of operative room temperature is still accepted. Thereby the potential costs of the HVAC system and the energy use in a building is reduced.
3.8 Implications
To assure good thermal comfort, the following goals should be aimed for:
— appropriate, average air temperature (winter ca. 19°C to 24°C, summer ca. 23.5°C to 26.5°C, max. 28°C) and minor levels of temperature stratifications
— balanced, comfortable surface temperature (minor radiant temperature asymmetry) — low air velocities (v < 0.15 m/s) und low turbulence intensities
With mechanical ventilation or in air-conditioned rooms, the positioning and the properties of the air supplies as well as the supply air conditions (temperature, velocity, turbulence intensity) are partic-ularly significant for the thermal comfort.
The goal must however be that the building is designed so that as little mechanical equipment measures as possible are required. With respect to thermal comfort it is imperative to aim for:
1. a very well and uniformly insulated building envelope 2. a high airtightness of the building envelope
In addition to the advantages of a simple HVAC system, a well-insulated and airtight building enve-lope brings about the most important secondary effect; that much less energy is required to keep the building comfortable (Chapter 9).
Problems
Problem 1: Human Sensation of Heat and the Influence of Clothing
Under normal conditions a relaxed seated person produces a thermal output of about 104 W. With a body surface area of about 1.8 m2 this amounts to a heat flow density q = 58.0 W/m2 = 1.0 met (Table 3.1). The core temperature of the body is at 37°C, the skin surface temperature is at 34°C.
a) Therefore, how large is the thermal resistance between the body core and skin surface?
b) The heat transfer coefficient of the clothing surface to the surroundings amounts to h = 10 W/m2K. How large is the corresponding heat transfer resistance?
c) The ambient temperature is at 15°C. How large must the total resistance between the body core and the surroundings therefore be, so that the upper given value of the heat flux density is not exceeded?
d) How large must the resistance of the clothing be, in order to reach this value?
e) Which clothing, with respect to the amount of "clo's", does this correspond to?
Problem 2: Optimal Room Temperature in a Laboratory
The workers in a laboratory wear clothes that correspond to „house clothing in winter“, with respect to thermal insulation. One can assume that standing „light activity“ is performed. How large is the optimal room temperature as well as the tolerance range of room temperature, within which the condition PPD < 10 % is fulfilled?
Thermal Comfort 66
Problem 3: Cold Air Downdraft near Windows
A full-height window in a room (H = 2.2 m) shall be designed so that in winter (θe = -5°C und θi = 20°C) no heating device (e.g. radiator) is required to limit the cold air downdraft, i.e. at a distance of 1 m from the window the air velocity should not be larger than 0.15 m/s. The heat transfer coeffi-cient on the internal side is 7.7 W/m2K. Determine the required thermal transmittance U for the window.
Problem 4: Optimal Room Temperature in a Thermal Bath and a Fitness Room In a resting room of a thermal bath the people typically wear a bathing suit with a bathrobe (thermal insulation about 0.04 m2K/W). The physical activity can be taken as “seated, relaxed”. In the adjacent fitness room the room temperature is set at 24°C. The people give off – based on their physical activity – on the average about 300 W and wear clothes that approximately corre-sponds to 0.4 clo. a.) What room temperature is optimal for the resting room of the thermal bath? b.) What range of room temperature would you recommend for the resting room? c.) What optimal room temperature would you recommend for the fitness room? d.) Which climate assessment (too cold/neutral/too warm) do you expect from the majority of us-
ers of the fitness room? e.) Which heat dissipation mechanism does the body of the fitness room user react with in this
situation?
Literature
[3.1] Silbernagel S., Despopoulos A., Taschenatlas der Physiologie, Georg Thieme Verlag Stutt-gart, 1983
[3.2] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006
[3.3] SIA 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Archi-tekten-Verein, Zürich, 1999
[3.4] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[3.5] EN ISO 7730, Ergonomie der thermischen Umgebung, Europäisches Komitee für Normung, Brüssel, 2005
[3.6] Willems W.M., Schild K., Dinter S., Vieweg Handbuch Bauphysik: Teil 1, Vieweg & Sohn Verlag, Wiesbaden, 2006
[3.7] Fanger P.O., Thermal Comfort, Danish Technical Press, Copenhagen, 1970
[3.8] Fanger P.O., Radiation and Discomfort, ASHRAE Journal, 28(2), 33-34, 1986
[3.9] Fanger P.O., Melikov A.K., Hanzawa H. and Ring J., Air Turbulence and Sensation of Draught, Energy and Buildings, 12, 21-39,1988
[3.10] Fanger P.O., Melikov A.K., Hanzawa H. and Ring J., Turbulence and Draft, ASHRAE Jour-nal, 31(4), 18-25, 1989
[3.11] Griefhahn B., Assessment of draught at workplaces, Fb 828, Dortmund, Schriftenreihe der Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, 1999
[3.12] Toftum J., Zhou G., Melikov A., Air flow direction and human sensitivity to draught, In: Proc. of CLIMA 2000, Brussels, 1997
Thermal Comfort 67
[3.13] Toftum J., Nielsen R., Draught sensitivity is influenced by general thermal sensation, Inter-national Journal of Industrial Ergonomics, 1996, 18(4), 295-305
[3.14] Toftum J., Nielsen R., Impact of metabolic rate on human response to air movements dur-ing work in cool environments, Int. J. of Industrial Ergonomics, 1996, 18(4), 307-316
[3.15] Heiselberg P., Draught risk from cold vertical surfaces, Building and Environment, 1994, 29(3), 297-301
[3.16] Heiselberg P., Overby H., Bjorn E., Energy-efficient measures to avoid downdraft from large glazed façades, ASHRAE Transactions, 1995, 1127-1135
[3.17] Manz H., Frank T., Analysis of thermal comfort near cold vertical surfaces by means of computational fluid dynamics, Indoor and Built Environment, 13 (3), 2004, 233-242
[3.18] ASHRAE Fundamentals Handbook, Chapter 8: Thermal Comfort, American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE), 2001
[3.19] ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy, Ameri-can Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE), 2004
Chapter 4
Steady-State Thermal Transmission
Steady-State Thermal Transmission 70
4 Steady-State Thermal Transmission In this chapter the heat flow through a building wall, floor or roof with constant boundary conditions with respect to time will be handled. The heat transmission is in this case referred to as steady-state. Non-steady-state thermal transmission will be presented in chapter 5. Both states of trans-mission are characterized in Table 4.1.
temperature difference heat flow thermal condition
steady-state constant constant flow equilibrium
non-steady-state not constant not constant time-varying
Tab. 4.1: Characteristics of „steady-state“ and „non-steady-state“
4.1 Standard Cross Section
The heat flow through a wall, floor or roof structure is determined by the thermal resistances of the individual material layers, the heat transfer resistance between the wall surfaces and the interior and exterior air, as well as the temperature difference between the interior and exterior.
In a steady-state condition thermal conductivity is the material quantity that dictates the heat flow in the material. Figure 4.1 gives the thermal conductivity of different materials plotted against their density (cp. Appendix).
Fig. 4.1: Thermal conductivity λ plotted against density [4.1]
The heat transfer coefficient h between the wall surface and the air is comprised of contributions from both radiation and convection (cp. chapter 1):
h = hr + hc (W/(m2·K))
Steady-State Thermal Transmission 71
Values for the heat transfer coefficient h are given in chapter 1.4. Figure 4.2 shows the resistance to the heat flow when crossing through an exterior wall. In this figure an analogy to electrical engi-neering is shown that illustrates a thermal equivalent circuit diagram with resistances.
Fig. 4.2: Thermal resistances of a multi-layered wall
The exterior heat transfer resistance Re, the interior heat transfer resistance Ri and the thermal re-sistance R through the layers of construction material can be calculated as follows:
⋅=== ∑
= WKm
hR,dR,
hR
ii
n
n n
n
ee
tot 2
1
11λ
dn denotes the thickness of the n-th layer. The total thermal resistance from the inside to the out-side adds up to:
⋅++=++= ∑
= WKm
hd
hRRRR
i
n
n n
n
eietot
tot 2
1
11λ
The thermal transmittance U is the reciprocal value of the total thermal resistance:
⋅++==
∑=
KmW
hd
hR
U
i
n
n n
n
e
tottot 2
1
1111
λ
The thermal transmittance U indicates the rate of heat transfer that flows by a temperature differ-ence of one Kelvin through a surface of one square meter. Thermal insulation is better with low values of U. The heat flux through the wall can be calculated as follows:
( )
−⋅= 2m
WUq ei θθ
∑n n
ndλ
eh
1 ih
1
U1
Rtot
Re Ri R
Re Ri R1 Rntot
θe θse θsi θi
Steady-State Thermal Transmission 72
θi denotes the interior temperature and θe the exterior temperature.
The SIA standard 180 [4.2] gives guidelines for the thermal transmittance U of building elements for heated rooms with regards to thermal comfort and moisture protection (i.e. no surface conden-sation and mold growth). For energy reasons, however, significantly lower values are almost al-ways required [4.3].
building element outdoors unheated room ground
sloped or flat roof 0.4 W/(m2⋅K) 0.5 W/(m2⋅K) 0.6 W/(m2⋅K)
vertical wall 0.4 W/(m2⋅K) 0.6 W/(m2⋅K) 0.6 W/(m2⋅K)
window, glass door, door 2.4 W/(m2⋅K) 2.4 W/(m2⋅K) -
floor 0.4 W/(m2⋅K) 0.6 W/(m2⋅K) 0.6 W/(m2⋅K)
Tab. 4.1: Maximum thermal transmittance coefficient U for thermal comfort and moisture protection [4.2]
Figure 4.3 shows the temperature profile for an insulated masonry wall. The temperature jumps at the wall surfaces can be calculated as follows:
eese h
q=−θθ and
isii h
q=−θθ
In layer number n the following temperature gradients occur:
nn
n qx λ∆θ∆
=
Fig. 4.3: Temperature profile in a masonry wall with internal insulation
The coordinate of the location is denoted by x. The temperature in depth xn amounts to:
i,...,,,en)(UR)x(totn
eneinen 21=−⋅⋅+= ∑
=
θθθθ
θe θse
θsi
θi
θ1
θ2
q
λ1 λn hi he
d1 d2 dn
x
λ2
Steady-State Thermal Transmission 73
As mentioned in chapter 1, the temperature profile can also be determined graphically. In Figure 4.4 the calculated and graphically determined temperature profiles in a multi-layered wall are shown.
Fig. 4.4: Calculated and graphically determined temperature profiles in an external wall [4.4]
Steady-State Thermal Transmission 74
The thermal transmittance from surface to surface of the building element, not including the heat transfer coefficients he und hi, is denoted by Λ (R = 1/Λ).
Fig. 4.5: Thermal resistances of building materials as a function of the layer thickness [4.5]
Fig.4.6: Thermal resistances of air layers as a function of the thickness [4.5]
The thermal resistance increases proportionally with the thickness of the building material in ac-cordance with the laws of heat conduction for a homogeneous solid. This is graphically presented in Figure 4.5 for different building materials. In air layers between building materials the heat is transported by three mechanisms: convection and conduction in the air and radiation exchange be-tween the material surfaces. It should be noted that proportionality of thermal resistance to the thickness is only valid for heat conduction and not for convection or radiation (Fig. 4.6). Convection
Steady-State Thermal Transmission 75
initiates with a given air layer thickness while the thermal radiation is independent of the air layer thickness. The high emissivities of many non-metallic surfaces result in the radiant flux becoming the predominant transport mechanism so that the influence of the air layer thickness in a wider range becomes minor to the thermal resistance. The radiant flux is of relatively less importance for metals with low emissivity. After the onset of convection, with an air layer of a couple of centime-ters, the thermal resistance decreases after an initial rise following the increasing conduction re-sistance (for the calculation of the equivalent thermal conductivity of hollow window frames etc. re-fer to chapter 4.3, and chapter 6.3 for insulated glazings).
4.2 Thermal Bridges
Regions in the building envelope where a higher heat flux occurs than in the standard cross sec-tion are designated as thermal bridges. Thermal bridges are relevant with respect to energy losses as well as respective structural damage. In wintertime, lower temperatures occur on the interior side at thermal bridges compared with adjacent areas. These locations are therefore critical with regard to surface condensation and the mold growth. With well-insulated buildings the heat loss through thermal bridges is no longer negligible as regards heating demand. Therefore, thermal bridges are to be avoided whenever possible or accordingly their effects should be minimized. This calls for careful detailing and construction of the building envelope. Figure 4.7 shows possible loca-tions for thermal bridges in a building.
Fig. 4.7: Possible locations for thermal bridges [4.6]
Thermal bridges can be divided into two groups. Material-induced thermal bridges are regions in the building envelope where a material with a larger thermal conductivity is surrounded by a mate-rial with a smaller thermal conductivity. Examples for this are metallic facade anchors, concrete or steel columns that penetrate the thermal insulation, timber beams between insulation material etc. Geometry-induced thermal bridges are regions in the building envelope at which a warm area on the interior side is located across from a larger cold area on the outer side. An external corner of a building creates such a thermal bridge. Figure 4.8 illustrates these two kinds of thermal bridges.
Steady-State Thermal Transmission 76
Fig. 4.8: Adiabats and isotherms in a material- and a geometry-induced thermal bridge
Fig. 4.9: Adiabats and isotherms in building corners
Fig. 4.10: Temperature distribution on the interior and exterior wall surface of a material-induced thermal bridge. The one-dimensional (“simplified”) consideration incorrectly describes the condition
[4.7]
Steady-State Thermal Transmission 77
Figure 4.9 shows adiabats and isotherms in two building corners, in which one is a homogeneous wall and the other one is a masonry wall with insulation in the middle. The lowest temperature oc-curs on the interior surface in the corner. Here, conversely, the heat flux is highest. Locations far away from the corner are handled as a one-dimensional problem (standard cross section).
Figure 4.11 shows the calculated isotherms for a floor slab support. The lowest surface tempera-ture occurs at the inner edge (18°C).
Fig. 4.11: Isotherms at a floor slab support. It is assumed that λmasonry = 0.4 W/(m⋅K) and λconcrete = 1.8 W/(m⋅K) [4.8]
Fig. 4.12: Typical building segments „old“ and „new“ [4.6]
„old“ „new“
Steady-State Thermal Transmission 78
Computer programs have been developed to evaluate the influence of thermal bridges. They are able to solve two- or three-dimensional steady-state thermal conduction problems (temperature distributions, heat flows). For planning thermal bridge catalogs are particularly suitable [4.9, 4.10]. In these catalogs typical thermal bridges are shown and their characteristic thermal values listed. In heat requirement calculations thermal bridges can be taken into account with so-called linear and point thermal transmittances by means of hand calculations. The total heat flow through a structural element with a thermal bridge totQ can be described as the sum of the heat flows through the uninterrupted area (standard cross section) homQ and the additional heat flow due to thermal bridges BrQ∆ :
Brhomtot QQQ ∆+=
whereby
)()(
)(
eiBreiBr
eihom
QorLQ
AUQ
θθχ∆θθψ∆
θθ
−⋅=−⋅⋅=
−⋅⋅=
A area m2
L length of thermal bridge m
U thermal transmittance of standard cross section W/(m2⋅K)
ψ linear thermal transmittance W/(m⋅K)
χ point thermal transmittance W/K
Figure 4.12 shows typical thermal bridges found in older buildings and the analogous construction in new buildings with a layer of insulation throughout.
In the following, a few strategies to the avoidance of thermally weak locations in the building enve-lope are expressed. In general:
- conventional construction materials without insulation today produce unsatisfactory results, un-less the construction becomes extremely thick
- insulation materials cannot be relied upon to carry loads, with the exception of compressive loads (foam glass, polystyrene foam), but not for tension or shear
- metallic penetrations can cancel the entire thermal insulation zone of its effectiveness or strong-ly compromise it
The following guidelines should be adhered to in order to avoid the limitations arising from thermal-ly weak locations:
- consistent wrapping of thermal insulation around the entire building
- no cavities connecting a cold to a warm side of a building element (radiation, convection)
- no metallic penetrations, or at most only punctiform ones (anchors and dowels made out of plastic when possible)
- supporting structure placed entirely on the warm (interior) side
- access stairways, balconies and similar external loads should be externally supported by pillars or suspended
Steady-State Thermal Transmission 79
4.3 Cavities in Window Frames etc.
Thermal computations of building elements with unventilated rectangular cavities (window frames, doors, masonry blocks, etc.) can be determined according to EN ISO 10077-2 [4.11] by an equiva-lent thermal conductivity:
Fig. 4.12: Rectangular cavity and heat flow direction.
Rd
eq =λ
d is the length of the cavity in the direction of heat flow and R is the thermal resistance, which is given by:
rc hhR
+=
1
The convective component of the heat transfer coefficient is given in the case of b > 5 mm by
dChc
1= with C1 = 0.025 W/(m⋅K)
otherwise
⋅= 31
21 TC;
dCmaxhc ∆ with C1 = 0.025 W/(m⋅K); C2 = 0.73 W/(m2⋅K4/3)
∆T is the maximum difference of the surface temperature in the cavity.
In the case that the temperature difference is not known, then ∆T = 10 K should be used. This gives:
= 3
1 C;dCmaxhc with C1 = 0.025 W/(m⋅K); C3 = 1.57 W/(m2⋅K)
The radiation component of the heat transfer coefficient is:
1114
21
3
−+
⋅⋅=
εε
s mr
TFh
The view factor F for a rectangular cavity can be calculated as follows:
Steady-State Thermal Transmission 80
−
++=
bd
bdF
2
1121
s denotes the Stefan-Boltzmann-constant (s = 5.67⋅10-8 W/(m2⋅K4)), ε1 and ε2 are the emissivities of each surface and Tm stands for the average temperature in the cavity.
For non-rectangular cavities the cross section can be converted to an equivalent rectangular sec-tion (Fig. 4.9) and then, as described above, an equivalent thermal conductance can be calculated.
Fig. 4.9: Conversion of a non-rectangular section into an equivalent rectangular section.
Problems
Problems 1 through 3: Determination of the U-value and temperature profile
The purpose is to become acquainted with the prevalent method to calculate the U-value of build-ing materials and the pertinent means. At the same time one should also develop a sense for the magnitudes of such values. The problem definition can be found on the following pages.
Problem 4: Facade color and surface temperature
A facade panel with 14 cm insulation (λ = 0.04 W/(m⋅K)) is heated on a summer day by the sun (I = 700 W/m2, θe = 30°C, θi = 26°C). Determine the exterior surface temperature for a dark (α = 0.8) and a light (α = 0.2) colored facade. The heat transfer coefficients (infrared-radiation and convec-tion) can be taken as he = 20 W/(m2⋅K) and hi = 8 W/(m2⋅K) respectively. A steady-state condition can be assumed.
A = A’ and 'b'd
bd
=
Steady-State Thermal Transmission 81
Problem 1: Exterior Wall
eθ = -10°C iθ = 20°C
Wall construction from outside to inside
Material thickness λ (m) (W/mK)
exterior plaster 0.010 0.87
mineral wool insulating board 0.180 0.036
adhesive mortar 0.010 0.87
masonry block 0.175 0.44
interior plaster 0.010 0.70
Steady-State Thermal Transmission 82
Graphic determination of problem 1
Steady-State Thermal Transmission 83
Problem 2: Roof
eθ = -10°C iθ = 20°C
roof construction from outside to inside
Material thickness λ (m) (W/mK)
gravel/extensive plant cover *
bitumen *
liquid membrane *
mineral wool 0.22 0.036
vapor retarder *
recycled concrete 0.31 1.8
* negligible thermal resistance
Steady-State Thermal Transmission 84
Graphic determination of problem 2
Steady-State Thermal Transmission 85
Problem 3: Floor against cellar
eθ = 8°C iθ = 20°C
Floor construction from interior to exterior (= cellar)
Material thickness λ (m) (W/mK)
concrete screed 0.03 1.8
load-distribution plate 0.08 1.5
PE-sheet *
impact sound insulation 0.09 0.038
reinforced concrete slab 0.3 1.8
* negligible thermal resistance
Steady-State Thermal Transmission 86
Graphic determination of problem 3
Steady-State Thermal Transmission 87
Literature
[4.1] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[4.2] SIA Norm 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Architekten-Verein, 1999
[4.3] SIA 380/1, Thermische Energie im Hochbau, Hrsg: Schweizerischer Ingenieur- und Archi-tekten-Verein, 2007
[4.4] Sagelsdorff, R., Frank, T., element 29: Wärmeschutz und Energie im Hochbau, Schweizeri-sche Ziegelindustrie, Zürich, 1990
[4.5] Gösele, K., Schüle, W., Schall, Wärme, Feuchte, Bauverlag GmbH, Wiesbaden, 1989
[4.6] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006
[4.7] Cziesielski, E. (Hrsg.), Bauphysik, in: Bautechnik, Bd. V, Konstruktiver Ingenieurbau 2, Springer-Verlag Berlin, 1988
[4.8] Brunner, C. U., Nänni, J., Wärmebrückenkatalog 1 (Neubaudetails), SIA D 099, Zürich, 1985
[4.9] Wärmebrückenkatalog, Bundesamt für Energie BFE, 2002
[4.10] G. Notter, U.P. Menti, M. Ragonesi, Wärmebrückenkatalog für Minergie-P-Bauten, In Er-gänzung zum Wärmebrückenkatalog des BFE, Schlussbericht, Bundesamt für Energie BFE, 2008
[4.11] EN ISO 10077-2, Wärmetechnisches Verhalten von Fenstern, Türen und Abschlüssen - Be-rechnung des Wärmedurchgangskoeffizienten – Teil 2: Numerisches Verfahren für Rah-men, Europäisches Komitee für Normung CEN, Brüssel, 2003
[4.12] EN ISO 10211, Wärmebrücken im Hochbau – Wärmeströme und Oberflächen-temperaturen, CEN, Brüssel, 1996
[4.13] EN ISO 14683, Wärmebrücken im Hochbau – Längenbezogener Wärmedurch-gangskoeffizient – Vereinfachte Verfahren und Anhaltswerte, CEN, Brüssel, 1999
[4.14] EN ISO 13370, Wärmetechnisches Verhalten von Gebäuden – Wärmeverluste ins Erdreich - Berechnungsverfahren, CEN, Brüssel, 1997
Chapter 5
Non-Steady-State Thermal Transmission
θ2 θ3 θ4 θ5 θ6
Non-Steady-State Thermal Transmission 90
5 Non-Steady-State Thermal Transmission In chapter 4 the thermal transmission through a building element was handled with constant tem-peratures with respect to time on the interior and exterior. In such a steady state the heat flow through a wall can be calculated by the thermal transmittance U of the building element.
In reality, however, the interior and exterior temperatures are not constant with respect to time but are subjected to daily and annual fluctuations. The amplitudes of the exterior temperature fluctua-tions are significantly larger than those on the interior side. Additionally, time-dependent solar radi-ation can also significantly influence the temperature fluctuations on the exterior surface of the building envelope. In order to correctly describe the variation of the temperature profile and the heat flow as a function of time, heat storage in the building element must be accounted for.
In this chapter, therefore, non-steady-state characteristic values shall be developed with which the reactions of material layers can be described with respect to time-dependent changes of boundary conditions.
5.1 Non-Steady-State Heat Propagation in a Material Layer
5.1.1 Heat Equation and Illustration
Given is a material layer with a thickness d and thermal conductivity λ. The surface temperatures on the interior and exterior are θsi and θse, whereby θsi > θse applies. The condition is steady-state. The heat flux q then amounts to (Fourier’s law of heat conduction):
dq sesi θθλ −
⋅= (W/m2)
The material layer has a density ρ und a specific heat c. If this layer is now brought from an iso-thermal state (isothermal = constant temperature throughout the layer) with a temperature θ1 into the isothermal state of temperature θ2, whereby θ2 > θ1, then the quantity of heat stored per m2 in the layer is given as:
( )12dcQ θθρ −⋅⋅⋅= (J/m2)
The product of the material quantities ρ⋅c characterizes how well heat can be stored in a material (unit: J/m3K).
In steady-state conditions the thermal conductivity λ sufficiently describes the material characteris-tics. In non-steady-state conditions the additional material quantities ρ⋅c are required. Based on Fourier’s law of heat conduction and the law of conservation of energy a second order partial dif-ferential equation can be derived – the so-called Fourier differential equation – that also describes the non-steady-state heat propagation (cp. chapter 1.1). In the three-dimensional case — x, y and z denote the coordinates in space and t the time — this gives:
++
⋅= 2
2
2
2
2
2
zyxct ∂θ∂
∂θ∂
∂θ∂
ρλ
∂∂θ
This differential equation for heat conduction, referred to as the heat equation, describes the tem-perature distribution in a given region over time. The initial condition, given by the temperature dis-tribution at time t = 0, as well as the boundary conditions are also required in order to solve the equation in a given case. The boundary conditions can be described by different forms. For exam-ple, the temperature or the heat flux can be given at the boundary of the region (note: different methods to solve Fourier’s differential equation analytically or numerically are discussed in the lit-erature, e.g. [5.1]).
Non-Steady-State Thermal Transmission 91
A graphic scheme for the one-dimensional propagation of heat is shown in Fig. 5.1. The material layer has a constant initial temperature (isothermal). On the left-hand surface the temperature jumps and is held constant afterwards. The following then takes place:
— The temperature increase on the surface causes a heat flow in the first sublayer of the material (→ arrow).
— Thereby the temperature in the first sublayer is increased. This binds a certain quantity of heat (→ bucket).
— Because of the temperature increase in the first sublayer a heat flow into the second sublayer is induced, whereby now less heat flows due to the heat storage in the first sublayer (→ slimmer arrow).
— etc.
Fig. 5.1: Model of non-steady-state thermal transmittance (from [5.2])
The material quantities have the following influence:
— The larger the thermal conductivity λ, the better the heat is transmitted.
— The larger the storage capacity ρ⋅c, the more the heat is retained and no longer available to propagate.
5.1.2 Thermal Diffusivity and Thermal Effusivity
A more exact treatment shows that with the two quantities λ and ρ⋅c as a product or as a ratio two new important characteristic values can be generated, which describe heat propagation.
The term λ/(ρ⋅c) is denoted as thermal diffusivity a and describes the speed and range of the tem-perature equalization in a material layer. The range is larger, the larger the thermal conductivity λ is („ability to transfer“) and the range is smaller, the more is retained in transit ρ⋅c („fill and empty buckets“).
θ1 θ2 θ3 θ4 θ5 θ6
Non-Steady-State Thermal Transmission 92
Thermal diffusivity: c
a⋅
=ρ
λ
sm2
The thermal effusivity b is a measure of how much heat „is lost“ by propagation in a material. This will be stronger the greater the heat conductivity λ is (“long-range capability”) and the greater the storage capability ρ⋅c is (larger heat storage).
Thermal effusivity: cb ⋅⋅= ρλ
⋅⋅ 212 sKmJ
/
In Table 5.2 the properties λ, ρ and c for different materials are shown as well as thermal diffusivity a and thermal effusivity b.
Material λ (W/m⋅K)
ρ (kg/m3)
c (J/kg⋅K)
ρ⋅c (kJ/m3⋅K)
a (m2/s)
b (kJ/m2⋅K⋅s1/2)
copper 380 8’900 380 3'382 11’236⋅10-8 35.8 aluminum 200 2’700 900 2'430 8’230⋅10-8 22.0 steel 50 7’800 450 3'510 1’424⋅10-8 13.2 concrete 1.65 2’200 1’000 2’200 75⋅10-8 1.9 reinforced-concrete 2.3 2’300 1’000 2'300 100⋅10-8 2.3 brick (clay) 0.44 1’100 900 990 44⋅10-8 0.7 sand lime brick 1.0 1’800 900 1'620 62⋅10-8 1.3 earth (sand/gravel) 2.0 2’000 1’000 2'000 100⋅10-8 2.0 earth (clay) 1.5 1’500 2’000 3'000 50⋅10-8 2.1 float glass 1.0 2’500 750 1'875 53⋅10-8 1.4 gypsum plasterboard 0.25 900 1’000 900 28⋅10-8 0.5 wood (spruce) 0.14 500 2’200 1'100 13⋅10-8 0.4 chipboard 0.14 600 1’700 1'020 14⋅10-8 0.4 mineral wool 0.04 80 600 48 83⋅10-8 0.04 expanded polystyrene 0.04 15 1’400 21 191⋅10-8 0.03 air (still, 20°C) 0.026 1.2 1’000 1.2 2’167⋅10-8 0.006 water (still, 10°C) 0.6 1’000 4’190 4'190 14⋅10-8 1.6
Tab. 5.2: Characteristic values of different materials (from [5.3, 5.4])
If two semi-infinite bodies with different temperatures θ1 und θ2 come into contact, the temperature θ0 at the contact surface can be calculated by means of the thermal effusivities b1 and b2 :
21
22110 bb
bb+
⋅+⋅=
θθθ (°C or K)
Let’s assume that a person’s body (θbody = 34°C, bbody = 1 kJ/m2⋅K⋅s0.5) comes into contact with a thick plate that is at room temperature. The plate is either made of polystyrene (bPS = 0.03 kJ/m2⋅K⋅s0.5) or copper (bCu = 35.8 kJ/m2⋅K⋅s0.5). The following applies: bCu > bbody > bPS. The tem-perature of the material with the larger thermal effusivity (“better dissipation of heat”) has a higher impact on the contact temperature:
C633301000
2030341000PS0 °=
+⋅+⋅
= .,θ
C420358001000
2035800341000Cu0 °=
+⋅+⋅
= .,θ
Since the contact temperature with the copper plate is considerably lower, one’s touch feels colder than with the polystyrene plate.
Non-Steady-State Thermal Transmission 93
To illustrate the impact of thermal diffusivity, the temperature development in a 40 cm thick wall is shown in Figure 5.2 after a sudden temperature change on the surface (0°C → 20°C). The back-side of the wall is adiabatic (= „perfectly“ insulated, i.e. no heat flows through the backside sur-face). The rate of temperature development differs according to each material: wood, concrete or polystyrene. It gives: aH < aB < aPS.
Fig. 5.2: Temperature development after a surface temperature jump [5.2]
5.1.3 Inertia of Walls: Charge and Discharge Performance
Often the boundary conditions of a wall suddenly change; outside, e.g., with a cold spell or a storm, inside, e.g., if a window is opened or a heater is turned on or off. It is, therefore, interesting to know how quickly a wall reacts to a sudden change of the ambient temperature. That is, one would like to be able to assess the thermal inertia of the wall. The transition from one steady-state condition to another one is named transient.
As an example, Figure 5.3 shows the discharge (“cooling down”) of a 20 cm thick concrete wall. The wall and its surroundings are for t < 0 at a constant temperature θi. At time t = 0 the ambient temperature abruptly sinks. The change in the temperature profile in the wall up to t = 36 h as well as the heat flow (normalized) to the surroundings are shown in Figure 5.3.
Concrete
aB = 75⋅10-8 m2/s
Wood
aH = 13⋅10-8 m2/s
Polystyrene
aPS = 191⋅10-8 m2/s
Time (h) Tem
pera
ture
(°C
)
Wall thickness
Time (h) Tem
pera
ture
(°C
)
Wall thickness
Time (h)
Tem
pera
ture
(°C
)
Wall thickness
0
10
20
0
10
20
0
10
20
0 40
20
0 40
20
0 40
20
0 12
24 36
48
0 12
24 36
48
0 12
24 36
48
Non-Steady-State Thermal Transmission 94
Fig. 5.3: Discharge (“cooling down”) of a concrete wall after a temperature jump (θi → θf)
The cooling proceeds more slowly, the larger the layer thickness d is and the smaller the thermal diffusivity a is. With these two quantities a characteristic time d2/a can be computed. During the cooling process the surface temperature decreases approximately exponentially and the character-istic time d2/a can very roughly be interpreted as a time constant [5.6]:
ad 2
≈τ (s)
With an exponential decay in time (e.g. t1
e0tt⋅−
⋅== τθθ )()( ) the time constant τ denotes the time with which the value subsides to the fraction 1/e (Euler’s number e = 2.71828, thus 1/e = 36.8%). The heat transfer coefficient to the surroundings likewise influences the cooling action. This is here however negligible. Time constants for a couple of materials with a thickness of 10 cm are:
Wood: h213600
1101310
8
2
≈⋅⋅
≈−
.τ
Concrete: h43600
1107510
8
2
≈⋅⋅
≈−
.τ
Mineral wool: h33600
1108310
8
2
≈⋅⋅
≈−
.τ
Copper: min513600
11023611
108
2
.'
.≈⋅
⋅≈
−τ
The term d2/a can be expressed as follows:
CRdcdcda
d 22
⋅=⋅⋅⋅=⋅⋅
= ρλλ
ρ
That is, the time constant is larger, the higher the thermal resistance R and the larger the surface storage capacity C of the layer are. Let’s consider two material layers.
Mineral wool (d = 30 cm):
t = 0
t = 2 h
t = 4 h
t = 6 h t = 8 h
t = 10 h t = 12 h
t = 24 h
t = 36 h
θi
θf
d = 0.2 m
0
0.2
0.4
0.6
0.8
1
0 10 20 30
Hea
t flo
w
Time (h)
Non-Steady-State Thermal Transmission 95
d251h304001457306008004030dcdCR .'..
..
==⋅=⋅⋅⋅=⋅⋅⋅=⋅≈ ρλ
τ
Masonry made of lightweight bricks (d = 47.5 cm, λ = 0.17 W/mK, ρ = 960 kg/m3, c = 900 J/kgK):
d13h31840041079247509009601704750dcdCR ≈≈⋅=⋅⋅⋅=⋅⋅⋅=⋅≈ '....ρ
λτ
The layer of mineral wool insulates (despite less thickness) almost 3 times better than the masonry made of lightweight bricks, however it has almost 30 times less storage capacity. As a result the masonry has more thermal inertia, by about a factor of 10!
After a period of about three time constants (e-3 ≈ 0.05), the previous state is almost completely “forgotten” and the system is in steady state. This occurs with the mineral wool layer after about 4 days, the masonry however needs noticeably longer than a month for this! Since the boundary conditions during this time have for the most part already changed, such walls are practically never in a complete steady state.
5.2 Reaction of a Material Layer to Periodic Changes
5.2.1 Material Layer with a Finite Thickness: Amplitude Damping und Phase Shift
Very often the boundary conditions fluctuate periodically. Daily and annual variations in the outside air temperature resemble a sine or cosine function (cp. chapter 2). It is, therefore, helpful to under-stand how a material layer reacts to a harmonic variation of the boundary conditions.
The surface of a material layer (x = 0) is subjected to a harmonic temperature oscillation with an amplitude ∆θ at an average temperature θ0:
( )
⋅
⋅⋅+== t
T20xt 0
πθ∆θθ cos, (°C)
The backside of the material layer is adiabatic. The temperature oscillation propagates from the front surface into the material as a “heat wave”. In doing so the temperature amplitude reduces with increasing depth.
Amplitude damping: 'θ∆
θ∆ν = (-)
With increasing depth into the material the temperature oscillation also sustains a lag. That is, the maximum and the minimum temperature shift back in time (Figures 5.4 and 5.5).
Phase shift: ε (s or h)
For the temperature oscillation at depth x, it gives:
( ) ( )
−⋅
⋅⋅+= 'cos', επθ∆θθ t
T2xt 0 (°C)
Non-Steady-State Thermal Transmission 96
Fig. 5.4: Temperature development in a concrete wall with periodic excitation [5.2]
0
5
10
15
20
0 12 24 36 48
Tem
pera
ture
(°C
)
Time (h)
Phase shift ε
Am
plitu
de ∆
θ
Am
plitu
de ∆
θ ''
Fig. 5.5: Front and back side surface temperature with periodic excitation
5.2.2 Semi-Infinite Material Layers: Penetration Depth
In the case of the surface of a semi-infinite material thickness subjected to a harmonic temperature oscillation, the time dependent temperature profile can be calculated simply. This case corre-sponds, for example, to the penetration of a temperature oscillation into the ground (chapter 2) or into a very thick wall. The temperature oscillation in the semi-infinite layer is given by:
( )
−⋅
⋅⋅+= −
sπθ∆θθ s xt
T2ext x
0 cos, / (°C)
Time t (h)
Tem
pera
ture
θ (
°C)
12
24
36
48
0
0
10
20
0 10
20 30
6
18
30
42
Material depth x
Phase shift ε
Non-Steady-State Thermal Transmission 97
Penetration depth: aTc
Tπρπ
λs =⋅⋅
⋅= (m)
With increasing depth the temperature amplitude decreases (Fig. 5.6). The penetration depth s denotes the depth in which the amplitude is reduced to the 1/e-part (1/e = 36.8%, Fig. 5.7). The penetration depth characterizes the range of temperature oscillation and is larger the larger the thermal diffusivity a of the material is, but also the larger the period T of the oscillation is.
-1
-0.5
0
0.5
1
0 0.1 0.2 0.3 0.4 0.5
Tem
pera
ture
(K)
Depth x (m)
t = 3 h
t = 6 h
t = 9 h
t = 12 h
t = 15 h
t = 18 h
t = 21 h
t = 0 Concrete a = 75 10-8 m2/sPeriod T = 24 hPenetration depth s = 0.144 m
.
Fig. 5.6: Penetration of a temperature oscillation into a semi-infinite material layer
Fig. 5.7: Envelope of temperature oscillations in a semi-infinite material layer and penetration depth s
The penetration depth s is proportional to T . Thus the annual oscillations penetrate the material layer about 19365 ≈ -times deeper than the daily oscillations. Table 5.3 shows the dependence
x = 3s
2⋅∆θ
x = s x = 2s
1e2 −⋅⋅ θ∆
100 %
36.8 %
13.5 % 5.0 %
2e2 −⋅⋅ θ∆ 3e2 −⋅⋅ θ∆
Non-Steady-State Thermal Transmission 98
of the penetration depth of different materials on the period. The annual oscillations in particular show penetration depths of more than a meter. These penetration depths are considerably larger than commonly constructed layer thicknesses. Slow oscillations go right through the building con-struction, as if the building was “transparent”! Faster oscillations from about T = 24 h to T = 1 h can still enter common layer thicknesses. Very fast oscillations have an effect only on the near surface.
Period T Material 1 h 4 h 12 h 24 h 1 Week 1 Month 1 Year aluminum 0.307 0.614 1.064 1.505 3.981 8.241 28.744 steel 0.128 0.256 0.443 0.626 1.656 3.428 11.958 concrete 0.029 0.059 0.102 0.144 0.380 0.787 2.744 reinforced concrete 0.034 0.068 0.117 0.166 0.439 0.908 3.168 brick (clay) 0.023 0.045 0.078 0.111 0.293 0.606 2.112 sand lime brick 0.027 0.053 0.092 0.130 0.345 0.714 2.489 earth (sand/gravel) 0.034 0.068 0.117 0.166 0.439 0.908 3.168 earth (clay) 0.024 0.048 0.083 0.117 0.310 0.642 2.240 gypsum plasterboard 0.018 0.036 0.062 0.087 0.231 0.479 1.670 wood (spruce) 0.012 0.024 0.042 0.059 0.157 0.324 1.130 mineral wool 0.031 0.062 0.107 0.151 0.401 0.829 2.892 expanded polystyrene 0.047 0.093 0.162 0.229 0.606 1.254 4.373
Tab. 5.3: Penetration depths s (m) for different periods and materials
With non-steady-state processes the penetration depth can be used as a measurement for the thermal effective layer thickness in a particular material. d denotes the geometric thickness of the material layer.
Dynamic layer thickness: sdz = (-)
Because the penetration depth depends on the period of excitation, the dynamic layer thickness also depends on the period. A wall with a thickness d can also appear thin (s large → z small) for slow oscillations, however thick (s small → z large) for fast oscillations.
The quantity of energy that flows into a semi-infinite material layer per period, that is stored there and subsequently flows out again, is given by:
θ∆π
θ∆ρλπ
⋅⋅=⋅⋅⋅⋅= b2T2c
2T2QT (J/m2)
∆θ denotes the amplitude of the temperature oscillation on the surface. The thermal effusivity b is a measurement of how much heat penetrates into a material layer. Since the stored heat is propor-tional to T , with annual oscillations more heat is stored than with daily oscillations.
Let’s consider as an illustration the following example. For an assessment we calculate the pene-tration depth of a wall. If good and bad weather periods follow one another, the outside tempera-ture rises and falls accordingly, so that the daily oscillations of a slower fluctuation becomes super-imposed (Fig. 5.8). The course of the outside temperature can then be depicted as the superposi-tion of two harmonic oscillations:
Non-Steady-State Thermal Transmission 99
Fig. 5.8: Course of the instantaneous and daily average temperature
( )
⋅
⋅⋅+
⋅
⋅⋅+= t
T2t
T2t
22
110
πθ∆πθ∆θθ coscos (°C)
Assuming the temperature amplitudes and periods according to Figure 5.8 and a light exterior wall construction with 30 cm of mineral wool insulation (U = 0.13 W/m2K) it is obtained for penetration depths and dynamic layer thicknesses:
Daily oscillation:
∆θ1 = 7 K, T1 = 24 h → s1 = 0.151 m → 991151030z1 .
..
== → 1370ee 991z1 .. == −−
10-day-oscillation:
∆θ2 = 6 K, T2 = 240 h → s2 = 0. 479 m → 6270479030z2 .
..
== → 5340ee 6270z1 .. == −−
The daily oscillation virtually does not penetrate through the wall construction (13.7%), the 10-day oscillation, however, becomes significantly less damped (53.4%).
5.2.3 Effective Thickness for Heat Storage
The capability of the interior building elements to store heat and then to release it again later in time often plays a significant role for the non-steady-state behavior of a room or building (chapter 8). If walls, ceilings and floors have a large heat capacity, the temperature fluctuations can be smoothed out. This is advantageous with regards to thermal comfort (chapter 3).
In section 5.2.2 it was shown that the layer thickness in which heat is stored varies depending on material characteristics and frequency of excitation. This effective storage layer thickness can be characterized by the penetration depth s. For a material layer with a thickness d the dynamic heat capacity per area Cdyn can be calculated as follows:
For „thin“ material layers with s⋅≤2
1d : dcCdyn ⋅⋅= ρ (J/m2K)
For „thick“ material layers with s⋅>2
1d : sρ ⋅⋅⋅=2
1cCdyn (J/m2K)
5
10
15
20
25
30
1
Ext
erna
l tem
pera
ture
(°C
)
Time (h)
2 3 4 5 6 7 8 9 10 11
May 22 - June 1, 2005Zurich SMA
Non-Steady-State Thermal Transmission 100
With a „thin“ layer the total thickness d is active in heat storage while with a „thick“ layer only the outer part is. The division between „thin“ and „thick“ is based on the penetration depth; i.e. on the material properties and the period of excitation. It follows by means of the thermal effusivity b:
b2Tc
2T
cT
21c
21cCdyn ⋅=⋅⋅⋅=
⋅⋅⋅
⋅⋅⋅=⋅⋅⋅=π
ρλπρπ
λρsρ
That is, with a „thick“ layer the storage capacity does not dependent on the thickness d! Figure 5.9 shows the dynamic heat capacity with respect to the layer thickness, plotted as multiples of the penetration depth s .
Fig. 5.9: Dynamic heat capacity ratio of a material layer as a function of multiples of the penetration depth s
For daily oscillations (T = 24 h) the effective storage layer thickness for typical massive construc-tion materials is only about 10 cm. If the wall is thicker, then with daily oscillations the additional layer thickness is essentially under-utilized (Tab. 5.4). Also an infinitely thick wall possesses only a finite dynamic storage capacity!
Penetration depth s for T = 24 h
(m)
Effective storage layer thickness 2/s
(m)
Dynamic heat capacity Cdyn
(kJ/m2K) concrete 0.144 0.102 224
sand lime brick 0.130 0.092 149
brick (clay) 0.111 0.078 78
Tab. 5.4: Heat storage characteristics of material layers with daily fluctuations
5.3 Non-Steady-State Properties of Opaque External Walls
Let’s consider an opaque wall in which the exterior air temperature is oscillating harmonically. In section 5.2.1 it was shown that with increasing depth of wall the temperature oscillation experienc-es a phase shift and a dampening of its amplitude. The amplitude of the temperature oscillation on the interior wall surface is thus smaller than that of the exterior temperature and the fluctuation ex-hibits a shift in time of the maxima (phase shift ε). The ratio of the amplitudes of the exterior air
Layer thickness
Dyn
amic
hea
t cap
acity
ratio
C
dyn/C
dyn,
∞ (-
)
0 s 2⋅s
3⋅s 4⋅s 5⋅s
0.2
0.4
0.6
0.8
1.0
0
ss⋅≈= 710
2d .
„thick“ „thin“
Cdyn,∞
Non-Steady-State Thermal Transmission 101
temperature to the amplitude of the interior surface temperature is denoted as amplitude damping ν (Fig. 5.10).
Fig. 5.10: Amplitude damping ν and phase shift ε
The heat transmission for a periodic excitation and multi-layered walls can also be presented by Heindl’s approach in a matrix [5.7, 5.8, 5.9]:
=
i
i
2221
1211
e
e
qWWWW
q ∆θ∆
∆θ∆
The building element properties are contained in the heat transfer matrix W, which describes the relationship between the temperature and the heat flow oscillations inside and outside. The matrix elements are represented by complex numbers. A more exact consideration shows that three properties characterize the non-steady state:
— amplitude damping ν
— phase shift ε
— dynamic thermal transmittance UT
In order to determine these characteristic values, the internal boundary conditions must be defined. In doing so two boundary cases are differentiated (Fig. 5.11).
The boundary condition I (θi = constant) approximates the case of an air-conditioned building or a building with a large thermal inertia. The boundary condition II (∆qi = 0) corresponds rather to the case of a building with little thermal inertia.
Because the heat equation is a linear equation the different solutions can be superimposed. If for boundary condition I the solution for the steady-state case is superimposed onto the solution for the non-steady-state case, the extreme heat fluxes can be expressed as follows:
( ) eTeiinstatstati UUqqq θ∆θθ ⋅±−⋅=±= maxmin
maxmin
(W/m2)
iθ internal air temperature °C
eθ mean value of the external air temperature °C
eθ∆ amplitude of the external air temperature K U thermal transmittance (steady-state) W/m2K UT dynamic thermal transmittance (non-steady-state portion) W/m2K
θe (t)
t
T
∆θe
θsi (t)
t
T
∆θsi
ε
θsi (t)
si
e
θ∆θ∆ν =
Non-Steady-State Thermal Transmission 102
The dynamic thermal transmittance UT corresponds to the maximum heat flux on the internal sur-face of the wall if the external air temperature oscillates periodically by ±1 K.
Figure 5.11: Boundary conditions to calculate the non-steady-state characteristic values
Figure 5.12 shows the non-steady-state characteristic values of differently constructed external walls. These properties apply to the idealized boundary conditions in accordance with Figure 5.11. It can be seen from figures 5.12 und 5.13 that the layer sequence influences the non-steady-state characteristic values. To dampen the external temperature oscillation as much as possible, a wall with external insulation is better suited than a wall with internal insulation. The better a wall is insu-lated and the more mass per unit area is available, the higher the amplitude damping and the larg-er the phase shift. High values of amplitude damping and phase shift are beneficial with respect to thermal comfort. Poorly insulated light wall constructions exhibit limited amplitude damping and phase shifting!
The idealized boundary conditions described are in reality practically never existing, so that the non-steady-state parameters ν, ε und UT are only suitable for rough estimates.
By way of illustration let’s compare the fluctuation of the heat fluxes of two different wall construc-tions with identical thermal transmittances (U = 0.27 W/m2K) on a nice summer day ( C24e °=θ ,
K10e =θ∆ , iθ = 22°C) and a winter day ( C5e °−=θ , K5e =θ∆ , iθ = 20°C). A negative sign corre-sponds to an inward heat flow:
(i) Externally insulated massive wall (1 cm external rendering / 12 cm insulation / 25 cm concrete / 1.5 cm internal plaster)
Summer: ( ) 230540100302422270 m/W....qqq maxmininstatstat
maxmini ±−=⋅±−⋅=±=
Winter: ( ) 21507565030520270 m/W...)(.qqq maxmininstatstat
maxmini ±=⋅±−−⋅=±=
Characteristic values:
- amplitude damping νT
- phase shift εT
- dynamic resistance
- dynamic U-value
- reduction factor
i
eT q
R∆
θ∆=
UUf T
T =T
T R1U =
Characteristic values:
- amplitude damping νH
- phase shift εH
.
.
.
T
Boundary condition II: Adiabatic
T
∆qi = 0 (adiabatic)
Exterior
Interior
Boundary condition I: Isothermal
T
θi = constant
∆qi ≠ 0
Exterior Interior
hi he
he
Non-Steady-State Thermal Transmission 103
Fig. 5.12: Non-steady-state characteristic values of external wall constructions [5.5]
Randbedingung I: Isotherm (∆θi = 0)
Randbedingung II: Adiabatisch
(∆qi = 0)
U UT εT εH
Non-Steady-State Thermal Transmission 104
(ii) Lightweight wall construction (0.1 cm aluminum / 14 cm insulation / 0.1 cm steel)
Summer: ( ) 2instatstati mW62540102602422270qqq /....max
minmaxmin ±−=⋅±−⋅=±=
Winter: ( ) 2instatstati mW317565260520270qqq /...)(.max
minmaxmin ±=⋅±−−⋅=±=
The fluctuation portion is with lightweight construction considerably more significant than with mas-sive construction and can easily surpass the steady-state portion in summer!
Fig. 5.13: An externally insulated wall dampens an external temperature oscillation better than a wall insulated on the interior (T = 24 h; boundary conditions: he = 25 W/m2K, interior adiabatic).
5.4 Structural Consequences
In order to ensure high thermal comfort in a building, the temperature fluctuations in the interior rooms must be kept small. This should be achieved, whenever possible, without HVAC (heating, ventilation and air conditioning) systems. Therefore, an appropriate building construction is essen-tial.
Massive construction that is well insulated on the exterior is most suitable in keeping the effect of the external temperature oscillations on the interior temperature small. Such building construction exhibits high amplitude damping whereby the impact of the phase shift is negligible since the am-plitudes are only tiny (Note: In the past one was worried that the effect of the external oscillations, for example, only reach the interior after working hours).
Because of absorption of solar radiation on the external surface of walls and roofs the fluctuations of the external surface temperature can be significantly raised. Light facade and roof surfaces, roof areas possibly with green vegetation, and possibly a ventilated air space reduce the effect of solar radiation (cp. Fig. 2.25).
The heat storage capacity of the interior structural elements (walls, ceilings and floors) is important to keep the effects from fluctuations of released heat — solar radiation, heat from people and ap-pliances — on the interior temperature small. Massive construction made of concrete or sand-lime bricks, for example, are especially good for this. However, it is important that the thermal re-sistance between the indoor air and the building element is not increased by suspended ceilings, raised floors, thick carpets etc.
Amplitude damping νH = 103
Amplitude damping νH = 3.6
External insulation Internal insulation
Insulation 0.2 m
Concrete 0.2 m
Concrete 0.2 m
Insulation 0.2 m
Non-Steady-State Thermal Transmission 105
Problems
Problem 1: Heat storage in a building element Given are three different material layers:
Thermal conductivity
W/(m·K)
Density
kg/m3
Specific heat
J/(kg·K) Thickness
m
concrete (reinforced) 2.3 2300 1000 0.2
gypsum plasterboard 0.25 900 1000 0.025
mineral wool 0.04 60 1080 0.2
Determine each of the following for a daily temperature oscillation as well as a monthly oscillation: a.) penetration depth b.) characterization of the layer with respect to the dynamic thermal properties („thick“ or „thin“) c.) dynamic heat capacity Compile your results in a table; one for the daily oscillations and one for the monthly.
Problem 2: Underground exhibition hall In the immediate vicinity of the pyramids in Gizeh (Egypt), an underground exhibition hall for visi-tors is planned. The distance between the ground surface and the exhibition hall is a minimum of 5 m. The annual mean temperature in Gizeh is 21°C, the annual amplitude is 10 K and the tempera-ture diffusivity of the ground can be taken as 10-6 m2/s. a.) How large is the penetration depth of the daily and annual oscillations? b.) Mathematically show in which range the temperature fluctuates at a depth of 5 m during a
year? c.) How great is the amplitude damping for an annual oscillation at a depth of 5 m? d.) How does the room temperature change when there are visitors in the room? Give reasons to
support your answer qualitatively.
Problem 3: Time constant of walls Given are two walls: a sand lime brick wall (d = 20 cm) and a wall constructed of spruce wood (d = 2 cm). Evaluate mathematically: a.) time constant of the sand lime brick wall b.) time constant of the wall constructed of spruce wood
Problem 4: Contact temperature of floors Three people stand barefoot each for a long period of time on a floor of wood, stone and steel. The room temperature is at 20°C, the temperature of the people can be taken as 34°C. The ther-mal effusivity for a person’s body is bbody = 1 kJ/m2⋅K⋅s0.5 and for the floors is bwood = 0.4 kJ/m2⋅K⋅s0.5, bstone = 1.5 kJ/m2⋅K⋅s0.5 and bsteel = 13.2 kJ/m2⋅K⋅s0.5. a.) Calculate the contact temperature for all three floors. b.) Interpret your results from a.).
Non-Steady-State Thermal Transmission 106
Literature [5.1] Grigull U., Sandner H., Wärmeleitung, Springer-Verlag, Berlin, 1990 [5.2] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006 [5.3] SIA 279, Wärmedämmstoffe, Schweizerischer Ingenieur- und Architekten-Verein, Zürich,
2004 [5.4] SN EN 12524, Baustoffe und -produkte - Wärme- und feuchteschutztechnische Eigenschaf-
ten - Tabellierte Bemessungswerte, Europäisches Komitee für Normung, Brüssel, 2000
[5.5] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[5.6] Keller B., Rutz S., Pinpoint: Fakten der Bauphysik zu nachhaltigem Bauen, vdf Hochschul-verlag, Zürich, 2007
[5.7] Sagelsdorff R., Frank T., element 29 - Wärmeschutz und Energie im Hochbau, Schweizeri-sche Ziegelindustrie, Zürich, 1990
[5.8] SIA 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Archi-tekten-Verein, Zürich, 1999
[5.9] EN ISO 13786, Thermal performance of building components - Dynamic thermal character-istics - Calculation methods, Europäisches Komitee für Normung, Brüssel, 199
Chapter 6
Transparent Building Elements
Transparent Building Elements 108
6 Transparent Building Elements Transparent elements of the building facade let daylight into the building and allow for a view from the inside to the outside. They also let in incident solar energy for heating the building in winter. To save on heating, the thermal losses in winter through the transparent building elements should be small. In general, thermal transmittances of glazings are significantly higher than those of adjacent opaque elements. To reduce heating demands it is desirable that glazings have a small thermal transmittance and likewise a high total solar energy transmittance. A small thermal transmittance is also advantageous regarding thermal comfort because the internal surface temperature of the glazing will then be close to the interior air temperature (chapter 3). In order to avoid the building overheating in summer, solar shading is mostly necessary. Thereby, the amount of solar energy that comes into the building interior can be controlled. The solar shading device can significantly influence the facade design and should, therefore, be included early on in the design and construc-tion process. Especially in work places attention should also be given to suitable measures to avoid the effects of glare.
In this chapter the characteristics of transparent building elements shall be introduced and the transport of solar radiation and heat through glazings and windows shall be investigated.
6.1 Classification and Characteristics
Basically there are several ways to fabricate transparent insulated building elements. Figure 6.1 shows a geometrical classification. The designation transparent is for some of these materials not actually applicable. The term translucent would be more suitable to apply because the linear prop-agation of light in some of these structures is hindered by scattering or reflection and it is not pos-sible to look through them (objects on the other side can not be clearly discerned). However given that the term transparent has already been established, it will be used here as well.
Fig. 6.1: Classification of transparent building elements [6.1]
For each of the four categories in Figure 6.1, examples of technical execution are illustrated. With glazings the individual layers – panes of glass or possibly plastic films – are arranged parallel to one another. If honeycomb or capillary structures are placed between two cover sheets (e.g. out of glass), then the solar radiation will be reflected forwards in the direction of the absorber or interior room. Thereby high transmittances of solar irradiance can be achieved. Large pore structures or
Microporous materials (aerogel)
Glass panes, possibly with films
Foams, closed-cell structures
Honeycomb or capillary structures
Transparent Building Elements 109
cavity structures are e.g. foams or a combination of layers that lay parallel and perpendicular to the bounded face sheet. When the pore size of microporous materials is significantly smaller than the wavelength of the sunlight, reflection will no longer occur in the pores. Thereby the material ap-pears homogeneous and is transparent.
Today in buildings, glazings are almost exclusively used as transparent building elements. Only with glazings is it possible to clearly see through and moreover the thermal — as well as the optical — properties have significantly improved in recent years so that today they can be referred to as technically superior.
If the solar irradiance strikes a transparent building element, part of the incident energy will be re-flected (ρe), i.e. directed back to the exterior, a part will be absorbed (αe) and a part will be trans-mitted (τe) from the building element into the building interior (Fig. 6.2). Based on the conservation of energy one obtains:
ρe + αe + τe = 1 (-)
The absorbed solar irradiance produces a warming of the building element. A part of this heat flows into the building interior. The total solar energy transmittance g denotes the proportion of the incident solar energy that is converted into heat in the interior and consists of the solar transmit-tance τe and the secondary internal heat transfer factor qi.
Total solar energy transmittance: g = τe + qi (-)
The solar transmittance τe depends on the incidence angle of solar radiation, the material proper-ties and on the geometric structure of the transparent building element. Also the secondary internal heat transfer factor qi depends on these quantities and is ultimately determined by the surface temperature occurring on the interior side as well as the heat transfer coefficient.
Fig. 6.2: Definition of solar transmittance τe, secondary internal heat transfer factor qi and total solar energy transmittance g
The thermal transmittance U results from the heat transport mechanisms in the transparent build-ing element — conductance in the material, conductance and convection in the gas filling and thermal radiation — plus the heat transfer coefficients at the exterior and interior surfaces.
Figure 6.3 shows energy properties of different glazings. Plotted are the total solar energy transmit-tance g and the thermal transmittance U. In order to minimize the heating demand in winter, glaz-ings with U-values (losses) as small as possible and g-values (gain) as large as possible are most suitable. A data point in the upper left corner of the figure corresponds to the highest gain/loss ra-tio. The more layers of glass panes and gaps in a glazing, the higher will be its thermal resistance (→ smaller U-value), but the solar radiation that passes through will be less (→ smaller values of τe
ie qg += τ
Total solar energy transmittance
Solar transmittance τe Incident solar radiation
Solar reflectance ρe
Secondary internal heat transfer factor qi
Transparent building element
Solar absorption αe
Transparent Building Elements 110
and g). The optical and thermal processes that determine these specific values will be investigated in the following.
Fig. 6.3: Total solar energy transmittance and thermal transmittance for double and triple glazings
6.2 Optical Properties of Glazings
In this section it will be examined how solar radiation is transmitted through a glazing (see e.g. also [6.2]). Given is a planar transparent layer that is absorbing but not scattering. The conservation of energy requires for a ray of light:
A + R + T = 1
A designates the absorption, R the reflection and T stands for the transmission. Fresnel’s Law for reflection of unpolarized light on a boundary layer between two mediums 1 and 2 gives (Fig. 6.4):
+−
++−
⋅=)(tan)(tan
)(sin)(sin
122
122
122
122
21R
φφφφ
φφφφ
The angle φ denotes the deflection of the light rays from a normal to the boundary layer. According to Snellius’ Law, n1 and n2 denote the refraction indices of both mediums, it gives:
2211 nn φφ s ins in ⋅=⋅
For normal (φ1 = 0) incident light it gives:
2
21
21
+−
=nnnnR
For a glass-air-boundary layer with n1 ≈ 1 (air) and n2 ≈ 1.5 (glass) and for normal incident light, the result is a degree of reflection R = 0.04.
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
Tota
l sol
ar e
nerg
y tra
nsm
ittan
ce g
(-)
Thermal transmittance U (W/(m2K))
Double glazings
Triple glazings
Transparent Building Elements 111
Fig. 6.4: Reflection und refraction of a light ray on a boundary layer between two mediums with different refraction indices
The intensity of a light ray decreases exponentially as it traverses a medium. According to the Bouguer-Lambert’s Law the transmission factor T' for a light ray in a medium with an absorption coefficient κ and the local coordinate x in the direction of the light ray is:
xe'T ⋅−= κ
Figure 6.5 shows how a light ray strikes a transparent layer (e.g. a glass pane). The amount of the total reflectance, absorptance and transmittance, ρ, τ and α, can be calculated from the quantities R and T', that are given by the material properties and the angle of incidence.
Fig. 6.5: Light paths in traversing a glass pane
The part R of the striking light is reflected. The part (1 – R) penetrates the material and is weak-ened by crossing through the layer due to absorption by the factor T'. The total transmittance τ is a result of the summation of the individual transmitted rays:
( )...''')( +++−= 44222 TRTR1TR1τ
This infinite geometric series can be added as follows:
22
22
0
22
111
'TR'T)R('TR'T)R( m
m
m
−−
=−= ∑∞
=
τ
With the same approach one obtains the total reflectance ρ:
( )
−−
+= 22
22
TR1R1T1R'
'ρ
φ1
φ2
T
R
n1
n2
n1 < n 2
R + T = 1
T’
air n1 ≈ 1
glass n2 ≈ 1.5
R
air n1 ≈ 1
(1-R)2⋅T’ (1-R)2⋅R2⋅T’3
R⋅(1-R)2⋅T’2
Transparent Building Elements 112
Based on the conservation of energy the total absorptance can now also be calculated:
α = 1 - ρ - τ
With very weak absorbing glazings is T' ≈ 1 and the total reflectance is determined only by the re-fraction index:
RR
+⋅
=12ρ
For a glass pane surrounded by air, very weak absorbing glass panes and normal light incidence (R = 0.04) one obtains ρ = 0.077. According to Fresnel’s Law the reflectance increases with in-creasing angle of incidence. With the same procedure of tracing the path of the light ray as shown in Figure 6.5, the values ρ, α1, α2 and τ of a double pane glazing can also be deduced. Figure 6.6 shows for a double glazing the angle dependence of reflectance ρ and transmittance τ , as well as the absorptance in the two glass panes α1 and α2. For φ1 → 90° all radiation will be reflected.
Fig. 6.6: Influence of the incidence angle of the solar radiation on transmittance, reflectance and absorptances (external and internal pane) of a double glazing [6.3]
The optical properties of transparent layers are in general dependent on the wavelength. Figure 6.7 shows the influence of the iron-oxide content on the spectral transmittance of a glass pane. Iron-oxide is an impurity that gives the glass a green tint. To reach high solar transmittances, e.g. in solar collectors, glass panes with limited iron-oxide content are used. Glass is opaque to radia-tion with wavelengths of λ > 3 µm. For thermal radiation of bodies at room temperature, glass is, therefore, opaque.
Incidence angle (°)
Tran
smitt
ance
, ref
lect
ance
, ab
sorp
tanc
e (%
)
Transparent Building Elements 113
Fig. 6.7: Influence of iron-oxide content on the spectral transmittance of 6 mm thick glass panes with normal light incidence [6.4]
The integral transmittance of a glazing for solar irradiance I(λ,φ) is dependent on both the wave-length and the angle of incidence. For a specific incident angle φ the solar transmittance can be calculated as follows:
∫
∫∞
∞
⋅
⋅⋅=
0
0
λφλ
λφλφλτφτ
d),(I
d),(I),()(
e
e (-)
The integral reflection can be determined analogously.
In the determination of the transmittance of visible light τv, the eyes’ sensitivity will additionally be considered [6.6]. The light transmittance with regard to providing daylight into the interior is also an important characteristic value of the glazing (see Building Physics III).
By means of very thin coatings (ca. 0.1 µm), notably metallic, the optical and thermal properties of the glazing can be modified. Insulating glazings should have a high transmittance for solar radi-ance (0.3 µm − 3 µm), including light (0.38 µm − 0.78 µm) and a little thermal transmittance.
To avoid a possible cooling load in a building it can be worthwhile to employ a glazing that selec-tively transmits solar radiation. Such solar control glazings should have a high light transmittance (0.38 µm − 0.78 µm), yet only a small transmittance for infrared solar radiance (0.78 µm − 3 µm). Figure 6.8 shows the spectral transmittance and reflection of a solar control glazing.
The spectral selectivity indicates how selective solar radiation is transmitted corresponding to the ratio between light transmittance τv and the total solar energy transmittance g.
Spectral Selectivity: g
S vτ= (-)
Solar control glazing possess spectral selectivity from e.g. 1.6; glazings without coatings and tint-ing from about 1.05 to 1.1. Glazings with S ≈ 1 are designated as non-selective.
0.02% Fe2O3 (colorless glass)
0.50% Fe2O3 (green glass)
0.10% Fe2O3 (standard-float-glass)
Wavelength λ (µm)
Tran
smitt
ance
τ (−
)
1.0
0.5
0 1.0 2.0 3.0 0.2
Transparent Building Elements 114
Fig. 6.8: A solar control glazing selectively transmits solar radiation [6.5]
6.3 Thermal Properties of Glazings
In order for the heat loss in a building to not be too large, windows must also exhibit, in addition to good optical properties, good thermal properties, i.e. a thermal resistance as high as possible. The heat flow through windows can be divided into two areas: (i) glazing and (ii) rim (spacer and frame). The heat flux in the rim region is in general higher than in the glazing, which is why the ar-ea of the frames should be kept low.
Fig. 6.9: Heat transport mechanisms in a glazing
The heat transfer in the gap between the glass panes takes place due to heat conduction, convec-tion, and radiation (Fig. 6.9). The heat transfer coefficient for convection and conduction (c.f. sec-tion 1.2.3) can be expressed as follows:
0
0.2
0.4
0.6
0.8
1
0.5 1 1.5 2 2.5
Tran
smitt
ance
or r
efle
ctan
ce (-
)
Wavelength (µm)
Transmission
Internal reflexion
External reflexionvisible
Heat conduction in spacer
warm kalt
Heat conduction in glass pane Heat conduction in gas filling
Convection in gap
Radiation exchange with the interior
Radiation exchange with the exterior
Convective heat transfer to the exterior
Convective heat transfer to the interior
Radiation exchange in the gas space
Transparent Building Elements 115
dPr),Ra(Nu
gasλΛ ⋅
= (W/m2K)
d denotes the distance between the panes, λ the conductivity of the gas filling and Nu the Nusselt Number (Nu = dimensionless number that indicates how many times larger the heat transport due to convection and heat conduction is compared with heat conduction only; see [6.7]). The heat transfer coefficient for thermal radiation between the two glass surfaces amounts to (c.p. section 1.3.2):
−+
⋅
+
⋅=111
12
TT421
321
r εεsΛ
//
(W/m2K)
T and ε denote the temperatures (unit: Kelvin) and emissivities, respectively, of both glass surfaces in the gap. The Stefan-Boltzmann-constant is s = 5.67·10-8 Wm-2K-4.
The total heat transfer coefficient in the gap is given as:
rgastot ΛΛΛ += (W/m2K)
The thermal transmittance of a glazing Ug additionally contains the contribution of the internal and external heat transfer resistances plus the thermal resistances of glass panes 1 and 2:
e2
2
tot1
1
ig h1d1d
h1
U1
++++=λΛλ
(m2K/W)
The thermal resistance of the glass panes d1/λ1 and d2/λ2, respectively, are small in comparison to the other quantities. By replacing the air in the gap with a gas with better properties (noble gases such as argon, krypton and xenon), the thermal insulation properties of the glazing can be im-proved (Tab. 6.1).
Table 6.1: Thermal conductivity, thermal diffusivity and kinematic viscosity for air and different gases at 10°C [6.7, 6.8]
Figure 6.10 shows the influence of different filling gases on the heat transport by convection and conduction in a gap as a function of the distance between panes. With small distances between panes the heat loss due to conduction is dominant. With larger distances between panes, due to a temperature difference in the glazing, the gas on the warm side rises up and sinks down on the cold side (convection). Depending on the physical properties of the gas, the convection is initiated at different distances between panes and a different heat flow results with a given distance be-tween panes.
Figure 6.11 shows the influence of one or two low-emissivity coating(s) on the radiative heat trans-fer in the gap. Today low-emissivity coatings with ε < 0.05 are commercially available. If both glass surfaces in the gap are coated in this way, the heat transfer coefficient for thermal radiation will reach values of about 0.1 W/m2K (Fig. 6.11). In contrast, the heat transfer coefficient for convection and conduction, even with a krypton- or xenon-filling, cannot be brought significantly below 1 W/m2K. Therefore, in modern glazings the heat transport through the gas filling is the dominant mechanism for heat loss.
Air Argon Krypton Xenon
Thermal conductivity λ (W/mK) 2.496⋅10-2 1.684⋅10-2 0.900⋅10-2 0.533⋅10-2
Thermal diffusivity a (m2/s) 2.010⋅10-5 1.910⋅10-5 1.032⋅10-5 0.575⋅10-5
Kinematic viscosity ν (m2/s) 1.429⋅10-5 1.274⋅10-5 0.674⋅10-5 0.377⋅10-5
Transparent Building Elements 116
0
0.5
1
1.5
2
2.5
3
0 0.01 0.02 0.03
AirArKrXe
Distance between panes (m)
Hea
t tra
nsfe
r coe
ffici
ent Λ
gas(W
/m2 K
)
∆T = 15 K
Fig. 6.10: Heat transfer coefficient for convection and conduction Λgas in a gap as a function of the distance between panes for different gas fillings ([6.9], calculated according to [6.7])
0
0.1
0.2
0.3
0.4
0.5
0 0.02 0.04 0.06 0.08 0.1Emissivity ε
1, ε
2 (-)
One pane coated(uncoated ε
1 = 0.84)
Two panes coated
Hea
t tra
nsfe
r coe
ffici
ent Λ
r (W/m
2 K)
Fig. 6.11: Heat transfer coefficient for thermal radiation in a gap between two glass panes as a function of the emissivities of the surfaces at 10°C [6.9].
Table 6.2 gives numerical values for Ug and g as well as the transmittance for visible light τV of glazings. Comparing to an older air-filled double glazing with a Ug = 3 W/m2K, the heat that flows with a given temperature difference through a modern triple glazing with a Ug = 0.5 W/m2K is only a sixth!
The spacers at the edges hold the glazing together mechanically and prevent the leakage of the filling gas (Fig. 6.12). The heat conduction through the spacer however increases the heat flux at this location. In winter, due to lower surface temperatures, if condensation occurs on the internal surface of the glazing, this is the most likely location.
Transparent Building Elements 117
In calculating the heat flow through a glazing, the thermal bridge effect of the spacer is evaluated with a linear thermal transmittance (Table 6.3).
Table 6.2: Values for Ug, g and τv of glazings [6.3](* with 10 % air)
Fig. 6.12: Cross-section of the edge region of an insulating glazing [6.10].
Table 6.3: Values for the linear thermal transmittance Ψ of different spacers [6.3]
Because glazings, spacers and window frames possess different insulation properties, these three regions must be considered separately in the calculation of the thermal transmittance of windows. Figure 6.13 shows a cross-section of a window in an exterior wall and the parameters to calculate
Ug (W/m2K)
g (-
)
τ v (-
)
Ug (W/m2K)
g (-
)
τ v (-
)
Spacer Ψ (W/mK)
Glazing
Ug (W/m2K)
glass
spacer
primary seal
secondary seal desiccant
Transparent Building Elements 118
the global thermal transmittance of the window Uw. The thermal transmittance of the window can now be calculated as follows:
w
ffggw A
LAUAUU
⋅+⋅+⋅=
ψ (W/m2K)
Ug Thermal transmittance of the glazing W/m2K Uf Thermal transmittance of the frame W/m2K ψ Linear thermal transmittance of the glazing edge W/mK Ag Projected area of the glass m2 Af Projected area of the frame m2 L Length of the glazing edge (spacer) m Aw Projected area of the window (Aw = Ag + Af) m2
Fig. 6.13: Cross-section through a window in a wall opening
Table 6.4: Uf –values for different window frames [6.3]
In addition, the interface between the window and the wall is accounted for with a linear thermal transmittance ψWall.
ψWall – wall interface
ψ - glazing edge
Uf Ug
Frame
Uf
(W/m2K)
Transparent Building Elements 119
6.4 Energy Fluxes Through Windows
The greater the thermal transmittance U and the greater the temperature difference between the interior and exterior is, the greater will be the transmission heat loss through the glazing. The solar energy flux produces a heat gain through the glazing and will be greater the greater the total solar energy transmittance g is and the greater the solar irradiance I is.
If IgU ⋅>⋅ θ∆ : Net energy loss
If IgU ⋅=⋅ θ∆ : Equilibrium (loss = gain)
If IgU ⋅<⋅ θ∆ : Net energy gain
Which situations arise now with different glazings in varying climates and according to the facade orientation? The energetic quality of a glazing can be expressed by the ratio g/U (c.p. Fig. 6.3) and the exterior climate by the quotient ∆θ/I. The interior temperature is assumed to be 20°C. Figure 6.14 shows that in Zurich in December (old) air-filled and uncoated double glazings at all façade orientations produce mean monthly heat losses. Because the solar irradiance on the north facade is the least, the net losses here are the greatest. In contrast a modern triple glazing exhibits, espe-cially on the south but also on the west and east facade, a positive monthly balance. In Figure 6.14 α denotes the gain-to-loss ratio:
θα
∆⋅⋅
=U
Ig
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2
g/U
(m2 K
/W)
∆θ/I (m2K/W)
Wes
t
α = 1/2
α = 1/4
α = 4α = 2
α = 1/8α = 1/16
α = 8 α = 1
Sou
th
Eas
t
Nor
th
Gain Loss
Triple glazing
Double Glazing
U = 0.4 W/m2K, g = 0.47
U = 1.0 W/m2K, g = 0.60
U = 2.9 W/m2K, g = 0.77
Single glazingU = 5.9 W/m2K, g = 0.87
Double Glazing
Fig. 6.14: Net gain and loss, respectively, through different glazings with different façade orienta-tions [6.15] (climate data for Zurich-SMA, monthly mean values for December [6.11])
6.5 Solar Shading Devices
Solar shading is understood as all methods that inhibit an over-heating of the interior from solar ir-radiation. Solar shading devices can be either fixed with respect to time, i.e. unchangeable, or var-
Transparent Building Elements 120
iable. The solar shading can be placed at different locations: at the exterior, integrated in the win-dow or at the interior (Table 6.5).
Variability with time Location Variable Fixed Exterior - textiles
- venetian blinds - overhangs
Integrated in window - roller blinds - textiles - venetian blinds - electrochromic devices
- solar control glazing
Interior - curtains - venetian blinds
Table 6.5: Classification of solar shading devices
External shading devices have the great advantage in that they can give off the absorbed solar en-ergy directly to the exterior surroundings (Fig. 6.15). With internal shading devices the absorption of the solar irradiance occurs within the thermal insulation. This is – with regards to over-heating of the interior – very disadvantageous. With external shading devices, therefore, significantly lower total solar energy transmittances can be achieved compared with internal ones.
Fig. 6.15: Energy flows and temperature profiles with external and internal shading devices
Fixed shading devices such as overhangs use the seasonal differences of the sun’s position: the sun’s altitude is small in winter and large in summer. These solar shading devices are however es-pecially suitable to screening direct solar irradiance on south facades. Their effect is limited with east and west facades and with respect to diffuse radiation. Fixed shading devices furthermore of-ten block a significant part of the daylight (zenith light), also during times when the solar irradiance is low, which is of course very disadvantageous.
In addition to the light transmittance τv, the total solar energy transmittance g is the most important property of a shading device. The total solar energy transmittance g applies to a layer sequence, e.g. for a triple glazing with external venetian blinds. Not only the optical properties of all the layers but also, for example, the thermal resistance of the glazing (U-value) influences the resulting g-value. The total solar energy transmittance indicates which portion of the incident solar energy with closed solar shading will accumulate as heat in the interior space. Total solar energy transmittanc-es g < 0.15 are easy to achieve with external or integrated, well (possibly mechanical) ventilated, solar shading devices and should be strived for.
g
Internal shading
Tem
pera
ture
g
External shading
Tem
pera
ture
Transparent Building Elements 121
Due to the multitudes of possible combinations it is reasonable in critical cases (e.g. with highly glazed office buildings), to determine the g-value of a transparent building element either experi-mentally (solar calorimeter) or numerically. Because the optical properties of the solar shading de-vices and glazings are in some cases strongly wavelength dependent, a calculation of the total so-lar energy transmittance (and the light transmittance) must be carried out, in general, wavelength dependent. Thus a solar control glazing can, for example, transmit well visible radiation, but be vir-tually opaque for infrared radiation (c.p. e.g. Fig. 6.8). Slats of venetian blinds can e.g. have a simi-lar solar reflectance but a very different visible reflectance (e.g. beige w.r.t. dark red in Table 6.6). Specialized software for planning purposes is available for the spectral calculation of τv and g that also contain data bases with numerous commercially available glazings and solar shading devices (e.g. [6.12]). With glass double-skin facades the occurring airflow patterns are important to the re-sulting total solar energy transmittance [6.13, 6.14].
Color Solar Visible UV Color Solar Visible UV
yellow VSR-720 0.552 0.493 0.068 light green 3040-G 0.274 0.320 0.071
white VSR-010 0.742 0.837 0.084 bronze VSR-780 0.252 0.249 0.155
grey VSR-130 0.392 0.461 0.079 dark green VSR-220 0.185 0.097 0.068
aluminum VSR-140 0.489 0.490 0.549 dark blue VSR-440 0.271 0.130 0.069
light beige VSR-240 0.585 0.575 0.087 dark red VSR-330 0.356 0.092 0.062
beige VSR-110 0.327 0.342 0.081 black 8505 0.064 0.065 0.063
Table 6.6: Weighted reflectances in three wavelength intervals for different colors of slats of vene-tian blinds [6.5]
In the selection of a suitable system from the many possible combinations of glazings and solar shading devices in different types and sequences (external/integrated/internal) and varieties of ventilation (natural/mechanical), one should bear the following in mind:
- An external, variable solar shading device is basically the best solution, if the costs, demands and architectural expression allow for it.
- The further inside a solar shading device is located, the more energy will be transmitted into the interior. From the shading device, absorbed energy can more easily flow into the interior, the lower the thermal resistance between the shading device and the interior is compared with the thermal resistance between the shading device and the exterior (→ U-value glazing).
- Solar shading devices fully or partially made of opaque materials can also serve as glare shields. However conflicting demands can arise.
- Venetian blinds (external, integrated or internal) also allow, to a certain extent, a redistribution of the daylight (light guiding due to reflection on the slats).
- The selection of shading device and glazing is also significant with regards to the resulting in-ternal surface temperatures and thermal comfort (chapter 3). Highly absorbing layers, especially if arranged on the internal side, have an adverse effect in summer.
- With wind exposed situations as with high-rise buildings, buildings in the mountains, etc. the wind pressure on the shading device must practically always be reduced with external glass panes: integrated solar shading – naturally ventilated to the exterior or with a mechanical venti-lation system – or solar control glazing.
- Electrochromic layers as shading devices, i.e. smart glass (switchable), are still in the develop-mental stages but could become more meaningful in the long term (costs, switching hub, ser-vice life, appearance).
Transparent Building Elements 122
Problems
Problem 1: Energy fluxes with glazings in winter
Given are two glazings:
(i) Double glazing: Ug = 1.2 W/m2K and g = 0.61
(ii) Triple glazing: Ug = 0.5 W/m2K and g = 0.45
The external and internal temperatures are θe = -5°C and θi = 20°C, respectively. Through these glazings the interior gains energy due to solar radiation, but also loses energy due to heat trans-mission.
a) Formulate the energy fluxes assuming an equilibrium of gains and losses. b) How great is the critical solar irradiance under these conditions, above which a net energy
gain for the interior results? c) With what weather conditions can this irradiance be reached? Problem 2: Temperature of a solar control glass
A glass pane (αe = 0.52) is placed as an apron in front of a facade. Calculate the temperature of the glass with the following boundary conditions:
θe = 35°C, he = 12 W/m2K, I = 600 W/m2, θi = θe and hi = 10 W/m2K.
Problem 3: Heat transport in a double glazing
Given is a double glazing with a krypton gas filling. The thicknesses of the glass panes are 6 mm each and they are spaced 10 mm apart. Both inner glass surfaces are coated (ε1 = 0.04 and ε2 = 0.08) and Λgas = 1 W/m2K can be taken for the heat transfer coefficient in the gap. The thermal conductivity of the glass is λ = 1 W/mK and the heat transfer coefficients at the glazing surfaces can be taken as he = 25 W/m2⋅K and hi = 7.7 W/m2⋅K, respectively.
a.) Draw the thermal flow diagram for the glazing including all thermal resistances.
b.) Calculate the thermal transmittance coefficient Ug, assuming that the average surface temper-ature in the gap is 5°C.
c.) Calculate the percentage of the thermal resistances ‘heat transfer at surfaces’, ‘glass panes’ and ‘gap’ assuming that the total resistance is 100%.
Problem 4: Thermal comfort next to a glazing in summer A double glazing possesses the following properties:
- thermal transmittance Ug = 1.3 W/m2⋅K - solar absorptance in the external pane α1 = 0.07 - solar absorptance in the internal pane α2 = 0.28 The boundary conditions are given by: - Solar irradiance I = 600 W/m2 - external air temperature θe = 33°C und internal air temperature θi = 26°C
- heat transfer coefficients he = 20 W/m2⋅K and hi = 8 W/m2⋅K Calculate the temperature of the internal pane and interpret your result.
Transparent Building Elements 123
Problem 5: Solar protection at an exposed location A restaurant with a mountain vista is planned in the alps. At this location, the external temperature can go down to -20°C and the solar irradiance reaches values up to 900 W/m2. Due to wind expo-sure an external shading system is not possible. Please comment on which and how parameters of the glazing must be chosen in order that
a) with low external temperature and little solar irradiance, the internal surface temperature lies as close as possible to the room temperature?
b) the glazing warms up only a little if the solar irradiance is high?
c) behind the glazing with high solar irradiance (direct sunshine!) one could still eat comfortably?
Problem 6: Secondary internal heat transfer factor of a single glazing Calculate the secondary internal heat transfer factor qi of a single glazing as a function of the inter-nal and external heat transfer coefficients (hi and he respectively) as well as the solar absorptance of the glass pane αe: a.) As a generally valid formula (hint: apply the conservation of energy, the definition of qi as well
as the assumption „internal temperature = external temperature“)
b.) with he = 25 W/m2⋅K, hi = 7.7 W/m2⋅K and αe = 0.1
Literature [6.1] Platzer W., Wittwer V., Transparent Insulation Materials, Chapter 3, in: Materials Science
for Solar Energy Conversion Systems, Ed. Granqvist C.G., Pergamon Press, Oxford, 1991
[6.2] Goetzberger A., Wittwer V., Sonnenenergie: Thermische Nutzung, Teubner, Stuttgart, 1989
[6.3] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[6.4] Duffie J.A., Beckman W.A., Solar Engineering of Thermal Processes, John Wiley & Sons, New York, 1991
[6.5] Manz H., Frank T., Thermal simulation of buildings with double-skin façades, Energy and Buildings, Vol. 37, 2005, 1114-1121
[6.6] EN 410, Glas im Bauwesen – Bestimmung der lichttechnischen und strahlungsphysikali-schen Kenngrössen von Verglasungen, Europäisches Komitee für Normung, Brüssel, 1998
[6.7] EN 673, Glas im Bauwesen – Bestimmung des Wärmedurchgangskoeffizienten (U-Wert) Berechnungsverfahren, Europäisches Komitee für Normung, Brüssel, 1997
[6.8] ISO/DIS 15099 (Draft), Thermal Performance of Windows, Doors and Shading Devices – Detailed Calculations, ISO Central Secretariat, Geneva, Switzerland, 2003
[6.9] Manz H., On minimizing heat transport in architectural glazing, Renewable Energy, Vol. 33, 2008, 119–128
[6.10] Platzer W. J., Fenster und Verglasungen, in: Thermische Solarenergienutzung an Gebäu- den (Hrsg: Marko A., Braun P.), Springer-Verlag, Berlin, 1997
[6.11] SIA 381/2, Klimadaten zu Empfehlung 380/1 „Energie im Hochbau“, Schweizerischer Inge-nieur- und Architekten-Verein, Zürich, 1991
[6.12] GLAD, Glasdatenbank und Rechenprogramm, Eidgenössische Materialprüfungs- und For-schungsanstalt, Dübendorf, 2008
[6.13] Manz H., Schaelin A., Simmler H., Airflow patterns and thermal behavior of mechanically ventilated glass double façades, Building and Environment, Vol. 39, 2004, 1023-1033
Transparent Building Elements 124
[6.14] Manz H., Total solar energy transmittance of glass double façades with free convection, Energy and Buildings, Vol. 36, 2004, 127-136
[6.15] Manz H., Menti U.-P., Energy performance of glazings in European climates, Renewable Energy 37 (2012) 226–232
Chapter 7
Air Exchange
Air Exchange 126
7 Air Exchange Due to wind and/or temperature differences, pressure differences can occur between the interior and exterior that produce airflows through the air leakages in the building envelope. If the windows and doors are closed the air exchange will particularly occur through joints in the building enve-lope. This unintentional air exchange is called infiltration (= airflow to interior) and accordingly exfil-tration (= airflow to exterior). The air exchange through open windows will be referred to as natural ventilation and that with an air-handling system as mechanical or controlled ventilation.
The air exchange in an interior room must satisfy requirements in the following areas:
— Indoor air quality: low concentration of pollutants (dust, allergens, smoke, etc.) and odors
— Thermal comfort: air velocity and turbulence not too high, air temperature and humidity within the comfort range
— Building construction and humidity: prevention of mold growth (removal of humidity that is pro-duced in the interior) and building damage (danger of moisture penetration into building com-ponents at leakages)
— Heat loss: minimize the energy consumption for heating
With regards to air quality and the removal of moisture, a high air change rate is advantageous. For thermal comfort and to keep the heat losses small, a low air change rate is demanded, where the requirements relating to heat losses are significantly stricter. The requirements listed above are partly conflicting as regards the air change rate in a room. One is confronted with a dilemma!
On the grounds of indoor air quality and to remove moisture, about a half of the air volume in an interior room must typically be replaced per hour in residential buildings. The heat loss due to the air exchange is secondary with poorly insulated buildings. If the thermal insulation is improved then the heat transmission losses decrease, i.e., that relatively the ventilation losses gain significance. If the building is well insulated, then the ratio of the ventilation heat losses to the total heat loss in-creases to more than a half (Fig. 7.1): The ventilation heat losses become larger than the trans-mission heat losses!
Fig. 7.1: Ratio of ventilation heat losses to total heat losses (total = transmission + ventilation) in a building [7.1]
For buildings in a climate with cold winters as in Switzerland, the solution to the dilemma concern-ing the air exchange described above is:
(i) The building envelope shall be as air-tight as possible [7.2].
Air change rate (1/h)
Rat
io o
f ven
tilat
ion
heat
lo
sses
to to
tal h
eat l
osse
s (-
)
Insulation level:
„Average“
„Low“
„High“
Air Exchange 127
(ii) The necessary air exchange (in winter) should be provided for by mechanical ventilation with heat recovery (Section 7.6).
In addition to the already mentioned features the ventilation can additionally be used to cool a building at night to keep it comfortable in summer (Section 7.7).
7.1 Wind Pressure on the Building Surface
When wind blows against a building, the pressure distribution on its surface changes. This topic will be considered in the following and the most important phenomena will be presented.
Bernoulli’s equation (Daniel Bernoulli, 1700-1782) describes a frictionless, incompressible, steady-state flow. Such an idealized flow in the vicinity of an obstacle is shown in Figure 7.2.
Fig. 7.2: Idealized flow around a cylinder
According to Bernoulli, for two points on the same streamline the following applies:
112100
20 phgv
21phgv
21
+⋅⋅+⋅⋅=+⋅⋅+⋅⋅ ρρρρ
p0 static pressure at reference point (free, undisturbed flow) Pa v0 velocity at reference point (reference velocity) m/s p1 static pressure at a given point Pa v1 velocity at a given point m/s ρ density of air kg/m3 g gravitational acceleration (g = 9.81 m/s2) m/s2 h height m
2v21
⋅⋅ ρ
dynamic pressure Pa
hg ⋅⋅ρ gravitational pressure Pa
p static pressure Pa
For small height differences — as e.g. with buildings — the gravitational pressure can approximate-ly be left out. Thus through rearrangement of Bernoulli’s equation the pressure difference between the reference point 0 and a given point 1 is obtained:
( )21
2001 vv
21ppp −⋅⋅=−= ρ∆
v1 < v0 : ∆p > 0 positive pressure (p1 > p0), with v1 = 0: 20v
21p ⋅⋅= ρ∆ (stagnation pressure)
Reference Point Streamline
h0 h1
v1, p1 v0, p0
Air Exchange 128
v1 > v0 : ∆p < 0 negative pressure (p1 < p0)
Velocity field and pressure distribution are coupled together. According to the flow pattern and the occurring velocities, in certain areas of the building envelope a higher pressure and in other areas a lower pressure will result.
In reality airflow around buildings also give rise to other phenomenon such as “flow separation” and “turbulence” that cannot be described by Bernoulli’s equation (Figures 7.3 and 7.4). On the up-stream flow side (= windward) the Bernoulli equation approximately gives good values, however not for the backside (= leeward side).
Fig. 7.3: Flow separation with real flow und leeward side wake zone
Fig. 7.4: Visualization of streamlines and eddy formations with smoke from air flowing diagonally against a square “building” in a wind tunnel test [7.3]
The flow around buildings is particularly dependent on:
— wind velocity and direction
— terrain properties in the vicinity of the building (wind profile see chapter 2)
— geometry of the building (basic shape, roof inclination, overhangs and protrusions)
— neighboring buildings
Figure 7.5 schematically shows the airflow around a rectangular building. In front of the building an eddy develops. Sharp corners and edges give rise to flow separation and wake flows behind the building.
flow separation wake
Air Exchange 129
Fig. 7.5: Airflow around a rectangular building (left: side view, right: perspective depiction)[7.3]
Figure 7.6 schematically shows the pressure distribution on the surface of a building due to a per-pendicular oncoming airflow. On the windward side of the facade a positive pressure occurs and a negative pressure on the roof as well as the side and leeward facade. The wind profile (cp. chapter 2) is dependent on the terrain properties (surface roughness) in the vicinity of the building. Different wind profiles give rise to different pressure distributions on the building surface.
Fig. 7.6: Schematic pressure distribution on the surface of a building due to a perpendicular on-coming airflow. (above: side view, below: top view) [7.3]
The occurring pressure on the building envelope is characterized by the pressure coefficient Cp. These coefficients refer to the dynamic pressure of the undisturbed airflow (stagnation pressure). The static pressure on the building envelope is designated by pF.
20p0F v
21Cpp ⋅⋅⋅=− ρ
Cp-values for typical building geometries and different airflow directions are available in the litera-ture. In utilizing these mostly experimentally determined values it is however necessary to use cau-tion. Among other things, because e.g. from neighboring buildings the incoming flow conditions on real buildings can deviate from the situations in experiments and thus develop different pressure distributions on the building surface.
Air Exchange 130
Fig. 7.7: Airflows between buildings
If two or more buildings are close to each other new flow patterns can develop compared with the case of a building without any neighboring buildings. Figure 7.7 shows some flow effects between buildings. With complicated situations wind tunnel tests can depict the expectable flow pattern (Fig. 7.8). With larger building projects such tests are sometimes conducted. The laws of similarity must be considered in wind tunnel experiments. In recent years research on airflow around and in build-ings has increased with the help of simulations (→ computational fluid dynamics = numerical fluid mechanics).
Fig. 7.8: In a wind tunnel test the streamlines that form with a group of buildings can be made visible with smoke.
Figure 7.9 shows the calculated frequency distribution of wind-induced pressure on a building fa-cade. The wind velocity v0 was taken from a weather data file [7.5] for the not very wind exposed location of Zurich-SMA; with a density ρ = 1.2 kg/m3 and pressure coefficient Cp = 0.1 / 0.5 / 1, re-spectively. The figure shows that in Zurich the wind-induced pressure is smaller than 2 Pa about 50% of the time. However, wind-induced pressures can often rise up to tens of Pascals.
„Gap effect“ „Nozzle effect“ „Redirection effect“
Air Exchange 131
Fig. 7.9: Calculated frequency distribution of wind-induced pressure on a building facade as a function of the pressure coefficient Cp at location Zurich-SMA (height 10 m above ground)[7.4]
7.2 Thermally Induced Pressure Differences
The air pressure p decreases exponentially with increasing height above ground in the still, iso-thermal atmosphere:
0
0p
hg
0 ephp⋅⋅
−
⋅=ρ
)(
p0 pressure at ground level ρ0 density at ground level g gravitational acceleration h height above ground
For small height differences, such as e.g. height differences in buildings, the equation can be line-arized:
hgphp 00 ⋅⋅−≈ ρ)(
The pressure difference ∆p between a reference height with an average pressure pm (z = 0) and height z thus amounts to:
zgzppzp 0m ⋅⋅=−= ρ∆ )()(
The temperature of the interior and exterior air and consequently also the density are often dif-ferent, so that the pressure increase from below to above proceeds differently.
zgzp ii ⋅⋅= ρ∆ )( respectively zgzp ee ⋅⋅= ρ∆ )(
Applying the ideal gas law (p = ρ⋅R⋅T), which describes the interrelationship between pressure, density and temperature, one gets for the pressure difference ∆pie between the interior and exteri-or:
−⋅⋅⋅⋅=−=
iemieie TT
zgR
p)z(p)z(p)z(p 111∆∆∆
20p0F v
21Cpp ⋅⋅⋅=− ρ
0
10
20
30
40
50
.1 1 5 10 20 30 50 70 80 90 95 99
99.9
Win
d-in
duce
pre
ssur
e on
the
faca
de (P
a)
Fraction of time (%)
Cp = 0.1
Cp = 0.5
Cp = 1
Air Exchange 132
R gas constant for air R = 287.1 J/kg⋅K
g acceleration of gravity g = 9.81 m/s2
pm atmospheric air pressure pm ≈ 95’000 Pa
Based on the reference height (z = 0), where the neutral zone with pi = pe = pm is located, in build-ings with Ti > Te a linear upwardly increasing positive pressure occurs with increasing coordinate z (Fig. 7.10). In halls, open stairwells (large heights) and chimneys (large temperature differences) considerable pressure differences can occur.
Fig. 7.10: Pressure profiles interior (warm) and exterior (cold)[7.6]
The spatial distribution of leakages in the building envelope influences these pressure differences between the interior and exterior. With a vertically uniform distribution of air leakages the neutral zone is located in the middle of the facade height. If one leakage is very much larger than all oth-ers, the neutral zone will shift towards this location.
Figure 7.11 shows thermally induced pressure profiles in multi-story buildings. In case A a large permeability exists between the individual stories and the pressure develops uninterrupted over the entire facade height. With full air-tightness between stories (case B), only the height of a story can be effective. With actual buildings (case C) mostly a mixture of both limit cases A and B is encoun-tered. It consists of neither full permeability nor complete tightness between stories. With regard to the total airflow resistance in a building interior, vertical shafts, e.g. staircases, are especially im-portant. The flow resistance is here much smaller than with the air leakages between stories.
Figure 7.12 shows a frequency distribution of the thermally induced pressure difference between the interior and exterior. The external temperature Te is taken from weather data for Zurich-SMA and the internal temperature Ti at 293 K or 20°C. The thermally induced pressure differences oc-curring in Zurich are mostly smaller than about 10 Pa.
warm cold
Stack effect Pressure profiles
Air Exchange 133
Fig. 7.11: Pressure profiles for multi-story buildings with varying leakage characteristics [7.6]
-5
0
5
10
15
.1 1 5 10 20 30 50 70 80 90 95 99
99.9
Ther
mal
ly in
duce
d pr
essu
re d
iffer
ence
s be
twee
n in
terio
r and
ext
erio
r (P
a)
Fraction of time (%)
z = 1 m
z = 5 m
z = 10 m
Fig. 7.12: Cumulative frequency distribution of thermally induced pressure differences between the interior and exterior as a function of the distance from the neutral zone at the location Zurich-SMA
[7.4]
7.3 Airflow Through Leakages
Due to wind (Section 7.1) or temperature differences (Section 7.2) pressure differences occur over the building envelope. In comparison to the atmospheric air pressure, approximately 95'000 Pa in Zurich, these pressure differences are very small (Fig. 7.13).
B. Air-tight floor levels A. Permeable floor levels
C. Permeable floor levels with staircase
Air Exchange 134
Fig. 7.13: Thermally and wind-induced pressure differences (θi = 20°C)
Air leakages in the building envelope can occur with window or door joints, connections (e.g. wall-floor or wall-roof), ductwork (installations), or built-in components (window frames, roller shutter housings). The airflow through such joints or gaps can be described as follows:
( )mpDV ∆⋅=
V air flow rate m3/h
D coefficient, characterizing permeability m3/h·Pam
∆p pressure difference over the leakage Pa
m exponent, dependent on the type of flow
m = 1: fully laminar; m = 0.5: fully turbulent -
The flow-exponent is often taken as m = 2/3, because actual flows through leakages are generally neither fully laminar nor fully turbulent. The permeability coefficient D for a joint can be described as follows:
laD ⋅=
a air leakage coefficient m3/(h·m·Pam)
l joint length m
The air-tightness of windows and doors can be determined in a laboratory experiment as a function of the different pressures [7.7]. Today’s window construction exhibit air leakage coefficients from about 0.01 to 0.04 m3/(h·m·Pa2/3), older windows and doors with poor sealing or no gaskets pos-sess air leakage coefficients from about 0.2 to 0.6 m3/(h·m·Pa2/3). Figure 7.14 shows the influence of the air leakage coefficient on the airflow rate per meter of joint length that arises with a given pressure difference.
−⋅⋅⋅⋅=
iemie T
1T1zg
R1pp∆
20p v
21Cp ⋅⋅⋅= ρ∆
Wind-induced pressure difference:
Thermally induced pressure difference (θi = 20°C):
0
5
10
15
20
-20 -10 0 10 20
0 1 2 3 4 5
Pre
ssur
e di
ffere
nce
∆p (P
a)
External air temperatur θe (°C)
Wind speed v0 (m/s)
z = 10 m
z = 5 m
Cp = 1
z = 1 m
Air Exchange 135
0
2
4
6
8
10
12
0 20 40 60 80 100a = 0.02 m3/(h m Pa2/3)
Air
flow
rate
per
met
er o
f
join
t len
gth
(m3 /h
m)
Pressure difference ∆p (Pa)
a = 0.1 m3/(h m Pa2/3)
a = 0.5 m3/(h m Pa2/3)
Fig. 7.14: Air flow rate per meter of joint length as a function of the pressure difference and air leakage coefficient
The wind-induced air exchange in a building with two openings can be modeled as shown in Figure 7.15. This arrangement can be considered with an analogy to electrical circuits as a series connec-tion of two resistors. According to the above equation it gives:
( )( )m
i
mi
ppDV
ppDV
222
111
−⋅=
−⋅=
The continuity equation (inflow = outflow) stipulates that
21 VV =
If the pressures on the facade, p1 and p2, as well as the parameters to describe the leakage flows, D1, D2 and m, are known then from the three equations the three unknowns, the interior pressure pi and the airflow volumes, 1V and 2V respectively, can be calculated. Contrary to Ohm’s law for elec-trical circuits the equations are however nonlinear (m = 2/3).
Fig. 7.15: Wind-induced air exchange in a building with two openings
Problems with multiple openings and zones (= areas with constant pressure) can be solved analo-gously. An example for a multi-zone scheme is shown in Figure 7.16. In addition to the airflow re-sistances in the building envelope resistances also occur in the building interior (doors). In each room a different interior pressure arises.
( ) 32pal
V /∆⋅=
Air Exchange 136
Fig. 7.16: Floor plan with corresponding network [7.6]
7.4 Indoor Air Quality
The indoor air should not contain any substances hazardous to health and should feel fresh and comfortable. By the term indoor air quality one means the non-thermal aspects of the interior air that is relevant to both the well-being and health of people. Pollutants in the indoor air can stem from different sources:
— Polluted outside air
— Sources of air pollution in the interior
— Radon in the ground
Especially in urban areas (traffic, heating, industry), the outside air has certain pollutants. Due to allergic reactions pollen can also, for example, be considered a pollutant. With mechanically venti-lated buildings there is the possibility to reduce the concentration of certain pollutants in the supply air with suitable filters. It makes most sense of course to avoid having pollution sources and not to have to provide excessive ventilation. For the interior rooms this means that construction materials and above all interior finishes (timber products, joint sealants, floor coverings, etc.) should be used that emit only very limited or no pollutants (solvents, fungicides, formaldehyde, etc.). A careful choice of materials based on clear product declarations can possibly avoid a lot of frustration and health ailments.
Certain pollutants cannot be avoided with the use of rooms. These substances must be removed by exchanging the air. In order to remove the exhaled carbon dioxide and body odors, a supply of fresh air of about 15 to 30 m3/h per person is recommended. As a relatively simple measurable quantity that characterizes the “freshness” of the room air, the concentration of carbon dioxide is generally used. As an upper limit of the hygienic range 1500 ppm (= 0.15 Volume-%) is recom-mended. The CO2-concentration of the external air amounts to just under 400 ppm.
Radon is a radioactive gas that can be emitted from certain rocks. The main source of radon is the ground below a building. The level of radon emissions depends largely on the geologic formation, which is why the radon emission throughout Switzerland is very different. High levels are particular-ly found in the regions of Graubünden, Ticino and Jura (Fig. 7.17).
Air Exchange 137
Fig. 7.17: Radon map of Switzerland based on interior room measurements [7.8]
According to the Swiss Federal Office of Health (2008) 200 to 300 people die in Switzerland each year from radon caused lung cancer. Hence radon is the most dangerous carcinogen in residential areas and is after smoking the greatest cause for lung cancer. The risk of lung cancer is greater the higher the radon concentration in the inhaled air is and the longer one breathes in this air.
Whether radon can penetrate into a house depends primarily on how tight the house foundation against the ground is. Especially disadvantageous therefore are buildings without a foundation slab made of concrete but with e.g. a pebble stone floor (high permeability between ground and indoor spaces), which otherwise possess a relatively tight building envelope. The influx of radon is there-by possible, but the exfiltration is hampered so that an accumulation is possible.
The most important measures to hinder the harmful radon accumulation in the interior rooms are therefore: (i) to minimize the radon entry from the ground by sealed basements, i.e. foundation slab made of concrete and possibly a film, (ii) airtight floors separating the cellar and living space sto-ries, as well as (iii) avoiding negative pressure in the building interior.
7.5 Airtightness of the Building Envelope
Thermally or wind-induced pressure differences over openings such as joints, open windows and doors produce an exchange of interior air with exterior air. This air exchange is also influenced by the building design (properties of the building envelope, arrangement of the interior rooms) and the building operation (opening/closing of windows and doors as well as possible use of air extract units). With a mechanical ventilation system pressure is produced on the room openings by fans that cause an air exchange.
Generally effective is that the building envelope which encloses the heated volume be as tight as possible. The required quantity of external air is ensured through the manual opening of the win-dows, other ventilation openings or through air-handling units [7.2].
The interior air is in general not still but is propelled by different causes:
- Upward and downward drafts result from temperature differences (such as cold window surfac-es, warm radiators, people and appliances, e.g. computers)
- Movement (people, fans, possible vehicles)
- Momentum of supply air (mechanical ventilation or window ventilation)
BAG 2007
Air Exchange 138
However, air flow patterns in the room are not of further interest here but instead the global degree for the exchange of interior air by exterior air. The so-called air change rate n indicates how often the room air is exchanged per hour:
VVn
= (1/h)
V air flow rate interior-exterior m3/h
V volume of room m3
The airtightness of a building envelope can be experimentally determined by means of the pres-sure difference method (blower door test) [7.9]. For the measurement in the building envelope in-stalled fans, mostly in a door, produce a pressure difference between the interior and exterior (Fig. 7.18). To eliminate weather influences as much as possible, this artificially produced pressure dif-ference must be significantly larger during the measurement than the naturally occurring pressure difference on the building envelope. The leakage airflow rate is measured as a function of the pressure difference over the building envelope. This relationship can be described by the flow equation for joints or gaps (section 7.3). The air change rate with a pressure difference of 50 Pa is denoted by n50.
Fig. 7.18: Pressure difference method to determine the air-tightness of a building envelope: princi-ple (left) and a blower installed in a door (right)
If a negative pressure is produced in the building interior with the blower installed in the building envelope at low external temperatures, the cooling of the inner surface of the building envelope can be visualized with an infrared image and thereby indicate where the leakages can be found in the building envelope.
With a carefully planned and executed building envelope an air-tightness value of n50 < 0.6 1/h (= requirement for passive house standard [7.10]) can be reached. However, it is somewhat easier to achieve lower values of n50 the more compact and large the building is, because the volume in-creases by the third power, while the envelope area increases only by the second power.
In the SIA standard 180 [7.2] the specific value used for the air-tightness of the building envelope refers to the envelope area Ae and a pressure difference of 4 Pa:
⋅= 2
3
e
44a mh
mAVv
,
∆p
V
( )mpDV ∆⋅=
∆p
V
Positive internal pressure
Negative internal pressure
Air Exchange 139
The ratio between the two specific values va,4 and n50 depends on the building geometry:
e
m
e50
4a
AV20
504
AV
nv
., ≈
=
m denotes the flow exponent (section 7.3). Table 7.1 shows the maximum allowable value for the air permeability of the building envelope according to SIA 180. For mechanically ventilated build-ings the target values are to be met.
va,4 max (m3/h⋅m2)
Limit value Target value
New construction 0.75 0.5
Renovation 1.50 1.0
Tab. 7.1: Limit- and target values for the air permeability of building envelopes [7.2].
To reach as much as possible the target of a continuously air-tight building envelope, the air tight layer of the construction has to be carefully designed and appropriate materials have to be chosen (i.e. concrete, plastered masonry, airtight membrane). With present day carefully constructed and executed envelopes, general connection interfaces of every kind are where leakages dominate (e.g. window/wall, wall/roof), especially also at ducts for electrical conduits (plugs) and pipes from sanitation or other technical installations. Careful workmanship and intermediary inspections on the construction site are recommended. The high air-tightness must not only be provided at the close of construction but must also be preserved during the service life of the building.
7.6 Mechanical Ventilation with Heat Recovery
The natural ventilation of buildings is often not considered optimal, because due to wind and tem-perature conditions as well as not clearly defined leakages, unwanted air exchanges arise. In con-trast a mechanical ventilation system can regulate the air exchange based on need. Many living, work, and school spaces are however only used for a small amount of the time. Contaminants need to be removed by ventilation only when someone occupies a room. If, e.g., a room is in use eight hours a day on weekdays, then the average time use is only 24%!
It makes sense to equip an air-handling unit with the possibility for heat recovery whereby in winter a significant portion of the ventilation heat losses (up to about 80 %) can be saved. Mechanical ventilation with heat recovery is thus an essential measure in a climate with cold winters in provid-ing buildings with a very low energy demand (e.g. Minergie or passive house). A prerequisite for the application of these systems is a tight building envelope.
Generally there are many possible systems to ventilate residential buildings (Fig. 7.19). However, for low energy buildings in climates with cold winters only ventilation systems with heat recovery are suitable.
Air Exchange 140
Fig. 7.19: Systems for residential ventilation [7.11]
Fig. 7.20: Residential ventilation system with a ground heat exchanger and heat recovery [7.10]
A typical residential ventilation system for low energy buildings is displayed in Figure 7.20. In addi-tion to the controlled supply and extract air flows and the heat recovery, a ground heat exchanger is often used. A ground heat exchanger consists of nearly horizontal pipes that are buried in the ground about 1.5 m to 3 m deep around the building excavation or also under free surfaces (e.g. a garden or a parking lot). In winter the cold outside air flows through these pipes in the warm ground (cp. section 2.3), whereby a preheating of the fresh air is obtained. In summer the ground heat ex-changer can also be used for cooling the air as needed, because the ground temperature is then in general considerably below the exterior air temperature.
Ground heat exchanger
Ventilation system with heat recovery
Natural Mechanical without heat recovery
Window Shaft central decentral
Residential ventilation
central decentral
Supply and extract air Extract air
Heat ex-changer: recuperator regenerator
Mechanical with heat recovery
Supply and extract air
Supply and extract air
Heat ex-changer and heat pump
Heat ex-changer: recuperator regenerator
Heat ex-changer and heat pump
Heat pump
Extract air Extract air
Air Exchange 141
In a mechanically ventilated housing unit it makes sense to supply the air where the fresh air de-mand is high and the odor and humidity load is relatively small, i.e. in bedrooms and living rooms. Through open doors or (acoustically insulated) air supply openings, the air then ends up e.g. in a corridor and from there out into the rooms with the most contaminants, namely in the bathroom/WC and kitchen, from where it is ultimately extracted (Fig. 7.21).
Fig. 7.21: Principle of cascades for mechanical ventilation [7.12]
7.7 Passive Cooling by Night-time Ventilation
The air exchange between the interior and exterior can also be applied to cool the building in summertime. Passive cooling by night-time ventilation takes advantage of the outside night air-temperature being mostly below the room temperature, which is generally the case in Switzerland also in summer. If a window is opened in a building at night, then the cool air flowing in can reduce the temperature of the interior building materials so that on the following day a heat sink is availa-ble to absorb the thermal load (Fig. 7.22). The windows can be opened and closed either manually or with automatically functioning mechanisms (→ rain- and wind sensors). Passive cooling by night-time ventilation is the simplest method of building cooling and requires practically no auxiliary energy! The climatic potential for this technology is considerable in a large part of Europe [7.13], especially in central, eastern and northern Europe.
Fig. 7.22: Principle of passive cooling by night-time ventilation: charging (warming up) and dis-charging (cooling down) the massive structural building elements with heat in day/night cycles
To reach a high level of thermal comfort in a non-airconditioned building, it is important, along with sufficiently cool air at night [7.14]:
— minimize the thermal loads
— sufficiently large air exchange (→ cross ventilation)
— enough (activatable) thermal mass in the room interior (e.g. concrete ceiling)
Solar gains
Internal gains
Supply air Extract air
Bedroom Living room Corridor
Bathroom Toilet
Kitchen
Through-flow zone
Air Exchange 142
This means that the external loads (size and orientation of the glazed areas, solar protection de-vices) as well as the internal loads (appliances, lighting) must be kept as small as possible. The larger the air exchange during the night the better the heat can be removed. With cross ventilation, the (window) openings are here placed on opposite sides of the room; a higher air exchange can practically always be achieved than with a single-sided ventilation. Driving forces are temperature differences as well as wind-induced pressure differences. The interior building elements must pos-sess a high heat capacity to produce a satisfactory effect. Concrete ceilings are suitable for this but also massive walls and floor construction. Thermal resistances between the room air and storage elements have an adverse effect, such as e.g. suspended ceilings, subfloors or carpets. In today’s office building construction the concrete ceiling is often the most important storage element.
Figure 7.23 shows a section through an office building with an atrium in which the cold external air flows through open windows, ideally flowing primarily as as a jet along the exposed concrete ceil-ing (bottom hung window) and in doing so absorbing the heat, and subsequently leaving the room through a second opening on the opposite side of the room (cp. also Fig. 7.22). In the middle of the atrium the warm air can rise and escape to the outside through openings in the roof.
Fig. 7.23: Passive cooling by night-time ventilation: airflow in an office building during the night [7.15]
Problems
Problem 1: Air exchange in an assembly hall
An assembly hall with a volume of 800 m3 offers space for a maximum of 100 people.
a) How great must the air exchange with the exterior be, in order to guarantee the air quality in the interior (carbon dioxide and odor)? Calculate the air exchange n assuming that a person re-quires 15 m3/h of fresh air.
b) The space has two opposite walls each with windows with a total joint length of 80 m each. All the air leakage coefficients are 0.05 m3/(h·m·Pa2/3). How great is the air exchange that arises with a pressure difference of 10 Pa over each of the joints of both walls (high- and low pressure respectively)?
Problem 2: Wind pressure and air exchange A floor plan for an apartment with a volume V = 200 m3 is given (drawing). The facades 1 and 2 have windows with the following joint characteristics:
Atrium Office Office
Air Exchange 143
- a1 = 0.2 m3/(h m Pa2/3) and l1 = 36 m
- a2 = 0.2 m3/(h m Pa2/3) and l2 = 18 m
Facade 1 is blown on by wind with a velocity of v0 = 5 m/s (ρ = 1.2 kg/m3). The pressure coeffi-cients are Cp1 = 0.8 and Cp2 = -0.4. Calculate:
a) the pressures p1 and p2 on the facade (Note: 2021p21 v
21Cp ⋅⋅⋅= ρ,, )
b) the relative interior pressure pi (Note: It can be assumed that all the interior apartment doors are open so that the same pressure prevails in the entire apartment).
c) the air flow rate V through the apartment.
d) the air change rate n between the interior and exterior.
e) the ventilation heat flow Q (heat loss) with a temperature difference of 30 K between the interi-or and exterior ; KmJ1200c 3
aa =⋅ ρ
Problem 3: Wind pressure on a living room glazing
How great is the wind pressure (assume stagnation pressure) and the force on a living room glaz-ing (3.62 m x 2.48 m) with each of the following wind velocities?
v1 = 50 km/h v2 = 100 km/h v3 = 150 km/h (ρ = 1.2 kg/m3)
Problem 4: Stack effect
In a 12 m high building a large window is opened below (z = 0 m), otherwise all the openings are closed. The interior temperature is 22°C, the exterior temperature and atmospheric air pressure are θe = 0°C and pe = 95'000 Pa respectively. The roof is finished on the inside with planking with-out a moisture or air barrier and is not airtight (a = 0.2 m3/(h m Pa2/3), joint length l = 120 m).
a) Where is the neutral zone located? Draw qualitatively the interior/exterior pressure profile.
b) What interior/exterior pressure difference results on the roof?
c) How great is the air flow rate through the planking?
1
2
Air Exchange 144
d) With this, how much water vapor is transported per hour if the room humidity is ρWD = 10 g/m3 (corresponding to 50 % relative humidity in the interior)?
Problem 5: Characteristic air-tightness values of a building envelope
In a single-family house (interior volume V = 400 m3, envelope area Ae = 400 m2) the values D = 100 m3/(h Pam) and m = 0.6, respectively, have been experimentally determined for the function
mpDV ∆⋅= .
a.) Calculate the n50- and va4-values.
b.) What relative pressure (sign?) develops in the building, if without additional openings an air-handling unit with an air flow rate of 100 m3/h is put into operation?
Literature [7.1] Moser A., Dorer V., Grundlagen der Raumluftströmung, Bundesamt für Energiewirtschaft (BEW) und Verband Schweizerischer Heizungs- und Lüftungsfirmen (VSHL), 1994 [7.2] SIA 180, Wärme- und Feuchteschutz im Hochbau, Schweizerischer Ingenieur- und Ar-
chtekten-Verein, Zürich, 1999 [7.3] Moor H., Physikalische Grundlagen der Gebäudeaerodynamik im Hinblick auf die Berech-
nung des Luftaustausches, Eidgenössische Materialprüfungs- und Forschungsanstalt, 1987 [7.4] Manz H., Huber H., Helfenfinger D., Lüftungstechnische und energetische Eigenschaften
von Einzelraumlüftungsgeräten mit Wärmerückgewinnung, 11. Schweiz. Status- Seminar Energie und Umweltforschung im Hochbau, ETH Zürich, 2000
[7.5] Meteonorm 6.0 (Edition 2007), Datenbanksoftware, Meteotest, Bern; http://www.meteonorm.com
[7.6] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[7.7] EN 12207, Fenster und Türen – Luftdurchlässigkeit - Klassifizierung, Europäisches Komitee für Normung, Brüssel, 1999
[7.8] Bundesamt für Gesundheit; http://www.bag.admin.ch/themen/strahlung, 2008
[7.9] SN EN 13829, Wärmetechnisches Verhalten von Gebäuden – Bestimmung der Luftdurch-lässigkeit von Gebäuden – Differenzdruckverfahren, Europäisches Komitee für Normung, Brüssel, 2000
[7.10] Passivhaus Institut, D-64283 Darmstadt; http://www.passiv.de, 2008
[7.11] Recknagel/Sprenger/Schramek, Taschenbuch für Heizung + Klimatechnik, R. Oldenburg Verlag, München, 1997
[7.12] Huber H., Komfortlüftung – Projektierung von einfachen Lüftungsanlagen im Wohnbereich, Faktor Verlag, Zürich, 2004
[7.13] Artmann N., Manz H., Heiselberg P., Climatic potential for passive cooling of buildings by night-time ventilation in Europe, Applied Energy, Vol. 84, 2007, 187-201
[7.14] Artmann N., Manz H., Heiselberg P., Parameter study on performance of building cooling by night-time ventilation, Renewable Energy (available online April 7, 2008)
[7.15] Bob Gysin & Partner BGP Architekten, Eawag Forum Chriesbach – ein nachhaltiger Neu-bau, Zürich, 2006
Chapter 8
Non-Steady-State Behavior of a Room
H·[θi(t)- θe(t)]
θi θe
G·I(t)
P’int
P’hc
System
Non-Steady-State Behavior of a Room 146
8 Non-Steady-State Behavior of a Room Buildings are subjected to variable boundary conditions with respect to time: given externally by the weather and internally by the use. Accordingly the temperatures of the building elements and the interior air fluctuate. In this chapter it will be shown which parameters determine the non-steady-state (= dynamic) thermal behavior of the interior and the influence of these parameters will be discussed. The fundamental strategy that leads to the minimization of energy needs for heating and cooling will be introduced and the consequences for design and construction will be drawn-out.
In the planning practice simulation programs are increasingly used to investigate the non-steady-state thermal behavior of buildings as well as to optimize the comfort and minimize the energy re-quirements. It will be illustrated with examples how the thermal comfort in an office building in summer can be analyzed with these tools.
8.1 Energy flows in a room
A room or an entire building represents an energy system (Fig. 8.1), in which different energy flows occur. These flows transfer energy in or out of the room. Thereby the stored heat in the room and consequently also its temperature is changed. The following energy flows occur:
- transmission heat flow - ventilative heat flow - solar radiation - heat absorption and heat release of building elements - internal heat sources - heating and cooling power -
Fig. 8.1: Energy flows in a room
Corresponding to the temperature difference between the interior and exterior, heat flows through all elements of the building envelope by transmission. The heat flow is greater the larger the ther-mal transmittance coefficient U and area A of the individual building elements are.
Transmission heat flow: ( ) ∑=
⋅⋅−=totk
kkkeiT UAQ
1θθ (W)
θi interior temperature °C θe exterior temperature °C Ak area of k-th building element (wall, window, roof, etc.) m2 Uk thermal transmittance of k-th building element W/m2K
The greater the air exchange and the temperature difference between the interior and exterior are, the greater is the heat flow due to ventilation.
H·[θi(t)- θe(t)]
θi θe
G·I(t)
P’int
P’hc
System boundary
Non-Steady-State Behavior of a Room 147
Ventilative heat flow: ( )eiaaV cV3600
nQ θθρ −⋅⋅⋅⋅= (W)
n air change rate 1/h V volume of room m3
aρ density of air ( aρ ≈ 1.2 kg/m3) kg/m3
ac specific heat of air ( ac ≈ 1005 J/kgK) J/kgK
The energy exchange with the environment takes places at the exterior surface of the building, which is why the parameters below relate to the building envelope area Ae [8.1] (Note: In contrast to this the energy consumption of a building is in general related to the floor area (cp. Chapter 9). Ventilative and transmission heat losses can be described together with a loss coefficient (without thermal bridges).
Mean loss coefficient:
⋅⋅⋅+⋅⋅= ∑
=
totk
1k
aakk
e 3600cVnUA
A1H ρ (W/m2K)
Ae total building envelope area m2
Solar energy can enter the building interior through transparent building elements. Decisive is the total solar energy transmittance (section 6.1) of the different elements as well as their respective areas.
Mean total solar energy transmittance: AgA1G k
k
1kk
e
tot
⋅⋅= ∑=
(-)
gk total solar energy transmittance of k-th building element -
Heat can be stored in the interior building elements such as ceilings, walls and floors and later re-leased again. The specific heat per area is:
dcC kkkk ⋅⋅= ρ (J/m2K)
ρk density of k-th building element kg/m3 ck specific heat of k-th building element J/kgK dk effective thickness for heat storage of k-th building element (see section 5.2.3) m
The heat capacity of individual building elements can be added and related to the building enve-lope area.
Mean specific heat: dcAA1C
totk
1kkkkk
e∑
=
⋅⋅⋅⋅= ρ (J/m2K)
The thermal power that is given off by people and appliances as well as the heating and cooling power can likewise be related to the building envelope area.
Interior heat sources: A
PP'P
e
AppPersint
+= (W/m2)
Heating/cooling power: AP'P
e
hchc = (W/m2)
Non-Steady-State Behavior of a Room 148
8.2 Energy Balance in a Room
The equation for the conservation of energy can be applied to the room (Fig. 8.1). According to this equation the difference in the energy flowing in and flowing out of the room equals the change of stored energy in the room:
( ) ( ) ( )[ ]dtdCttHPPtIG i
eihcθθθ ⋅=−−++⋅ ''int (W/m2)
I solar irradiance W/m2
t time s
If one assumes that the room is neither heated nor cooled (P’hc = 0), and also no heat is given off by people and appliances (P’int = 0), then the natural room temperature or free-running temperature is reached. The energy balance equation can be written as follows [8.1]:
( ) ( ) ( )tIHGt
dtd
HCt e
ii ⋅+=⋅+ θθθ (°C)
The time-dependent room temperature θi is on the left side of the equation, and its derivative (= change) respectively. On the right side of the equation is the time-dependent weather, namely the external temperature θe and the solar irradiance I. Interestingly the characteristics of the room are described by only two characteristic values.
Time constant: HC
=τ (s or h)
Gain/loss-ratio: HG
=γ (m2K/W)
8.3 Time Constant and Gain/Loss-Ratio
As a first example, the cooling off of a building is considered to illustrate the time constant. Under the assumption that neither solar gains (G = 0) nor internal gains (P’int = 0) occur and it is neither heated nor cooled (P’hc = 0), the room temperature with respect to time θi (t) can be found analyti-cally from the solution to the following equation:
( ) 0dtdt i
ei =⋅+−θτθθ (°C)
The external temperature θe is assumed to be constant. An exponential function of the form
( ) ( )[ ] τθθθθt
eiei ett−
⋅−=+= 0 (°C)
( )0=tiθ room temperature at time t = 0 °C
τ time constant s or h
describes the solution to this equation. Figure 8.2 shows the influence of the time constant on the cooling down process. At time t = 0 the room temperature is at 20°C and the external temperature is constant at 0°C. The better the heat storage (C large) is, but also the better insulated and air-tight (H small) a building is, the larger is its time constant. Also the building geometry is of im-portance: the larger and more compact a building is, the smaller is its envelope area per volume, and the smaller is the thermal loss and the slower is the cooling down. The time constant thereby designates the time with which the temperature difference between the interior and exterior sinks to 1/e (= 36.8 %).
in - out = increase
Non-Steady-State Behavior of a Room 149
Fig. 8.2: Cooling down of buildings with different time constants
The second example illustrates the significance of the time constant τ, as well as the gain/loss-ratio γ. Figure 8.3 shows the external temperature and the solar irradiance on a south facade in May in Zurich. Assumed is a building with no interior gains (P’int = 0) and which is neither heated nor cooled (P’hc = 0):
( ) ( ) ( )tItdtdt e
ii ⋅+=⋅+ γθ
θτθ (°C)
In the Figures 8.4 und 8.5 the numerical solutions to this equation are shown for the weather data from Fig. 8.3 with different values of γ and τ..
-30
-20
-10
0
10
20
30
0
100
200
300
400
500
0 5 10 15 20 25 30
Ext
erna
l tem
pera
ture
θe (°
C)
Sol
ar ir
radi
ance
sout
h fa
cade
I (W
/m2 )
Time t (d)
Fig. 8.3: Weather data May 2005 (Zurich-SMA)
well insulated, airtight, large building with a high heat capacity
poorly insulated, non-airtight, small building with a low heat capacity 0
5
10
15
20
0 24 48 72 96 120
Inte
rnal
tem
pera
ture
θi (°
C)
Time t (h)
τ = 20 h
τ = 100 h
τ = 500 h
( ) ( ) τθθt
ii e0tt−
⋅==
Non-Steady-State Behavior of a Room 150
Fig. 8.4: Influence of time constant τ on the free-running temperature of the room
Fig. 8.5: Influence of the gain/loss-ratio γ on the free-running temperature of the room
Fig. 8.6: Influence of γ and τ on the room temperature
In general the time constant τ represents a measure for the thermal inertia of a building or room, i.e. the ability to remain unresponsive. The room is less responsive, the greater its storage ability, i.e. its specific heat per area (C) is, and respectively the smaller its thermal losses (H) are. The time constant τ increases, and respectively decreases, the amplitude of the room temperature fluc-tuations (Fig. 8.6). The gain/loss-ratio γ shifts the free-running temperature, and also influences the amplitude. High values of γ produce high room temperatures and large amplitudes. Buildings with
Comfort range
10
15
20
25
30
35
0 5 10 15 20 25 30
γ = 0.1 m2K/W
Time t (d)
Roo
m te
mpe
ratu
re θ
i (°C
) τ = 20 h
τ = 500 h
10
15
20
25
30
35
0 5 10 15 20 25 30Time t (d)
Roo
m te
mpe
ratu
re θ
i (°C
)
τ = 100 h
γ = 0.15 m2K/W
γ = 0.05 m2K/W
Comfort range
Too warm
Roo
m te
mpe
ratu
re
Comfort range
γ
γ
τ
Too cold
Non-Steady-State Behavior of a Room 151
large time constants are very fault tolerant. If for example the heating system fails temporarily, it will have almost no effect on the room temperature.
Figure 8.7 schematically shows the external temperature over the course of a year and the comfort range. In summer a somewhat higher temperature is preferred given that the people are then mostly lightly clothed. To design buildings that need little operating energy, the values of τ and γ should be selected such that the free-running temperature (including the heat given off from people and appliances) remains as long as possible in the comfort range. No or virtually no heating and cooling is then required.
Fig. 8.7: Free-running temperature of buildings and comfort range
The technical means to influence the two parameters τ and γ are:
Gain/loss-ratio: HG
=γ
Time constant: HC
=τ
In the selection of the two parameters τ and γ it should be noted that
- the time constant τ should be large to keep the room temperature fluctuations small
- a variable gain/loss-ratio γ makes it possible to influence the level of the free-running tempera-ture and to keep it in (or nearby) the comfort range (→ summer/winter)
Therefore, it is beneficial for the thermal behavior of a building to have:
- a small loss coefficient (H ↓): - a good insulation, which is free of thermal bridges - small (thermally relevant) air exchange:
- air-tight building envelope
Tem
pera
ture
Winter Summer Winter
“Ideal” building
“Poor” building
External air
Comfort range
Window areas, solar transmittances, orienta-tions, solar protection devices (variable)
U-values, areas, air exchange possibly with heat recovery, nigh-time ventilation (variable)
Internal surface areas, heat capacity of materials, layer thickness
U-values, areas, air exchange possibly with heat recovery, nigh-time ventilation (variable)
Non-Steady-State Behavior of a Room 152
- heat recovery in the air-handling unit - large heat storage capacity (C ↑) - variable solar gain: variable solar protection devices (G ↓↑) The building geometry is also relevant: Buildings with a small ratio of the envelope area to volume – i.e., large compact buildings – tend to exhibit higher time constants.
8.4 Building Simulation
The earlier considerations (section 8.2 und 8.3) are helpful in order to develop an understanding for the non-steady-state behavior of a building. As already mentioned, the parameters τ and γ are not constant for actual buildings because solar shading devices and windows can be opened or closed – whereby the characteristics of a building are considerably changed. Additionally, internal sources are time-dependent and the solar irradiance varies with time, depending however also on the orientation of the windows. Often the layer sequence of a construction is relevant to how well the heat can be stored. For precise questions regarding non-steady-state behavior of a building it is for these reasons common in practice to use the method of numerical building simulation [8.2] instead of an analytical or semi-analytical approach.
Building simulation can be applied particularly:
- to optimize the thermal comfort in summer and minimize the cooling load respectively, especial-ly for buildings with large glazed areas and relatively high internal loads (commercial buildings)
- to size cooling units (required maximum output) as well as to investigate control strategies
- to design low energy buildings: optimization of solar gains, sizing of solar collectors, etc.
The method of building simulation is based on a thermodynamic, as well as a fluid-dynamic, net-work model (Fig. 8.8). The strength of the method lies in that all the relevant energy flows in a building — building structure and HVAC systems — can be simulated at the same time. The exter-nal boundary conditions are given by the weather (air temperature, solar irradiance, etc.) and the internal boundary conditions through the use (heat given off from people and appliances). The non-steady-state heat transfer through the building envelope, but also the heat storage processes in the interior building elements, are taken into account. In the interior rooms it is often differentiated between convective and radiative heat transport. The overall energy conservation equation in the programs is typically solved in intervals of one hour. Many programs also allow the modeling of multiple zones.
Fig. 8.8: Network model for building simulation
θg
θi,2
θe
θi,1
θe
θe
θe
θg
θe
IS IN
θi,3
Non-Steady-State Behavior of a Room 153
8.5 Building Simulation Example: Office Room in Summer
In our climate particularly office buildings tend to overheat in summer because the internal loads (people and appliances) are generally higher than in residential buildings. In addition, modern of-fice buildings often are extensively glazed, that can also — depending on the solar protection de-vices and facade orientations — lead to considerable solar loads. West-orientated rooms are often at greatest risk, because in the late afternoon high solar irradiances and high external air tempera-tures occur simultaneously (Fig. 8.9), and at a time of day when the room can already be consider-ably heated up.
Fig. 8.9: Typical daily cycles of solar irradiances and external air temperature [8.3]
To illustrate the building simulation method [8.4] a west-orientated office room is considered with a 4 m × 5 m floor area, a room height of 2.6 m and a percentage of glass to facade area of 40% (0.4 × 2.6 m × 4 m = 4.16 m2 glass surface). It is assumed that the energy exchange between the room and the environment takes place solely over the facade (= adiabatic boundaries at the neighboring zones in the building). Windows and solar shading devices exhibit the following characteristics:
- thermal transmittance Uw = 1.1 W/m2K
- total solar energy transmittance without shading, gwithout = 0.6
- total solar energy transmittance with shading gwith = 0.15
- solar shading device closed, if I > 300 W/m2
The air exchange rate will be different according to the time of day, whereby a higher air exchange occurs at night for passive cooling (section 7.7):
- day: n = 2 1/h
- without night-time ventilation: n = 0.5 1/h
- with night-time ventilation: n = 6 1/h
Sola
r irr
adia
nce
(W/m
2 )
Time (h)
Exte
rnal
te
mpe
ratu
re (°
C)
Non-Steady-State Behavior of a Room 154
Ceiling, floor and wall of the room are constructed according to Fig. 8.10.
Fig. 8.10: Construction of ceiling, floor and wall
The internal heat loads are made up of the heat given off from people, appliances and lights and have a typical output in the course of the day for office use (Fig. 8.11).
Fig. 8.11: Course of internal loads in the day
With the help of building simulation it can now be investigated how both measures, solar shading and passive cooling by night-time ventilation, have an effect on the summery comfort. Figure 8.12 shows the course of the external temperature and solar irradiance on a west-facade in Zurich dur-ing a week in June. This course comes from a semi-synthetic DRY-weather data set (DRY = De-sign Reference Year) that corresponds to a “typical” year. In the simulation the time period from May 1 to September 30 is used.
The effectiveness of the solar shading and night-time ventilation is apparent in Figure 8.12. The comfort level reached is indicated through the operative room temperature (section 3.3). If neither solar shading nor night-time ventilation is deployed, then the operative room temperature stays in a range of about 33°C to 40°C! If either the solar shading or the night-time cooling is used then the average room temperature can be reduced by about 8 K. On sunny days the solar shading is more effective and on cloudy days the night-time ventilation is. The combination of both measures leads to a further reduction of the operative temperature by about 4 K.
gypsum board 2.5 cm mineral wool 7 cm gypsum board 2.5 cm
internal wall external wall
carpet 0.5 cm screed 8 cm impact sound insulation 4 cm concrete 18 cm
ceiling and floor
interior plaster 1.5 cm sand-lime brick 15 cm insulation 15 cm exterior plaster 2 cm
0
5
10
15
20
25
30
7 8 9 10 11 12 13 14 15 16 17 18 19 20
Zeit (h)
Last
(W/m
2 )
GeräteBeleuchtungPersonen
Appliances Lighting People
Time (h)
Non-Steady-State Behavior of a Room 155
Figure 8.13 shows the cumulative frequency distribution of the operative room temperature with the different measures. In this plot it is apparent what comfort level is reached at what amount of the time. If both solar shading and night cooling are used, the operative room temperature during the entire summer will remain below 26.5°C (= good comfort level) for the subject office room.
Fig. 8.12: Course of exterior climate (above) and operative temperature of the office room (below) during a week in June in Zurich
20
25
30
35
40
0 0.2 0.4 0.6 0.8 1
Ope
rativ
e ro
om te
mpe
ratu
re (°
C)
Fraction of time (-)
without shading / without night-time ventilation
without shading / with night-time ventilation
with shading / without night-time ventilation
with shading / with night-time ventilation
too warm
good comfort
Fig. 8.13: Cumulative frequency distribution of the operative room temperature (May 1 – September 30)
Temperature
Solarstrahlung
8
14
20
26
32
17.06. 18.06. 19.06. 20.06. 21.06. 22.06. 23.06. 24.06.
Tem
pera
tur (
°C)
0
200
400
600
800
Sol
arst
rahl
ung
(W/m
2)Zurich DRY
Sola
r irr
adia
nce
(W/m
2 )
Tem
pera
ture
(°C
)
18
22
26
30
34
38
42
17.06. 18.06. 19.06. 20.06. 21.06. 22.06. 23.06. 24.06.
Ope
rativ
e R
aum
tem
pera
tur (
°C)
Ope
rativ
e ro
om te
mpe
ratu
re (°
C)
with shading / without night -time ventilation without shading / with night-time ventilation with shading / with night-time ventila-tion
without shading / without night ven-tilation
Non-Steady-State Behavior of a Room 156
The strength of the method of building simulation lies particularly in that parameter changes can be quickly carried out and their impact on the level of comfort analyzed. Already in the planning phase it can be shown which comfort level can be reached with a given configuration of glazings, solar shading devices, building elements (walls, ceilings and floors), air exchange and internal loads.
Generally the following strategies help to achieve a high comfort level in summer without active cooling:
- minimize internal loads: energy efficient appliances and lighting
- minimize solar gains: areas and orientation of windows, effective (g < 0.15) solar shading devic-es
- good use of daylight: minimize electrical lighting (better luminous efficiency with sunlight!)
- large storage capacity of interior building elements: ceilings, walls and floors (Attention: thermal decoupling)
- passive cooling with night-time ventilation: storage capacity of interior building elements is im-portant!
8.6 Structural Consequences
In this section the parameters that determine the thermal dynamic behavior of an interior room or building (H, C and G and respectively τ and γ) have been presented. The influence of these pa-rameters on the free-running temperature of the building has been illustrated. The goal is to keep as long as possible the free-running temperature in the comfort range! Then a building can be real-ized that hardly needs energy for heating and cooling. This results in consequences for design and construction:
- loss coefficient H as small as possible: good insulation, high airtightness, mechanical ventilation with heat recovery, only ventilate as much as necessary
- heat storage capacity C as large as possible: interior building elements
- variable solar energy transmittance G: variable (external) shading devices
The non-steady-state behavior of buildings can be significant particularly in summer. Building simu-lation presents a valuable tool for analyzing problems of overheating in summer.
Problems
Problem 1: Cooling Down of a Single-Family House
The heating system of a single-family house heated to 20°C suddenly fails in winter. Calculate, un-der the assumption that there are no heat sources in the interior and no solar gains, the interior temperature after one hour, one day and one week. The external temperature of the environment is constant at 4°C. The ratio between the heat capacity and heat losses of the building is C/H = 200 h.
Problem 2: Warming of a Cold Storage House
A windowless, cubic, empty cold storage house out of concrete with an edge length of 10 m is in contact on all sides with the exterior climate and has a mechanical air exchange of n = 0.5 h-1 with a “cold recovery” (heat exchanger, h = 0.8; air: ρa = 1.2 kg/m3, ca = 1005 J/kgK). The air exchange
Non-Steady-State Behavior of a Room 157
due to infiltration is negligible. The building envelope is identically constructed on all six sides: 15 cm concrete on the inside (λC = 2.5 W/mK, ρC = 2400 kg/m3, cC = 1000 J/kgK) and 20 cm insulation on the outside (λIns = 0.04 W/mK). The interior room is cooled to 5°C, the exterior is at a constant temperature of 20°C. Suddenly the cooling system fails.
a.) Calculate the heat capacity C of the building. It can be assumed that the entire concrete
thickness is effective in heat storage. The storage capacity of the insulation can be neglect-ed.
b.) Calculate the loss coefficient H of the building. c.) Write the balance of energy flows. d.) Formulate from c.) the emerging differential equations using the time constant τ. e.) Determine the analytical solutions of the differential equations. f.) How large is the time constant of the building? g.) What temperature can be expected after 24 h, 72 h, 240 h and 720 h respectively in the inte-
rior? h.) Graphically illustrate the interior as well as the exterior temperature in the time interval 0 ≤ t ≤
1200 h.
Literature
[8.1] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006
[8.2] Clarke J.A., Energy Simulation in Building Design, Butterworth-Heinemann, London, 2001
[8.3] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004 [8.4] HELIOS, Gebäudesimulationsprogramm, Eidgenössische Materialprüfungs- und For-
schungsanstalt, Dübendorf, 2008
Chapter 9
Energy and Sustainability
Image: The Earth at night (a composite assembled from satellite images from NASA)
Energy and Sustainability 160
9 Energy and Sustainability Without the large use of energy human development would have taken an entirely different course in the last 200 years. The cheap availability of energy significantly shaped the development of the industry and service sectors as well as our society. Many technical achievements that we use to-day are based on the use of energy. Energy consumption and economic performance appears to be closely dependent on one another, whereby very large differences between different countries exist (Fig. 9.1).
100
1000
104
1000 104 105
Ene
rgy
cons
umpt
ion
per c
apita
(kg
oil e
quiv
alen
t/per
son
year
)
Gross national product per capita(US $/person year)
Switzerland
China Brazil
GermanyRussia
Nigeria
Bangladesh
Pakistan
USA
UAEBahrain
Katar
South AfricaMexico
EritreaSenegal
Columbia
UK
Ethiopia
Congo
Japan
Indonesia
Usbekistan
India
Fig. 9.1: Energy consumption and gross national product per capita in different countries
The use of energy is however increasingly linked with problems like environmental pollution, cli-mate change and shortage of resources. This set of problems will be briefly outlined in the follow-ing.
Energy is needed in transportation, buildings, industry and agriculture. Nearly half of the energy demand in Switzerland arises in buildings: heating, cooling, hot water, ventilation, lighting and ap-pliances. The building envelope design especially determines, quite significantly, the emerging en-ergy demand. The expenditure of energy must be considered during the full life cycle of a building: construction, operation, refurbishment, and lastly demolition (“embodied energy”). All of these as-pects will be highlighted and the strategies for sustainable buildings depicted. Thereby the reduc-tion of energy required for operation has a high priority.
9.1 Energy and Sustainability Challenges
The world population has dramatically increased in the last century (Fig. 9.2). Today (2014) 7.3 bil-lion people live on our planet. This corresponds to a growth by a factor more than four since the year 1900. According to a prediction by the UN the world population will increase to nearly 10 bil-lion by the year 2050, although the yearly growth is declining since about 1990 (2014: growth about 80 million).
Source: World Resource Institute & CIA World Factbook, 2007
Energy and Sustainability 161
0
1000
2000
3000
4000
5000
6000
7000
-1000 -500 0 500 1000 1500 2000
Pop
ulat
ion
(mill
ions
)
Year
2000: 6.07 billion
1900: 1.65 billion
1800: 0.98 billion1700: 0.6 billion
+ 268%
+ 68%+ 63%
Fig. 9.2: Development of the world population
In the beginning of the 1970s the general public became aware of the finiteness of the Earth and the ramifications of unregulated growth. This was, among other things, a consequence of the Club of Rome report The Limits to Growth [9.1]. In the earth’s system both the sources, i.e. the natural resources of materials and fossil fuels, and the sinks, i.e. the capacity of the environment to absorb all kinds of pollution as well as waste heat, are limited. Figure 9.3 (left) shows the estimated future depletion of the world’s natural gas reserves under the assumption that the present day supply can cover today’s consumption for 240 years. This means that three times more reserves exist than are known today. As an example for the anthropogenic burden on sinks, Figure 9.3 (right) shows the increase of the carbon-dioxide content in the atmosphere. This increase is a result of burning fossil fuels and the slash-and-burn of large forest areas. As has long been known, the increase of carbon dioxide in the atmosphere leads to the decrease of long-wave thermal radiation of the earth to out-er space and thereby to a warming of the earth’s surface with partially unpredictable consequences for people, animals and vegetation. The burden on sinks is largely seen as a greater threat than the depletion of resources.
0
50
100
150
200
250
2000 2050 2100 2150 2200 2250
Rem
aini
ng re
sour
ces:
rem
aini
ng ti
me
for
use
at to
days
con
sum
ptio
n ra
te (Y
ears
)
constant consumption rate
1 % increaseper year
5 % increaseper year
280
300
320
340
360
380
1830 1860 1890 1920 1950 1980 2010
Atm
osph
eric
CO
2 co
ncen
tratio
n (p
pm)
Keeling et al., 2005 (Mauna Loa, atmosphere)
Etheridge et al., 1998(ice cores)
Fig. 9.3: Depletion of global natural gas reserves [9.2](left) and increase of carbon dioxide in the atmosphere (right)
Source: U.S. Census Bureau, Popu-lation Division, 2007
Energy and Sustainability 162
Calculations from environmental economists have shown that the total human activities today ex-ceed the long-term carrying capacity of the earth by roughly a fourth (Fig. 9.4). That is to say, we actually need 1¼ Earths to be able to cover our current needs. This means that we use up re-sources faster than they are regenerated. In this context the term ecological footprint is often used. Like the per capita energy consumption, the ecological footprint per capita also varies very strongly according to country.
Fig. 9.4: Development of the ecological footprint of humanity compared to the long-term carrying capacity of the Earth [9.3]
In addition to the mentioned global limitations of resources and absorption capacity of the environ-ment, it is also essential to contain local pollution. Especially in air of urban areas, mainly as a con-sequence of combustion, considerable concentrations of particulate matter, nitrogen oxide (NOx), volatile organic compounds (VOC), sulfur dioxide (SO2) and ozone (O3) can arise that lead to res-piratory diseases.
Fig. 9.5: Development of energy consumption in Switzerland (1910-2006)[9.4]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1960 1970 1980 1990 2000
Num
ber o
f Ear
ths
ecological footprint of humanity
carrying capacity of the Earth
+
Energy and Sustainability 163
In the course of the 20th century the energy consumption in Switzerland (Fig. 9.5) increased by a factor of about eight! A notable growth in electricity, natural gas and petroleum took place in the last 30 years. The consumption of oil has slightly declined since the 1970’s. The renewable energy (wood, solar, geothermal, wind) still plays a marginal roll at this time. Overall consumption today appears to have somewhat stabilized but at a high level.
A totally different picture arises worldwide (Fig. 9.6). The international energy agency expects that from the years 2004 to 2030 the global energy demand will increase by about a half! Considering the population growth (Fig. 9.2) and the fact that the per capita consumption in many developing and emerging countries today still lies below Europe or North America by a factor of five to ten (i.e., that in many countries a huge pent-up demand for energy exists), this is not surprising.
Fig. 9.6: Development of global energy demand [9.5]
The use of fossil fuels (natural gas, oil, coal) gives rise to an immense release of carbon-dioxide. The worldwide CO2-emissions in the year 2004 amounted to about 26 gigatons (Giga = 109). Ac-cording to the International Energy Agency [9.5] this value will increase by the year 2030 from 34 Gigatons per year (“alternative policy scenario”) to 40 gigatons per year (“reference scenario”). Ac-cording to [9.5], a stabilization of emissions will be possible in 2030, at the earliest, particularly if energy efficiency and renewable energy are pushed further.
35.1 % Space heating
5.5 % Hot water2.7 % Ventilation & air conditioning
3.4 % Lighting1.4 % Information & communication
13.0 % Process heat
8.9 % Mechanical power, other processes
28 % Mobility (domestic)
2 % Others
Fig. 9.7: Energy use in Switzerland [9.6]
Reference Scenario
Prim
ary
ener
gy (M
toe)
Energy and Sustainability 164
The distribution of the Swiss energy requirements according to end-use shows (Fig. 9.7) that just under half of the requirements arise in buildings. The most important designated use is space heat-ing (35.1%), followed by hot water (5.5%), ventilation and air conditioning (2.7%) and lighting (3.4%). The sum gives that about 47% of the energy requirements in Switzerland occur in build-ings.
Also in many other industrialized countries buildings are responsible for a large portion of the total energy needs. For example, in the USA 39% of the primary energy is used in buildings, 29% in transportation and 32% in industry [9.7].
If different energy sources are assessed and compared with one another then the entire chain of energy conversion must be considered. So, for example, the crude oil from boreholes (primary en-ergy) is converted in the refinery into fuel oil (secondary energy), afterwards it is delivered to the consumer (end energy) and in the end converted into heat (useful energy). The definitions of terms used in the energy business are given in Table 9.1.
Definition Example
primary energy unprocessed energy crude oil, coal, uranium, hydro energy, solar energy
secondary energy (at least once) processed energy heating oil, fuel rods for nuclear power plants
end energy energy delivered to the consumer heating oil (delivered), electricity
useful energy effectively used energy heat, light, process energy, kinetic energy
Tab. 9.1: Definition of terms from the energy business
Buildings are not only important with respect to energy, but also regarding the flow of materials, because about half of the mass flow that our society generates is incurred in the construction sec-tor (Fig. 9.8). From this point of view the building can be seen as a gigantic temporary store of ma-terials. With renovation and demolition, waste is generated which is to date only partially recycled. Therefore, also waste disposal requirements arise and with that a need for – especially in densely populated areas – valuable land. With this the construction waste, depending on its composition, can leach pollutants into the soil and ground water over time at the disposal site. For that reason with the selection of materials not only the costs and appearance should be considered, but also the contaminant potential, the recyclability, the embodied energy and the influence on the direct energy consumption during operation.
Fig. 9.8: Material flows in the Swiss construction sector [9.8]
Energy and Sustainability 165
9.2 Heating Energy Demand
9.2.1 Balancing the Energy Flow in a Building
In this section it will be shown how the heating energy demand of a building can be calculated. In general only steady-state models are used [9.9, 9.10]. Energy that flows in and out of a building is balanced (Fig. 9.9) over a long time period, such as a month. The net heat loss corresponds to the heating energy demand Qh that is required to maintain a constant temperature in the building. It can be calculated as follows (nomenclature according to SIA 380/1):
( )siVTh QQQQQ +⋅−+= h (J)
QT transmission losses J QV ventilation losses J h utilization factor - Qi internal gains (people, appliances, lighting) J Qs solar gains J
Not all internal and solar gains are usable. The utilization factor corresponds to the portion of heat gain that can be used for space heating and is dependent on the heating demand and the storage capacity of the building, the control of the heating system (response time) as well as the user’s ac-ceptance of temperature fluctuations in the interior. The utilization factor for heat gain h can be ap-proximately determined from Figure 9.10 [9.9]. In this figure the utilization factor depends on the gain/loss ratio; the ratio between the total heat gain (Qi + Qs) and the sum of heat losses due to transmission and ventilation (QT + QV). Thus the utilization factor is high in winter and small in the transition period. The time constant of the building τ is given by the ratio between the heat capacity C and the loss coefficient H of the building, τ = C/H (compare chapter 8).
Fig. 9.9: Energy flows in a building assuming steady-state conditions
The energy losses and respective gains can be calculated as follows (compare Chapter 8). Trans-mission losses (including thermal bridges) are considered according to [9.9].
Transmission losses: ( )
⋅+⋅+⋅⋅⋅−= ∑ ∑∑
= ==
tot tottotk
1k
i
1iii
j
1jjjkkeiT zlUAtQ χψ∆θθ (J)
QT
θi θe
Qs
Qi
Qh
system
Energy and Sustainability 166
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3
50 h100 h200 h
Util
izat
ion
fact
or h
(-)
Gain/loss ratio (-)
Time constant τ
Fig. 9.10: Utilization factor for thermal gains in relation to the gain/loss ratio and the time constant of the building [9.9]
θi interior temperature °C θe exterior temperature °C ∆t time period (e.g. 1 month) s Ak area of k-th building element (wall, window, roof etc.) m2 Uk thermal transmittance of k-th building element W/m2K lj length of j-th linear thermal bridge (e.g. roof/wall-interface) m
ψj linear thermal transmittance of j-th thermal bridge W/mK zi number of i-th point thermal bridges (e.g. pillar) - χi point thermal transmittance of i-th thermal bridge W/K
Ventilation losses: ( ) tcV3600
nQ eiaaV ∆θθρ ⋅−⋅⋅⋅⋅= (J)
n air exchange 1/h V volume of room m3
aρ air density ( aρ ≈ 1.2 kg/m3) kg/m3
ac specific heat of air ( ac ≈ 1005 J/kgK) J/kgK
Solar heat gain: kk
k
1kkks GAgFQ
tot
⋅⋅⋅= ∑=
(J)
Fk reduction factor due to shading and frames of k-th building element - gk total solar energy transmittance of k-th building element - Gk solar irradiation on the k-th building element J/m2
Monthly mean values for exterior temperature and solar irradiation are available in the appendix for a number of Swiss locations in different climate regions. Standard values for internal thermal sources (people, appliances) for different uses (residence, office, indoor swimming pool, hospital etc.) are available in [9.9].
Energy and Sustainability 167
9.2.2 Heating Degree Days
The transmission and ventilation losses during a certain time period are proportional to (θi – θe)·∆t. One can assume that the heating system is only in operation if the time-averaged exterior air tem-perature eθ falls below a certain critical temperature, the so-called heating limit θli. To simplify the calculation of emerging heat losses during a heating period, the quantity HDD (Heating Degree Days) is defined.
HD (Heating Days) denotes the number of days during which the time-averaged exterior tempera-ture eθ falls below the heating limit θli. HDD designates the area between the curves iθ and
)(teθ for ≤eθ θli (gray area in Fig. 9.11). The heating limit depends on the thermal quality of the building. Well-insulated buildings exhibit low heating limit temperatures. The HDD- and HD-values are available for different locations and different heating limit temperatures (cp. SIA 381/2 in the Appendix).
Fig. 9.11: Daily mean values of exterior temperature eθ in the course of the year and heating de-gree days
The energy required to cover the transmission as well as the ventilation losses can be calculated as follows:
)(360024 JHDDAUQT ⋅⋅⋅⋅=
)(24 JHDDcVnQ aaV ⋅⋅⋅⋅⋅= ρ
The cooling degree days can also be calculated as with the heating, in order to calculate the cool-ing energy demand [9.11]. The accuracy is nevertheless not very high. Degree day methods pro-vide however a very consolidated picture of the climate. The disadvantage lies in that a heating and respectively a cooling limit must be assumed. In the current SIA 380/1 standard [9.9] the de-gree day method is not used for the heating demand calculation.
Energy and Sustainability 168
9.3 Protection Against Overheating in Summer
If a building is well designed it is possible in most cases in moderate central-European climates to ensure comfortable conditions in the interior rooms in summer without active cooling. If the building must nevertheless be cooled then the cooling load has to be minimized. Because comfort de-mands are increasing, buildings having large-area glazings are increasing (solar load), internal loads are increasing (appliances, lighting) as well as gradual climate warming (Sect. 9.9), summer heat protection is gaining, especially in commercial buildings, a lot more in importance. Within the EU the floor area requiring air-conditioning has increased by a factor of 4 in the last 20 years (Fig. 9.12). The largest growth rate thereby is apparent in southern Europe (Fig. 9.13).
Fig. 9.12: Increase of cooled floor area in the 15 EU-countries [9.12]
Fig. 9.13: Predicted change over time of cooled floor areas in the 15 EU-counties [9.12]
0
2
4
6
8
10
12
14
16
18
Coo
led
floor
are
a (m
2 /inha
bita
nt)
Belgium
Denmark
German
y
GreeceSpa
in
France
Irelan
dIta
ly
Luxe
mbourg
Netherl
ands
Austria
Portug
al
Finlan
d
Sweden
United
King
domEU-15
20002020
Energy and Sustainability 169
The measures to protect against overheating in summer can be grouped as follows:
- reduction of external loads (area and orientation of windows, shading devices, solar control glazing, cp. Sect. 6.5)
- reduction of internal loads (lighting, appliances)
- increase of thermal storage capacity of the interior building elements (massive, thermally active)
- ventilation (passive cooling with nigh-time ventilation, cp. Sect. 7.7)
In order to allow for a reliable statement about the expected thermal comfort of a particular building in summer, the process of thermal storage in the internal building elements has to be taken into consideration. This can be accomplished with the help of building simulation programs (Sect. 8.5).
9.4 Renewable Energy
Energy is designated as renewable if it comes from a source that is inexhaustible from a human scale. The sources for usable energy flow are thus:
- nuclear fusion in the sun and, therefore, solar irradiation: solar energy, hydro energy, wind en-ergy, wave energy, bioenergy
- radioactive decay in the Earth’s interior: geothermal energy
- earth’s rotation: tidal energy
The so-called fossil fuels (crude oil, natural gas, coal) stem from energy from earlier solar irradia-tion. Because the time period of the formation (millions of years) in comparison to the time period of utilization (a couple of hundred years) differs by many magnitudes these fuels are not consid-ered renewable. For utilization in buildings, solar energy, geothermal energy and bioenergy are most interesting as renewable energy.
Fig. 9.14: Fuel wood and carbon cycle
Wood is a renewable, carbon-neutral fuel. During the growth phase in the forest the same amount of carbon-dioxide is absorbed as is released by burning (Fig. 9.14). Heating with wood is especially prevalent in rural areas of Switzerland. The disadvantage is the emission of particulate matter that
Energy and Sustainability 170
result from burning. Improved combustion chambers and suitable electric filters can reduce the emissions significantly. The latter are mainly used in large facilities.
In connection with buildings the use of near-surface geothermal energy is of interest. By means of ground-coupled (earth-to-air) heat exchangers (Sect. 7.6), i.e. tubes laid approximately horizontal in the earth, the supply air in a ventilation system can be pre-heated in winter and possibly pre-cooled in summer.
Using ground loops, i.e. tubes placed in vertical boreholes in the soil for the heat exchange, the heat is transported to the surface by means of a heat transfer fluid. Typically heat pumps are em-ployed for heating buildings in such a system. An important characteristic value of heat pumps is the coefficient of performance COP or, because the temperature boundary conditions change in the course of a year, the seasonal energy efficiency ratio SEER. It gives the ratio of output heating energy to input electrical energy over the year. A heat pump with a SEER of 3 produces – based on the intake of electrical energy – triple the heat energy. The relatively high demand for electricity can be considered a disadvantage of the heat pump.
In buildings solar thermal energy is today mainly used for providing hot water; used to a less extent also for heating. For the temperature range from around 40°C to 100°C flat plate collectors are typ-ical (Fig. 9.15). These solar collectors are in general covered with a glass pane to reduce the heat loss. They have an absorber that is mostly selectively coated, a heat-transport fluid flowing through the absorber to remove heat, and a heat insulating backing. With these solar collectors the direct as well as the diffuse solar radiation can be utilized. The heat-transport fluid typically contains an anti-freeze, to prevent freezing in winter.
Fig. 9.15: Cross-section through a thermal solar collector (flat plate collector)
The efficiency of a solar collector can be derived from the law of conservation of energy applied to the absorber:
( )inout TTcmTAUIA −⋅⋅=∆⋅⋅−⋅⋅⋅ ατ (W)
gains – losses = useful heat
τ solar transmittance of glass pane - α solar absorptance of absorber - A absorber area m2
thermal insulation
absorber
glass pane heat-transport fluid
beam
diffuse Tout
Tin
Energy and Sustainability 171
I solar irradiance W/m2 U thermal loss coefficient W/m2K ∆T temperature difference between absorber and environment K m mass flow rate of heat-transport fluid kg/s c specific heat of the heat-transport fluid J/kgK Tin, Tout input and output temperature °C
The average temperature difference between the absorber and the exterior is approximately:
eoutin TTTT −
+≈∆
2
The collector efficiency is given by the ratio of the useful heat, i.e. the convective heat flow due to the heat-transport fluid, and the amount of irradiated solar energy:
(-)
The outcome of this is the collector efficiency:
ITU ∆ατh ⋅−⋅= (-)
This is a linear equation: Collector efficiency h as a function of the boundary conditions ∆T/I. The product τ⋅α is also referred to as the optical efficiency. U corresponds to the slope of the straight line. Different efficiencies are reached (Fig. 9.16) depending on the input temperature of the fluid, the solar irradiation as well as the ambient temperature. In the simplified consideration above it was assumed that ideal heat transfer exists between the absorber and the fluid (heat exchange factor F ≈ 1).
0
0.5
1
0 0.05 0.1 0.15
Col
lect
or e
ffici
ency
h (-
)
∆T/I (m2K/W)
τ α
U1
U1
> U2
τ α optical losses
thermal losses
useful heat U2
Fig. 9.16: Characteristic curves of two thermal solar collectors with different thermal loss coeffi-cients
A solar water heating system comprises, in addition to collectors, also a closed-loop piping system, a heat exchanger, a tank to store the hot water, a pump as well as controls. Solar hot water heat-ing is regarded today as a proven and economic technology.
Energy and Sustainability 172
Photovoltaics (PV) denotes the direct conversion of solar radiation into electric energy. The physi-cal basis is the photovoltaic effect. The energy conversion takes place in the solar cells that are bonded to the modules. The efficiency of today’s commercially available solar modules is between about 6 to 18 percent. If the PV system is connected to a grid, the direct current produced by the solar cells is converted to an alternating current with a power inverter. PV systems are to date not very prevalent in Swiss buildings mainly due to their relatively high costs.
When solar components are integrated in buildings, it can be attractive to directly build them into the facade or roof. Ideally these elements can, in addition to producing heat or electricity, also take on the function of weather protection. As a consequence other elements are not required anymore and costs can be saved.
9.5 Total Energy Expenditure During a Life Cycle
The energy used for heating and possibly also for cooling of a building is more or less constant as yearly consumption during the service life of a building. It can be designated as operating energy or direct energy.
Additional energy is necessary particularly for the production of materials, but also for the construc-tion of buildings, for repair and rehabilitation work as well as in the end for the building demolition and waste disposal. This energy is referred to as indirect or embodied energy [9.13]. In contrast to direct energy, the indirect energy doesn’t accumulate continuously over the life cycle, but instead only in specific phases.
For many materials the energy required for production is known from investigations of the manu-facturing processes (Tab. 9.2).
Material Embodied energy (kWh/t)
aluminum steel plastics glass cement mineral wool
34'183 8'138 14'650 5’700 1'383 4'070
Tab. 9.2: Energy required to produce different materials [9.14]
In order to illustrate the significance of embodied energy the thermal insulation of a building is con-sidered. The heat loss of a building in operation (direct energy) decreases with the increase in thickness of the thermal insulation. The required energy for production (indirect energy) however increases with the increasing thickness of the thermal insulation. What is then, energetically, the optimal insulation thickness? The area-related energy loss through the thermal insulation during its service life (direct energy) amounts to:
⋅⋅⋅⋅= 2360024
mJHDDnUqdir
n service-life of thermal insulation (number of years) -
U thermal transmittance W/m2K
HDD heating degree days K⋅d
The embodied energy contained in the thermal insulation (indirect energy) amounts to:
⋅= 2ind m
Jxq γ
Energy and Sustainability 173
γ specific embodied energy of the thermal insulation J/m3
x insulation thickness m
The total energy q is the sum of the direct and indirect energy:
inddir qqq +=
The total energy should be a minimum, thus:
0dxdq
optxx
==
In very rough approximations it is assumed that the number of heating degree days is not depend-ent on the insulation thickness and the contributions of the heat transfer resistance in the thermal transmittance U are negligible (U ≈ λ/x). The second assumption is very well fulfilled with larger in-sulation thicknesses. According to this, the optimal thickness of the thermal insulation is:
)(360024 mHDDnxopt γλ ⋅⋅⋅⋅
=
The relationship between direct, indirect and total energy und insulation thickness are graphically displayed in Fig. 9.17 (left). This figure also shows (right) that the energetically optimal insulation thickness is larger the longer the service life is. For this the following numerical values are as-sumed:
location of Zurich: HDD = 3260 K⋅d
mineral wool: λ = 0.04 W/mK and ρ = 80 kg/m3
0
200
400
600
800
1000
1200
0 0.2 0.4 0.6 0.8 1
direkt
indirekt
total
Ene
rgy
(MJ/
m2 )
Thickness of insulation (m)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100
Opt
imal
thic
knes
s of
insu
latio
n (m
)
Service life (year)
Fig. 9.17: Direct, indirect and total energy as a function of the insulation thickness for n = 1 (left) and optimal insulation thickness as a function of the service life of the thermal insulation (right).
The embodied (indirect) energy of the mineral wool is applied in accordance with Table 9.2. The graphic shows that today’s common insulation thicknesses are far below the energetically optimal insulation thickness. This means that with today’s common insulation thicknesses the total energy
Energy and Sustainability 174
needs are largely determined by the direct energy. Similar considerations can basically be carried out for entire buildings.
Figure 9.18 shows the distribution of required indirect energy for the production and construction of an office building [9.15]. The supporting structure contributes to nearly half of the total embodied energy. The thermal insulation, the windows and doors as well as a portion of the building equip-ment are relevant for direct energy demand. These building components comprise up to about 30% of the total embodied energy.
bearing structure 49%
thermal insulation 1%cladding 3%
windows, doors 14%
interior finish 7%HVAC 18%
construction site 9%
Fig. 9.18: Embodied energy of a low-energy office building [9.15]
In Switzerland the average service life of buildings is about 80 years. The operating energy can be summed up over the entire service life and compared with the embodied energy. Studies have shown [9.15] that the portion of indirect energy in old buildings is only about 10% and about 20% in newer. I.e. that the energy embodied in building elements relevant for operating energy is only re-sponsible for about 3% to 6% of the total energy consumption! A greater investment of a few per-cent in embodied energy of building elements relevant for operating energy can however reduce the operating energy requirements in certain circumstances by 50% and more. That is to say that the investment in embodied energy for better thermal insulation, windows and building equipment is in general practically negligible in comparison to the operating energy savings.
The consideration of embodied energy however becomes important with low- or zero-energy build-ings. Some of today’s zero-energy buildings (100% embodied energy) were made possible by the application of technical equipment that contain considerable amounts of embodied energy and ac-cordingly, environmental pollution. Therefore, an optimum as regards total energy, or still better, an ecological optimum is something to strive for. Different studies indicate that this optimum lies rela-tively close to zero-energy for operation. In any case however, buildings should be constructed with materials as little polluting as possible and using as little amounts of material as possible.
9.6 Energy Demand per Floor Area and Energy Standards
Figure 9.19 shows the energy flow diagram of a building with nomenclatures according to [9.9]. It can be differentiated between the system boundaries for the heating demand (1), the heating de-mand for hot water (2), the heating and hot water system (3) as well as for the entire building (4).
The demands on energy consumption can either be formulated by end energy (EEl and Ehww) or by the useful energy (Qh und Qww) (Tab. 9.1). In the Swiss standard SIA 380/1 for thermal energy in buildings [9.9] the requirements are defined based on useful energy. The energy consumption per year in MJ (= 106 Joule) is based on the so-called energy reference area (m2). The energy refer-ence area is the sum of all floor areas both above and below ground that have to be heated or cooled for the use. The requirements are different depending on the building category and geome-try (Fig. 9.20). They are formulated either as limits (= mandatory to comply with) or target values (=
Energy and Sustainability 175
to strive for). Less strict requirements are given for refurbishments (= 140 % of the limit values). The limit of heating demand as a function of the building geometry is according to the SIA 380/1 standard:
E
thlih0lihlih A
AQQQ ⋅+= ,,, ∆ (MJ/m2a)
Ath thermally weighted building-envelope area m2 AE energy reference area m2
The thermally weighted building-envelope area Ath is defined as the outer surface area of the build-ing in which areas adjacent to unheated rooms and adjacent to the ground are weighted less (for details refer to [9.9]). That is, small values of Ath/AE correspond to large compact buildings and large values of Ath/AE to small buildings (Fig. 9.20). The requirements are thus stricter for large buildings because it is easier in these cases to achieve low consumption values.
1 system boundary of heating demand 2 system boundary of heat demand for hot
water 3 system boundary of heating and hot wa-
ter system 4 system boundary of building EEl energy demand for electricity Ehww energy demand for heating and hot water Qg heat gains Qh heating demand Qhww heat demand for heating and hot water
Qi internal heat gains QiEl internal heat gains from electricity QiP internal heat gains from people QL heat losses of heating and hot water
systems Qr gained environmental heat Qs solar heat gains QT transmission heat losses Qtot total heat losses Qug usable heat gains QV ventilation heat losses Qww heat demand for hot water WRG heat recovery
Fig. 9.19: Energy flow diagram [9.9]
end energy useful energy
Energy and Sustainability 176
Fig. 9.20: Limits for the heating demand according to [9.9]; the target value is 60% of the limit value
The energy demand can of course also be expressed in in terms of end energy (Fig. 9.19). This value is a quantity for the annual demand for energy per unit area for the provision of heat or elec-tricity in a building (reference area = energy reference area).
Energy demand for heat (space heating + hot water): Ehww (MJ/m2a)
Energy demand for electricity: EEl (MJ/m2a)
Bemerkung: Werte gültig für 20°C Raumtemperatur
Tab. 9.3: Limit and target values for thermal transmittances U according to [9.9]
In the SIA 380/1 standard the requirements are either expressed in terms of heating demand per floor area Qh (see above) or the thermal transmittance of building elements (Tab. 9.3). According
Building Category Limits* Qh,li0
MJ/m2a ∆Qh,li MJ/m2a
I residence MFH 80 90 II residence SFH 90 90 III office 85 95 IV school 100 95 V shop 75 95 VI restaurant 115 95 VII assembly hall 120 95 VIII hospital 100 100 IX industry 85 90 X warehouse 85 85 XI gymnasium 105 85 XII indoor swimming pool 90 140 *at 8.5°C annual mean exterior temperature
Energy and Sustainability 177
to [9.9] no heating demand calculation for the whole building (Sect. 9.2) must be made if limit val-ues for thermal transmittances are fulfilled.
The energy demand per floor area of buildings increased significantly from the beginning of the 20th century up until the 1970s. Due to an increased push for savings, a reversal of the trend set in. It is expected that this trend will continue in the next years (Fig. 9.21).
Fig. 9.21: „SIA – reduction path“: Development of the energy demand per floor area for new build-ings
For buildings with low heating demand, the required power for heating is also smaller (Tab. 9.4). With low-energy buildings the (installed) power of internal sources can typically achieve the re-quired heating demand (Tab. 9.5). That is to say, when the internal sources are in operation, the demand for heating can thereby be covered. A possible heating system then has only a compensa-tory function.
Energy
(MJ/m2a)
Power
(W/m2)
old buildings ca. 600 ca. 70
newer buildings ca. 300 ca. 35
low-energy buildings ca. < 100 ca. < 12
Tab. 9.4: Typical values for heating in terms of energy and power
Use Installed Power (W/m2)
lighting office 10 – 15 residence 4 – 6 people office 8 – 10 residence 2 – 6 appliances office 15 – 50 residence 2 – 10
Tab. 9.5: Typical values for internal heat sources [9.15]
Energy and Sustainability 178
Minergie and Minergie-P are quality labels for buildings that stand for high comfort with low energy consumption and an economic construction [9.16]. Figure 9.22 gives an overview of the require-ments on a building according to the Minergie and Minergie-P standards. With regards to construc-tion costs, it is encouraged that any additional costs in construction, compared to conventional construction, not be higher than 10% (Minergie), and 15% (Minergie-P).
Fig. 9.22: Comparison of Minergie and Minergie-P building properties [9.16]
9.7 Strategies for Low-Energy Buildings
Based on previous statements (see Chap. 8) basic strategies can be formulated for the design of buildings with a very low energy demand for heating and cooling. In doing so a distinction can be made between the building structure (= building envelope and interior building elements) and the building equipment (= technical installations) as well as other factors.
Building Structure:
- continuous, good thermal insulation of transparent (U ≤ 0.9 W/m2K) and opaque (U ≤ 0.1 W/m2K) elements of the building envelope
- thermal-bridge-free building envelopes: load bearing structure on the warm side, no penetra-tions through the insulation layer with materials with a high thermal conductivity (metal, con-crete, stone)
- air-tight building envelope (n50 ≤ 0.6 1/h)
- solar gains in winter: large glazed areas preferably facing south, try to avoid shading from bal-conies, overhangs, etc.
- solar gains in summer reducible: best with external, variable shading devices (g < 0.15)
Energy and Sustainability 179
- active thermal-mass in building interior: e.g. concrete ceiling, brick walls etc. (elements not thermally uncoupled by suspended ceilings, subfloors or carpets)
- building geometry optimized: small outer surface area (= heat loss area) in relation to building volume; i.e., advantageous are large, compact buildings
Building Equipment (HVAC):
- mechanical ventilation with heat recovery (efficiency > 0.8)
- demand-regulated, optimized controls
- solar collectors (hot water, possibly also heating/cooling or photovoltaic)
- use geothermal heat (earth-to-air ground heat exchanger, heat pump)
- individual heating-cost billing
Other Factors:
- environmentally-friendly materials with little embodied energy
- correct user behavior: e.g. permanently opened (tilt-) windows can drastically increase the en-ergy demand in a low-energy building, reasonable room temperatures etc.
9.8 Existing Building Stock and Refurbishment
Mainly due to the tightening of the SIA 380/1 standard as well as the regulations in the Cantons, newly constructed buildings today require considerably less energy than existing. The analysis of the building stock shows however that this only very slowly affects the total energy consumption (Fig. 9.23). In Switzerland the average energy demand per floor area of buildings still amounts to about 600 MJ/m2. The buildings that were constructed before circa 1980 primarily dominate the to-tal consumption!
Fig. 9.23: Energy demand of residential buildings (data from [9.17])
Energy and Sustainability 180
Construction is a slow process. In Switzerland only about 1% to 2% of buildings are erected or re-furbished annually. In contrast to this, for example, each year about 9% of the cars are replaced. If a new “energy-efficient” technology comes on the market and is declared as mandatory, then to-day’s automobile fleet can be replaced within approximately 20 years. By today’s low building modernization rate it takes however at least 100 years in order to replace todays building stock (Fig. 9.24). If we decided today to construct, as of now, only zero-energy buildings, it would thus take decades before the energy demand of the total building stock drops considerably. Thus in or-der to reduce the energy demand of buildings as quickly as possible not only strict energy regula-tions are important, but also the rate of building refurbishment must be boosted with suitable incen-tives.
Fig. 9.24: Rate of renewal and penetration curve [9.15]
9.9 Climate Change and Energy Demand
The gradual increase of temperatures due to climate change (cp. Sect. 2.5) means that the bound-ary conditions of buildings are slowly changing. Considered over a long period, this can lead to significant changes in the energy balance of buildings. Taking the typical service life of buildings to be about 80 years this also means that the buildings that are constructed today must also function some day in a warmer climate.
Studies show [9.18] that in the period between 1901 to 2003 the heating degree days have de-creased by 11% to 18%. During the same time period, the cooling degree days have increased by 50% to 170% (starting from low absolute values). This tendency will be even more pronounced in the 21st century (Figures 9.25 and 9.26) so that it can be taken with high probability that in the fu-ture our buildings will have to be heated less but will need to be cooled more. In this study, tem-peratures measured by MeteoSchweiz [9.19] were employed for the past and temperature projec-tions of the IPCC [9.20] were used for the future.
Energy and Sustainability 181
0
1000
2000
3000
4000
5000
6000
7000
1900 1950 2000 2050
Hea
ting
degr
ee d
ays
(Kd)
Year
Zurich Geneva
Davos
Lugano
θg = 10°C
Fig. 9.25: Measured (1901 – 2003) and projected development of heating degree days [7.18]
0
200
400
600
800
1000
1200
1900 1950 2000 2050
Coo
ling
degr
ee d
ays
(Kd)
Year
Zurich
Geneva Davos
Lugano
θbal
= 18.3°C
Fig. 9.26: Measured (1901 – 2003) and projected development of cooling degree days [7.18]
9.10 Summary
"Sustainable development meets the needs of the present without compromising the ability of fu-ture generations to meet their own needs" (Brundtland-Commission, 1987). Sustainable construc-tion means to minimize the flow of energy and materials during the entire life cycle of a building (construction, operation, refurbishment, demolition). A high priority has to be given to the reduction of the energy demand during operation. In comparison to typical old buildings, the heating demand in buildings can today be reduced by a factor of 5 to 10 with an economically justifiable investment. Higher costs can be outweighed by better comfort – surface temperatures closer to the interior air temperature as well as better air quality due to controlled ventilation. To strive for is to at least par-tially cover the remaining energy demand with renewable energy.
The basic principles and strategies for buildings with very low energy demand have been present-ed. The practice shows that very large architectonic diversity is also possible with low-energy build-ings.
Energy and Sustainability 182
Problems Problem 1: Energy Flows in a Room
Given is an interior room of a building (drawing). The floor, ceiling and interior walls are adiabatic, i.e. heat can flow only through the exterior wall. A steady state can be assumed.
a.) Provide a balance of all energy flows.
b.) How much heating power is required so that θi = 20°C = constant? Use the following: exterior climate: I = 200 W/m2, θe = -5°C exterior wall: U1 = 0.3 W/m2K, A1 = 7 m2, window: U2 = 2 W/m2·K, A2 = 3 m2, F·g = 0.4 heat output from people and appliances: PAP = 150 W air-flow rate, interior – exterior: V = 30 m3/h
Problem 2: Transmission and Ventilation Heat Losses of an Apartment An apartment in a multi-family house in Zurich has a volume of V = 250 m3 and a portion of the fa-cade area of A = 120 m2. The air exchange rate is n = 0.5/h. Heat flows to the adjacent rooms in the building interior can be neglected.
a.) What can the maximum average thermal transmittance of the facade U be, in order that the transmission heat losses will not be greater than the ventilation heat losses?
b.) Relatively, how much energy could be saved from transmission and ventilation losses, if the apartment was heated to an interior temperature of only 18°C during the heating period in-stead of 20°C? This assessment should be conducted for a heating limit of θg = 12°C (Zurich-city: HGT20/12 = 3260 Kd/a and HT12 = 208 d/a).
Problem 3: Transmission and Ventilation Heat Losses SFH vs. MFH Given are two cubic shaped buildings, a single family house (SFH) (edge length s1 = 9 m) and a multi-family house (MFH) (edge length s2 = 30 m), that both exhibit an identical average thermal transmittance U = 0.3 W/m2K for the building envelope (incl. floor) and the same air exchange rate of n = 0.5 h-1 (Assume: ground temperature = exterior air temperature). a.) What is the ratio between transmission and ventilation heat losses for both buildings? b.) Describe your results in a short sentence.
Literature
[9.1] Meadows D. L., Meadows D. H., Zahn E., Milling P., The Limits to Growth, Universe Books, New York, 1972
V
θi I,
PAP
Ph
U2, A2, F, g
U1, A1
Energy and Sustainability 183
[9.2] Meadows D. H., Meadows D. L., Randers J., Beyond the Limits, Chelsea Green Publishing Company, Vermont, 1992
[9.3] M. Wackernagel, zitiert in „Limits to Growth: The 30-Year Update“, D. Meadows et al., Chelsea Green Publishing Company, 2004
[9.4] Schweizerische Gesamtenergiestatistik 2005, Bundesamt für Energie, Bern, 2006
[9.5] World Energy Outlook 2006, International Energy Agency, Paris, 2006
[9.6] Analyse des schweizerischen Energieverbrauchs 2000-2006 nach Verwendungszwecken, Bundesamt für Energie, Bern, 2008
[9.7] Glicksman L.R., Energy efficiency in the built environment, Physics Today, July Issue, 2008 [9.8] Impulsprogramm Bau - Erhaltung und Erneuerung, Eidgenössische Drucksachen- und Ma-
terialzentrale, Bern, 1991 [9.9] SIA 380/1, Thermische Energie im Hochbau, Hrsg: Schweizerischer Ingenieur- und Archi-
tekten-Verein, 2009 [9.10] EN 832, Wärmetechnisches Verhalten von Gebäuden – Berechnung des Heizenergiebe-
darfes – Wohngebäude, CEN, Brüssel, 1998
[9.11] ASHRAE Fundamentals Handbook 2001 (SI Edition), Chapter 31, American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Atlanta, GA, 2001
[9.12] Adnot J. et al., Energy Efficiency and Certification of Central Air Conditioners, Study for D.G. Transportation-Energy (DGTREN) of the Commission of the EU, Final report, Armines, Paris, 2003
[9.13] Spreng D., Graue Energie, vdf Hochschulverlag, Zürich, 1995
[9.14] Kohler N., Analyse énergétique de la construction, EPF-Lausanne, 1986
[9.15] Keller B., Bauphysik: Die Energetik des Gebäudes, Vorlesungsskript ETH, Zürich, 2006
[9.16] Verein Minergie, Bern; http://www.minergie.ch, 2010
[9.17] Energieplanungsbericht 2002 für den Kanton Zürich, Bericht des Regierungsrates über die Energieplanung, AWEL, Abteilung Energie, Zürich, 2003
[9.18] Christenson M., Manz H., Gyalistras D., Climate warming impact on degree-days and build-ing energy demand in Switzerland, Energy Conversion and Management, Vol. 47, 2006, 671-686
[9.19] Begert M., Seiz G., Schlegel T., Musa M., Baudraz G., Moesch M., Homogenization of measured time series of climatic parameters in Switzerland and computation of norm val-ues 1961-1990. Final project report NORM90, MeteoSwiss, Zurich, 2003
[9.20] Intergovernmental Panel on Climate Change: http://www.ipcc.ch. Retrieved Octo
Chapter 10
Daylight
Daylight 186
10 Daylight In prehistoric times humans lived out in the open air and resided in their caves primarily at night. The light that penetrated through the cave opening during the day highlighted the cave exit, but on-ly produced a very poor light within. Today many people in the so-called industrialized countries spend about 90% of their time indoors.
The good daylighting of interior spaces brings multiple benefits:
- psychological & physiological: It creates a connection to the outside world. The weather, or at least the outside light situation, can also be perceived in the interior.
- ecological & economical:
- If daylight is used, then artificial lighting – and with that electrical energy – can be saved.
- The use of artificial lighting in summer can contribute to an overheating of the building. In the case of excessive heat the thermal comfort in the interior can therefore be improved with daylighting (better light output, refer to Section 10.2). In the case of an air-conditioned build-ing, through the use of daylight, in addition to the energy savings with lighting, the energy to operate the refrigerator unit can be reduced. In winter the released heat from the electrical lighting is however of use: the artificial light can also be considered as “expensive” supple-mentary heating.
- Architectural: "There is no architecture without light", once remarked the physicist J.M. Waldram. Daylight is a design element of architecture.
10.1 Solar Radiation and Spectral Luminous Efficiency of the Human Eye
During the course of evolution the human eye developed its sensitivity in the same wavelength range in which the solar radiation has the highest intensity (Fig. 10.1).
Fig. 10.1: Spectral distribution of solar radiation [10.1] and spectral sensitivity of the human eye (photopic vision).
Visible light is understood as electromagnetic radiation in the wavelength interval of 380 to 780 nm, in which the human eye is sensitive. For high intensities (photopic vision V(λ); normal, daytime) the maximum sensitivity of the eyes lies at a wavelength of 555 nm (yellow-green). With lower intensi-
Daylight 187
ties (scotopic vision V‘(λ); low illuminance levels, nighttime) the maximum sensitivity shifts to the wavelength 507 nm (Fig. 10.2).
Fig. 10.2: Spectral sensitivity of the human eye (photopic and scotopic vision)[10.2].
10.2 Fundamental Photometric Terms and Relationships
10.2.1 Luminous Flux Φ
The „amount“ of visible light emitted by a source is referred to as luminous flux Φ with the unit lu-men (lm). The luminous flux corresponds to a certain energy flow, or power, in Watt.
The conversion of power into luminous flux can be carried out by means of the spectral radiative flux Φeλ and the spectral luminous efficiency V(λ) (Fig. 10.3). This is referred to as photometric weighting.
W/lmK)lm(d)(V)(K m
nm
nmem 683
780
380
=⋅⋅⋅= ∫ λλλΦΦ λ
The scaling factor Km is called maximum luminous efficacy.
The same power produces e.g. with 450 nm (blue-violet) much less lumens than with 555 nm (yel-low-green), the maximum spectral sensitivity. Monochromatic light of a 555 nm wavelength corre-sponds to the maximum luminous efficacy of 683 lm/W. Daylight has a luminous efficacy of about 90 to 100 lm/W. The luminous efficacy of daylight is not constant, but depends on the cloud condi-tion, the solar elevation angle and on whether the solar radiation is direct or diffuse (Fig. 10.4). The lower the solar elevation angle is, the redder the light is and so the lower is the luminous efficacy.
Table 10.1 shows the luminous efficacy for different light sources. The luminous efficacy in lumen per watt can also understood as visual performance of a light source.
Daylight 188
Fig. 10.3: Determination of the spectral luminous flux Φλ for a given spectral radiative flux Φeλ by means of the spectral luminous efficiency of the human eye V(λ)
Fig. 10.4: Luminous efficacy as a function of the solar elevation angle [10.3]
Daylight 189
Light Source Visual Performance
daylight ca. 90 – 100 lm/W
incandescent light-bulb ca. 14 lm/W
halogen lamp ca. 25 lm/W
fluorescent tube ca. 40 – 90 lm/W
light-emitting diode (LED) ca. 30 – 200 lm/W
sodium-vapor lamp ca. 90 – 145 lm/W
monochromatic light (λ = 555 nm) 683 lm/W
Tab. 10.1: Visual performance of light sources
10.2.2 Illuminance E
The illuminance E is a measure of the luminous flux Φ incident per surface area A and is given in the unit lux (lx).
)lxmlm(
AE == 2
Φ
In the case of light striking a surface at an oblique angle, the angle of incidence must then be con-sidered according to cosine law.
The illuminance on a horizontal surface varies depending on the solar elevation angle and the at-mospheric conditions (Fig. 10.5). Table 10.2 gives the illuminance outdoors for different conditions. For daylight it can approximately be taken that: 1 W/m2 ⇔ 100 Lux. Table 10.3 gives the illumi-nance levels required to perform different visual tasks.
Setting Illuminance E (lx)
direct irradiation 60'000 – 100'000
cloudy summer day 20'000
high fog cover in winter 10'000
cloudy winter day 3'000
full moon night 0.25
new moon, starlight 0.01
Tab. 10.2: Illuminance outdoors [10.3]
Visual Task Illuminance E (lx)
orientation, only temporary presence (e.g. circulation area) 50
easy visual task (e.g. restaurant) 200
normal visual task (e.g. home, office) 500
difficult visual task (e.g. office, laboratory, workshop, retail store) 1000
very difficult visual task (e.g. precision assembly, watchmaking) 2000
Tab. 10.3: Illuminance levels required to perform different visual tasks
Daylight 190
Fig. 10.5: Course of horizontal illuminance outdoors in Zürich [10.2]
10.2.3 Luminous Intensity I
Many light sources emit the luminous flux in different intensities in different directions (direction-dependent radiation characteristic). The luminous intensity I specifies which luminous flux Φ falls in a certain solid angle Ω and is given in the unit candela (cd).
)cdsrlm(I ==
ΩΦ
Fig. 10.6: Solid angle
Daylight 191
The solid angle is defined by the ratio of the area of a spherical calotte to the square of the sphere radius (Fig. 10.6):
)sr(rA
2=Ω
The unit of the solid angle is called steradian (sr). The total surface area of a sphere corresponds to a solid angle Ω = 4π. The correlation between luminous flux Φ, luminous intensity I and illumi-nance E is shown in Figure 10.7. The luminous intensity corresponds to the luminous flux that falls in a certain solid angle. For example, with a headlamp the luminous flux is focused. That is, the light is bounded by a small solid angle. So, with a given luminous flux, a much higher luminous in-tensity is generated. The illuminance E describes the effect on the target, i.e. how intense the light acts on a surface.
Fig. 10.7: Relationship between luminous flux Φ, luminous intensity I and illuminance E
10.2.4 Photometric Inverse-Square Law
A light source with a luminous intensity I lights up an area A at a distance r from the light source. The linear extent of the surface A is small in comparison to the distance r. The surface A deter-mines the following solid angle:
2rA
=Ω
The luminous flux that strikes the surface A is:
2rAII ⋅=⋅= ΩΦ
The illuminance E on the surface A amounts to:
2rI
AE ==
Φ
The illuminance E that is produced by a given light source with the luminous intensity I thus in-creases inversely proportional to the square of the distance r (photometric inverse-square law).
Daylight 192
10.2.5 Luminance L
A light source displays a surface area. If one refers to the luminous intensity of the source on their surface A (projection perpendicular to the visual line), one obtains the luminance of the source:
= 2m
cdAIL
Luminance is the quantity that is relevant for human sight. Whether an object can be recognized, depends on the luminance contrast to the surroundings. The physiological contrast is defined as:
Studies have shown that the human eye exhibits a maximum contrast sensitivity, and accordingly visual performance, with a background luminance of about 200 to 2000 cd/m10.
Each illuminated surface turns itself into a light source by its reflectance. The illuminance E that falls on an area together with its reflectivity ρ determines the luminance, under which the area ap-pears to the eye. The luminance of a surface in the case of an ideal diffuse reflection is:
πρ⋅
=EL
Given that the human eye needs a luminance at a minimum of 200 cd/m2 for good visual perfor-mance, the required illuminance, for white paper (ρ = 0.8) amounts to (cp. Table 10.3):
lx .
LE 78580
200=
⋅=
⋅=
πρ
π
Fig. 10.8: Luminous flux Φ, illuminance E and luminance L
10.2.6 Overview
In summary one can say:
- The luminous flux Φ describes the total output of the light source.
- The illuminance E describes how much the incident light illuminates the lit object, that itself be-comes a source of light with a luminance L as a result of reflection.
Daylight 193
- Luminance L and luminous intensity I describe the light source (lamp as well as the illuminated object).
10.3 Luminance Distribution of the Sky
To achieve a better comparability, one uses with daylight planning a so-called standard sky. The standard sky corresponds to a uniformly overcast sky, i.e. one assumes that 100 percent of the sky is covered with clouds. This sky condition is, precisely in mid-winter, unfortunately a relatively common situation on the Swiss plateau. It is also the sky condition with which the use of daylight is critical. If a lot of direct solar radiation exists then often rather too much daylight exists and glare effects can occur.
The CIE-standard sky is defined by the Commission Internationale de l´Eclairage, or International Commission on Illumination, and is given as the relative luminance distribution of the illuminant ”sky” (Fig. 10.9). α denotes the sun elevation angle.
°⋅⋅+
= 90321 Lsin)(L αα
According to this distribution the luminance is three times larger at the zenith (α = 90°) than at the horizon (α = 0°).
3=Horizont
Zenit
LL
Fig. 10.9: Relative luminance distribution of the CIE-standard sky
The result of this luminance distribution is that the illuminance on a vertical surface amounts to just barely 40% of the illuminance on a horizontal surface.
3970.EE
horizontal
vertikal =
Therefore, skylights utilize daylight significantly more efficient than vertical glazings.
Daylight 194
10.4 Transmittance Factors of the Building Envelope
How much daylight can reach into an interior room depends on the transmission properties of the building envelope. The visible light transmittance of a glazing can be calculated by a weighing of the spectral transmittance properties of the glazing with the spectral luminous efficiency of the hu-man eye [10.4]:
)(d)(VD
d)(V)(D
nm
nm
nm
nmV −
⋅⋅
⋅⋅⋅=
∫
∫780
380
780
380
λλ
λλλττ
λ
λ
τ(λ) denotes the wavelength-dependent transmittance of the glazing, V(λ) spectral luminous effi-ciency of the eye and Dλ the relative spectral distribution of „standardized“ light [10.4].
Table 10.4 gives typical visible light transmittances of glazings. To provide interiors well with day-light, high values of τV are desirable.
visible light transmittances τv (-)
single glazing 0.9
double glazing 0.82
insulating glazing unit (double) 0.77
insulating glazing unit (triple) 0.65
solar control glazing 0.2 – 0.6
Tab. 10.4: Typical visible light transmittances of glazings
With regards to the different demands – daylight, glare protection, solar control in summer and passive use of solar energy in winter – often arise conflicting requirements. Today the different demands are accommodated mostly with variable additional elements – external shading and in-ternal glare protection devices. Electrochromic devices have to date still not achieved an apprecia-ble prevalence.
A substantial portion of window surfaces is often taken up by frames and muntins that reduce the light transmission. This can be accounted for with a reduction factor K1 which considers the area share in the wall aperture.
)(11 −−=−ApertureWall
Frame
AAK
Depending on air pollution – countryside or densely populated industrial areas – as well as clean-ing schedules light transmission is further reduced. The reduction factor K2 accounts for dirt (K2 = ca. 0.5 – 0.9).
Depending on the frame depth and height, an angle-dependent frame shading can occur as well (Fig. 10.10) that can be accounted for with a reduction factor K3.
Daylight 195
Fig. 10.10: Reduction factor K3 due to frame shading
10.5 Daylight Factor
In order to be able to evaluate the illumination of a room by daylight, the illuminance on a horizon-tal surface in the room interior E1 at a defined point (e.g. table surface) is compared to the illumi-nance on a horizontal surface outdoors E0 for an overcast sky (CIE-standard sky). The ratio that is composed of these two illuminances is called daylight factor TLQ (Fig. 10.11).
(%)EETLQ 100
0
1 ⋅=
Fig. 10.11: Definition of the daylight factor TLQ
10.5.1 Components of Daylight Factor
The daylight factor can be described as follows (Fig. 10.12):
( ) (%)KKKTTTTLQ VRVH 321 ⋅⋅⋅⋅++= τ
TH sky component (direct from sky)
TV externally reflected component (reflection of opposite lying obstructions and/or ground)
TR internally reflected component (reflection of internal surfaces)
Daylight 196
τV light transmittance of glazing
K1 reduction factor for frame and muntins
K2 reduction factor due to dirt
K3 reduction factor due to frame shading (non-perpendicular light incidence)
Fig. 10.12: Components of daylight factor
The larger the daylight factor is, the brighter a room appears and the better connected one feels with the outdoor environment (Fig. 10.13).
Fig. 10.13: Perception of daylight factors [10.3]
The sky component TH arises from the visible patch of sky through the window. The qualitative course of the sky component of the daylight factor as a function of the distance from the window in the interior is evident in Figure 10.14. The light colored portion of the hemisphere on the horizontal surface corresponds to the direct sunlight from a patch of sky visible at the point considered, and becomes smaller with increasing distance from the window.
Daylight 197
Fig. 10.14: Dependency of the sky component of the daylight factor on the interior location in the absence of obstructions
In simple cases, as for example with a vertical glazing, the daylight factor can be manually (rough-ly) calculated. This method will be introduced in the following. In complicated cases daylight factors can be determined with the aid of computer programs.
10.5.2 Sky Component TH
The sky component TH can be determined quantitatively with the aid of the so-called skylight or Waldram diagram. This diagram (Fig. 10.15) depicts a projection of half of the celestial dome (cor-responding to TH = 50%). The division was so chosen that every little square in the grid constitutes the same illuminance on a horizontal surface. The procedure is as follows:
- From the reference point in the room one extends the perpendicular line to the plane of the win-dow and determines the angles to the two side edges as well as upper and lower edges of the window (azimuth angle left βFl and right βFr , elevation angle low εF1 and high εF2).
- One plots the “angle-picture” in the Waldram diagram, utilizing the mesh lines for the horizontal and vertical window outline.
- One determines analogously possible obstructions with respect to their silhouette within the lines of the window angle-picture and plots it likewise in the diagram.
- One counts out the contained squares from the angle-picture of the window minus the angle picture of the obstruction (visible sky) (nH).
For the sky component TH it amounts to:
(%).nT HH 050⋅=
10.5.3 Externally Reflected Component TV
One determines analogously as with TH the contained number of houses nV from the angle-picture of the obstruction. The contribution to the daylight factor is now co-determined by the reflective power of the obstruction (Table. 10.5). The luminance of the portion that corresponds to the ob-structed area, is less than the one of the sky and the contribution to the daylight factor is reduced.
(%).nT VV ρ⋅⋅= 050
Often an average value of ρ = 0.15 is assumed for the reflectance.
Daylight 198
Fig. 10.15: Projection of half of the celestial dome: Waldram diagram
Tab. 10.5: Reflectances of building materials and surfaces [10.3]
10.5.4 Internally Reflected Component TR
The internally reflected component TR can be approximately determined with the Hopkinson formu-la:
Daylight 199
( ) ( ) (%)ffAAT DWuBWo
mR
FR 100
11
⋅⋅+⋅⋅−
⋅= ρρρ
AF window area (wall aperture) m2
AR total room surface areas (floor, ceiling, walls) m2
ρm average reflectance of all room surfaces -
ρBW average reflectance of floor and lower part of walls (lower half from mid-height of window) without window wall -
ρDW average reflectance of ceiling and upper part of wall (upper half from mid-height of window), without window wall -
fo, fu window factors, according to Fig. 10.16 -
α obstruction distance angle, measured from mid-height of window °
reflectance of windows: ρF = 0.1
Daylight 200
Fig. 10.16: Window factors fo, fu as a function of the obstruction distance angle α
10.5.5 Example to Calculating the Daylight Factor
Figure 10.17 shows a room with a floor area 4 m x 5 m and a window size of 1.4 m x 3.6 m. For this layout the daylight factor at the level of the windowsill is calculated at 1 m into the room, and respectively at 4 m. The Figures 10.18 to 10.20 illustrate the approach to the solution.
Daylight 201
Fig. 10.17: Layout to the example [10.3]
Daylight 202
Fig. 10.18: Section and plan to the example [10.3]
Daylight 203
Fig. 10.19: Waldram diagram to the example for 1 m into the room (above) and 4 m (below) [10.3]
Daylight 204
Fig. 10.20: Calculation of the daylight factor (example) [10.3]
Daylight 205
10.6 Influence of Fenestration
The position of a window, not only its size, influences considerably the resulting daylighting condi-tions in the interior. In particular the light that falls nearly vertical can produce high illuminance on the horizontal surfaces, because not only is the luminance highest at the zenith (CIE standard sky), but also the cosine law has an effect (Fig. 10.21). Therefore, skylights are more effective than ver-tical windows.
Fig. 10.21: Three openings of different sizes that produce the same illuminance on a horizontal surface.
Fig. 10.22: Influence of the vertical window position on the course of the daylight factor with single-sided illumination [10.2].
Fig. 10.23: Double-sided illumination of a room [10.2]
Daylight 206
The influence of the vertical position of the window on the course of the daylight factor in the case of a single-sided illumination of a room is shown in Figure 10.210. With higher positioned windows a more uniform illumination can be achieved. The usable room depth increases. A further im-provement can be gained by a double-sided illumination (Fig. 10.23). The illuminances overlap and the minimal value shifts in the direction of the center of the room.
Figure 10.24 shows how rooms can be very efficiently and uniformly illuminated with skylights.
Fig. 10.24: Impact of the type of skylight opening on the course of the daylight factor (γ = window area/floor area = 1/6). In addition, for TLQmin = 5% the required γ-value is indicated [10.5]
Fig. 10.25 shows the influence of an overhang on a vertical and horizontal surface, respectively.
Daylight 207
Fig. 10.25: Influence of an overhang on the vertical and horizontal surfaces, respectively [10.6]
10.7 Rules for Good Daylighting
In the following, a few rules for daylighting shall be formulated.
Skylights are especially efficient with respect to daylighting. Solar control and glare protection can however also be required here.
With vertical glazings applies:
- The clear room height determines how much light, at the most, can enter the room: the greater the room height, the more light.
- The proportion of the room height to the room depth determines the supply of daylight: A large room height and a small room depth is beneficial.
- The maximum room depth that can be illuminated is ca. 5 – 6 m with conventional room heights.
- A large area glazing with a high transmittance is beneficial.
- The lintel should be as small as possible. That is, high-lying windows are favorable.
Daylight 208
- The glazing region below the work level provides only a small contribution to the daylighting, but can have considerable consequences for the cooling load.
- Inner surfaces should be preferable light colored.
- A second sidelight can improve the daylighting, in particular the illuminances becomes more uniform.
- Disadvantageous are fixed shading devices or balconies over the window. They especially shield the direct skylight and reduce the daylight factor, particularly near the window.
10.8 Daylight Planning
Rules of thumb and Waldram diagrams aren’t always adequate for daylight planning. In order to allow for reliable information about the daylighting conditions in rooms already in the planning phase, computer programs are made available, with which – on the basis of calculations with picto-rial display of the results – can do the same work with much more detail. A strength of powerful programs is the photo-realistic rendering of the results. Thanks to such visuals also laypersons can quickly imagine the daylight situation in a room (Fig. 10.26). In such representations also lines of equal illuminance or equal daylight factors can be incorporated.
Fig. 10.26: Daylight simulation of an atrium
Daylight experiments with models of the relevant building parts can also be carried out. The illumi-nation can thereby take place through natural or artificial sunlight (Fig. 10.27). With the help of sensors in the model and photo-cameras quantitative as well as qualitative analysis can be made.
By means of Fig. 10.28 the daylight contribution with a given daylight factor and certain required illuminances at a workplace (winter: 7.00 – 17.00 MEZ; summer 8.00 – 18.00 MESZ) can be esti-mated. For example artificial light can be turned off for a required illuminance of 500 lx with a day-light factor of 5% during 50% of the time.
Daylight 209
Fig. 10.27: Laboratory set-up to the investigation of daylighting conditions in buildings with direct (left) and diffuse radiation (right)) [10.7]
Fig. 10.28: Times of operation solely with daylight for different daylight factors and required illumi-nances [10.6]
Daylight 210
Problems
Problem 1: Determination of the Daylight Factor
The daylight situation at the specified point P in a room is defined by the information given below:
Window
azimuth angle: βFr = 35°, βFl = 35° elevation angle: εF = 40°
Obstruction
azimuth angle: βVr1 = 15°, βVr2 = 20° elevation angle: εV = 35°
obstruction distance angle: α = 15°
Reflectivity
walls: ρW = 0.8
ceiling: ρD = 0.8
floor: ρB = 0.2
window: ρF = 0.1
reflectance of obstruction: ρV = 0.2
visible transmittance of glazing: τV = 0.75
reduction factor for frame and muntins: K1 = 0.7
reduction factor for dirt: K2 = 0.8
A perspective of the interior, a section and a plan with the location of P can be found in the follow-ing pages. The drawings are not to scale! Using the Waldram diagram determine:
a) the sky component TH at point P
b) the externally reflected component TV at point P
c) the internally reflected component TR at point P
d) the daylight factor TLQ at point P
e) the percentage share of the sky component, externally reflected component and internally re-flected component to the TLQ (=100%), that has been calculated in d).
Problem 2: Sheens on Computer Screens
Annoying sheens on computer screens are caused by differences in luminance. This results in the lights or irradiation mirroring themselves on the monitor screen. Think about measures to prevent the annoying sheen and nevertheless maintain an acceptable illuminance:
a) for providing daylight b) for artificial light
Problem 3: Photometric Fundamental Terms
A point light source has a power of 10 W and a luminous efficacy of 60 lm/W. The light is emitted with a solid angle of 1 sr. Calculate the maximum illuminance on two surfaces at a distance of 1 m and 3 m.
Daylight 211
Geometry to problem 1:
Daylight 212
Waldram diagram (to problem 1):
Daylight 213
Problem 4: Daylight factor in the office
Sketch the course of the average daylight factor TLQ qualitatively at desk-height as a function of the distance from window x for the following cas-es:
a.) Only the skylight exists.
b.) Only the window exists.
c.) Both openings exist.
Literature [10.1] Iqbal M., An Introduction to Solar Radiation, Academic Press, Toronto, 1983
[10.2] Zürcher C., Frank T., Bauphysik: Bau und Energie, vdf, Zürich, 2004
[10.3] Keller B., Bauphysik: Städtebaulich relevante Faktoren, Vorlesungsskript ETH, Zürich, 2006 [10.4] EN 410, Glas im Bauwesen – Bestimmung der lichttechnischen und strahlungsphysikali-
schen Kenngrössen von Verglasungen, Europäisches Komitee für Normung, Brüssel, 1998 [10.5] Fischer U., Tageslichttechnik, Rudolf Müller, Köln, 1982 [10.6] Keller B., Rutz S., Pinpoint – Fakten der Bauphysik zu nachhaltigem Bauen, vdf Hoch-
schulverlag, Zürich, 2007 [10.7] Scartezzini J.-L., ETH Lausanne, LESO Solar Energy and Building Physics Laboratory, ,
http://leso.epfl.ch/e/research_dl_scansky.html, 2010 [10.8] Haas-Arndt D., Ranft F., Tageslichttechnik in Gebäuden, C.F. Müller Verlag, Heidelberg,
2007
x
window
skylight
Appendix
Appendix 216
A Weather Data Tabelle 1: Globalstrahlung und Monatsmitteltemperatur einiger Standorte (Quelle: SIA 381/2, 1991)
Appendix 217
Tabelle 1 (Fortsetzung)
Appendix 218
Tabelle 1 (Fortsetzung)
Appendix 219
Tabelle 1 (Fortsetzung)
Appendix 220
Tabelle 1 (Fortsetzung)
Appendix 221
Tabelle 1 (Fortsetzung)
Appendix 222
Tabelle 1 (Fortsetzung)
Appendix 223
B Properties of Building Materials Tabelle 2: Rechenwerte von Dämmstoffen für bauphysikalische Nachweise (Quelle: SIA 279, 2004)
Appendix 224
Tabelle 3: Wärmeschutztechnische Bemessungswerte für Baustoffe, die gewöhnlich bei Gebäuden zur Anwendung kommen (Quelle: SN EN 12524:2000)
Stoffgruppe oder Anwendung Rohdichte Bemessungs-wärmeleit- fähigkeit
Spezifische Wärmespeich
erkapazität
Wasserdampf- diffsions-
widerstandszahl ρ λ cp µ kg/m3 W/(m·K) J/(kg·K) trocken feucht Asphalt
2100 0,70 1000 50000 50000 Bitumen
als Stoff 1050 0,17 1000 50000 50000 Membran / Bahn 1100 0,23 1000 50000 50000
Beton (a) Mittlere Rohdichte 1800 1,15 1000 100 60 2000 1,35 1000 100 60 2200 1,65 1000 120 70 Hohe Rohdichte 2400 2,00 1000 130 80 Armiert (mit 1% Stahl) 2300 2,3 1000 130 80 Armiert (mit 2% Stahl) 2400 2,5 1000 130 80
Fussbodenbeläge Gummi 1200 0,17 1400 10000 10000 Kunststoff 1700 0,25 1400 10000 10000 Unterlagen, poröser Gummi oder
Kunststoff 270 0,10 1400 10000 10000
Filzunterlage 120 0,05 1300 20 15 Wollunterlage 200 0,06 1300 20 15 Korkunterlage <200 0,05 1500 20 10 Korkfliesen >400 0,065 1500 40 20 Teppich / Teppichböden 200 0,06 1300 5 5 Linoleum 1200 0,17 1400 1000 800
Gase Luft 1,23 0,025 1008 1 1 Kohlendioxid 1,95 0,014 820 1 1 Argon 1,70 0,017 519 1 1 Schwefelhexafluorid 6,36 0,013 614 1 1 Krypton 3,56 0,0090 245 1 1 Xenon 5,68 0,0054 160 1 1
Glas Natronglas (einschliesslich Floatglas) 2500 1,00 750 ∞ ∞ Quarzglas 2200 1,40 750 ∞ ∞ Glasmosaik 2000 1,20 750 ∞ ∞
Wasser Eis bei –10 °C 920 2,30 2000 Eis bei 0 °C 900 2,20 2000 Schnee, frisch gefallen (< 30 mm) 100 0,05 2000 Neuschnee, weich (30…70 mm) 200 0,12 2000 Schnee leicht verharscht
(70…100 mm) 300 0,23 2000
Schnee, verharscht (< 200 mm) 500 0,60 2000 Wasser bei 10 °C 1000 0,60 4190 Wasser bei 40 °C 990 0,63 4190 Wasser bei 80 °C 970 0,67 4190
Metalle Aluminiumlegierungen 2800 160 880 ∞ ∞ Bronze 8700 65 380 ∞ ∞ Messing 8400 120 380 ∞ ∞ Kupfer 8900 380 380 ∞ ∞ Gusseisen 7500 50 450 ∞ ∞ Blei 11300 35 130 ∞ ∞ Stahl 7800 50 450 ∞ ∞ Nichtrostender Stahl 7900 17 460 ∞ ∞ Zink 7200 110 380 ∞ ∞
(a) Die Rohdichte von Beton ist als Trockenrohdichte angegeben.
Appendix 225
Tabelle 3 (Fortsetzung)
Stoffgruppe oder Anwendung Rohdichte Bemessungs-wärmeleit- fähigkeit
Spezifische Wärmespeich
erkapazität
Wasserdampf- diffsions-
widerstandszahl ρ λ cp µ kg/m3 W/(m·K) J/(kg·K) trocken feucht Massive Kunststoffe
Akrylkunststoffe 1050 0,20 1500 10000 10000 Polykarbonate 1200 0,20 1200 5000 5000 Polytetrafluorethylenkunststoffe (PTFE) 2200 0,25 1000 10000 10000 Polyvinylchlorid (PVC) 1390 0,17 900 50000 50000 Polymethylmethakrylat (PMMA) 1180 0,18 1500 50000 50000 Polyazetatkunststoffe 1410 0,30 1400 100000 100000 Polyamid (Nylon ) 1150 0,25 1600 50000 50000 Polyamid 6.6 mit 25% Glasfasern 1450 0,30 1600 50000 50000 Polyethylen /hoher Rohdichte 980 0,50 1800 100000 100000 Polyethylen/niedriger Rohdichte 920 0,33 2200 100000 100000 Polystyrol 1050 0,16 1300 100000 100000 Polypropylen 910 0,22 1800 10000 10000 Polypropylen mit 25% Glasfasern 1200 0,25 1800 10000 10000 Polyurethan (PU) 1200 0,25 1800 6000 6000 Epoxyharz 1200 0,20 1400 10000 10000 Phenolharz 1300 0,30 1700 100000 100000 Polyesterharz 1400 0,19 1200 10000 10000
Gummi Naturkautschuk 910 0,13 1100 10000 10000 Neopren (Polychloropren) 1240 0,23 2140 10000 10000 Butylkautschuk, (Isobuten-Kautschuk),
hart/heiss geschmolzen 1200 0,24 1400 200000 200000
Schaumgummi 60 - 80 0,06 1500 7000 7000 Hartgummi (Ebonit), hart 1200 0,17 1400 ∞ ∞ Ethylen-Propylenedien, Monomer
(EPDM ) 1150 0,25 1000 6000 6000
Polyisobutylenkautschuk 930 0,20 1100 10000 10000 Polysulfid 1700 0,40 1000 10000 10000 Butadien 980 0,25 1000 100000 100000
Dichtungsstoffe, Dichtungen und wärmetechnische Trennungen
Silicagel (Trockenmittel) 720 0,13 1000 ∞ ∞ Silikon ohne Füllstoff 1200 0,35 1000 5000 5000 Silikon mit Füllstoffen 1450 0,50 1000 5000 5000 Silikonschaum 750 0,12 1000 10000 10000 Urethan-/Polyurethanschaum (als wärmetechnische Trennung)
1300 0,21 1800 60 60
Weichpolyvinylchlorid (PVC-P) mit 40% Weichmacher
1200 0,14 1000 100000 100000
Elastomerschaum, flexibel 60 - 80 0,05 1500 10000 10000 Polyurethanschaum (PU) 70 0,05 1500 60 60 Polyethylenschaum 70 0,05 2300 100 100
Gips Gips 600 0,18 1000 10 4 Gips 900 0,30 1000 10 4 Gips 1200 0,43 1000 10 4 Gips 1500 0,56 1000 10 4 Gipskartonplatten (b) 900 0,25 1000 10 4
Putze und Mörtel Gipsdämmputz 600 0,18 1000 10 6 Gipsputz 1000 0,40 1000 10 6 Gipsputz 1300 0,57 1000 10 6 Gips, Sand 1600 0,80 1000 10 6 Kalk, Sand 1600 0,80 1000 10 6 Zement, Sand 1800 1,00 1000 10 6
(b) Die Wärmeleitfähigkeit schliesst den Einfluss der Papierdeckschichten ein.
Appendix 226
Tabelle 3 (Fortsetzung)
Stoffgruppe oder Anwendung Rohdichte Bemessungs-wärmeleit- fähigkeit
Spezifische Wärmespeich
erkapazität
Wasserdampf- diffsions-
widerstandszahl ρ λ cp µ kg/m3 W/(m·K) J/(kg·K) trocken feucht Erdreich
Ton oder Schlick oder Schlamm 1200 – 1800 1,5 1670 – 2500 50 50 Sand und Kies 1700 – 2200 2,0 910 – 1180 50 50
Gestein Kristalliner Naturstein 2800 3,5 1000 10000 10000 Sediment-Naturstein 2600 2,3 1000 250 200 Leichter Sediment-Naturstein 1500 0,85 1000 30 20 Poröses Gestein, z.B. Lava 1600 0,55 1000 20 15 Basalt 2700 – 3000 3,5 1000 10000 10000 Gneis 2400 – 2700 3,5 1000 10000 10000 Granit 2500 – 2700 2,8 1000 10000 10000 Marmor 2800 3,5 1000 10000 10000 Schiefer 2000 – 2800 2,2 1000 1000 800 Kalkstein, extraweich 1600 0,85 1000 30 20 Kalkstein, weich 1800 1,1 1000 40 25 Kalkstein, halbhart 2000 1,4 1000 50 40 Kalkstein, hart 2200 1,7 1000 200 150 Kalkstein, extrahart 2600 2,3 1000 250 200 Sandstein (Quarzit) 2600 2,3 1000 40 30 Naturbims 400 0,12 1000 8 6 Kunststein 1750 1,3 1000 50 40
Dachziegelsteine Ton 2000 1,0 800 40 30 Beton 2100 1,5 1000 100 60
Platten Keramik/Porzellan 2300 1,3 840 Kunststoff 1000 0,20 1000 10000 10000
Nutzholz (c) 500 0,13 1600 50 20 700 0,18 1600 200 50
Holzwerkstoffe Sperrholz (d) 300 0,09 1600 150 50 500 0,13 1600 200 70 700 0,17 1600 220 90 1000 0,24 1600 250 110 Zementgebundene Spanplatte 1200 0,23 1500 50 30 Spanplatte 300 0,10 1700 50 10 600 0,14 1700 50 15 900 0,18 1700 50 20 OSB-Platten 650 0,13 1700 50 30 Holzfaserplatte, einschliesslich MDF (e) 250 0,07 1700 5 2 400 0,10 1700 10 5 600 0,14 1700 20 12 800 0,18 1700 30 20
(c) Die Rohdichte von Nutzholz und Holzfaserplattenprodukten ist die Gleichgewichtsdichte bei 20 °C und 65% relativer Luftfeuchte. (d) Als Interimsmassnahme und bis zum Vorliegen hinreichend zuverlässiger Daten können für Hartfaserplatten (solid wood panels,
SWP) und Bauholz mit Furnierschichten (LVL, laminated veneer lumber) die für Sperrholz angegebenen Werte angewendet wer-den.
(e) MDF bedeutet Medium Density Fibreboard (mitteldichte Holzfaserplatte), die im sog. Trockenverfahren hergestellt worden ist. ANMERKUNG 1 Für Computerberechnungen kann der ∞-Wert durch einen beliebig grossen Wert, wie z. B. 106, ersetzt werden. ANMERKUNG 2 Wasserdampf-Diffusionswiderstandszahlen sind als Werte nach den in prEN ISO 12572:1999 festgelegten “Dry
cup-” und “Wet cup-Verfahren” angegeben.
Appendix 227
Tabelle 4: Wärmeschutztechnische Bemessungswerte für Mauerwerke, Mörtel und Verputze Stoffgruppe oder Anwendung Rohdichte Bemessungs-
wärmeleit- fähigkeit
Spezifische Wärmespeich
erkapazität
Wasserdampf- diffsions-
widerstandszahl ρ λ cp µ kg/m3 W/(m·K) J/(kg·K) trocken feucht Mauerwerk unverputzt
Modulbackstein Einstein 1100 0,44 900 6 4 Modulbackstein Verband 1100 0,37 900 6 4
Isolierbackstein 1200 0,47 900 6 4 Sichtbackstein 1400 0,52 900 8 6 Kaminstein 1800 0,80 900 10 8 Kalksandstein 1600 0,80 900 25 10 1800 1,00 900 25 10 2000 1,10 900 25 10 Zementstein 2000 1,10 1000 15 10 Zementblockstein 1200 0,70 1000 15 10 Porenbetonstein 300 0,10 1000 10 5 400 0,13 1000 10 5 500 0,16 1000 10 5 600 0,19 1000 10 5
Putze, Mörtelschichten Innenputz für normale Berechnungen 1400 0,70 900 10 6 Aussenputz für normale Berechnungen 1800 0,87 1000 35 15 Wärmedämmputz aussen 450 0,14 1000 15 10 Wärmedämmputz aussen 300 0,08 1000 15 10 Kalkmörtel 1800 0,87 1000 35 15 Kalkzementmörtel 1900 1,00 1000 35 15 Zementmörtel 2200 1,40 1000 35 15 Leichtmörtel 450 0,16 1000 20 5 600 0,21 1000 20 5 900 0,32 1000 20 5 1600 0,80 1000 35 15