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Herausgeber: Wiley-VCH
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch

Beschreibung

Bad experiences with construction quality, the energy crises of 1973 and 1979,complaints about 'sick buildings', thermal, acoustical, visual and olfactory discomfort, the need for good air quality, the move towards more sustainability - all these have accelerated the development of a field that, for a long time, was hardly more than an academic exercise: building physics. The discipline embraces domains such as heat and mass transfer, building acoustics, lighting, indoor environmental quality and energy efficiency. In some countries, fire safety is also included. Through the application of physical knowledge and its combination with information coming from other disciplines, the field helps to understand the physical phenomena governing building parts, building envelope, whole building and built environment performance, although for the last the wording 'urban physics' is used. Building physics has a real impact on performance-based building design. This volume on 'Applied Building Physics' discusses the heat, air and moisture performance metrics that affect building design, construction and retrofitting.

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Veröffentlichungsjahr: 2016

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Leseprobe

Cover

Series Page

Title Page

Dedication

Preface

Chapter 0: Introduction

0.1 Subject of the Book

0.2 Building Physics Vs. Applied Building Physics

0.3 Units and Symbols

Further Reading

Chapter 1: Outdoor and Indoor Ambient Conditions

1.1 Overview

1.2 Outdoors

1.3 Indoors

Further Reading

Chapter 2: Performance Metrics and Arrays

2.1 Definitions

2.2 Functional Demands

2.3 Performance Requirements

2.4 A Short History

2.5 Performance Arrays

Further Reading

Chapter 3: Whole Building Level

3.1 Thermal Comfort

3.2 Health and Indoor Environmental Quality

3.3 Energy Efficiency

3.4 Durability

3.5 Economics

3.6 Sustainability

Further Reading

Chapter 4: Envelope and Fabric: Heat, Air and Moisture Metrics

4.1 Introduction

4.2 Airtightness

4.3 Thermal Transmittance

4.4 Transient Thermal Response

4.5 Moisture Tolerance

4.6 Thermal Bridges

4.7 Contact Coefficients

4.8 Hygrothermal Stress and Strain

4.9 Transparent Parts: Solar Transmittance

Further Reading

Chapter 5: Timber-framed Outer Wall as an Exemplary Case

5.1 In General

5.2 Assembly

5.3 Heat, Air, Moisture Performances

Chapter 6: Heat-Air-Moisture Material Properties

6.1 Introduction

6.2 Dry Air and Water

6.3 Materials, Thermal Properties

6.4 Materials, Air-Related Properties

6.5 Materials, Moisture Properties

6.6 Surfaces, Radiant Properties

Further Reading

Appendix A: Solar Radiation for Uccle, Belgium, 50° 51′ North, 4° 21′ East

End User License Agreement

List of Tables

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 1.5

Table 1.6

Table 1.7

Table 8.1

Table 1.9

Table 1.10

Table 1.11

Table 1.12

Table 1.13

Table 1.14

Table 1.15

Table 1.16

Table 1.17

Table 1.18

Table 1.19

Table 1.20

Table 1.23

Table 1.24

Table 1.25

Table 1.26

Table 1.27

Table 1.28

Table 1.29

Table 1.30

Table 2.1

Table 2.2

Table 2.3

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

Table 3.7

Table 3.8

Table 3.9

Table 3.10

Table 3.11

Table 3.12

Table 3.13

Table 3.14

Table 3.15

Table 3.16

Table 3.17

Table 3.18

Table 3.19

Table 3.20

Table 3.21

Table 3.22

Table 3.23

Table 3.24

Table 3.25

Table 3.26

Table 3.27

Table 3.28

Table 3.29

Table 3.30

Table 3.31

Table 3.32

Table 3.33

Table 3.34

Table 3.35

Table 3.36

Table 3.37

Table 3.38

Table 3.39

Table 3.40

Table 3.41

Table 3.42

Table 3.43

Table 3.44

Table 3.45

Table 3.46

Table 3.47

Table 4.1

Table 4.2

Table 4.3

Table 4.4

Table 4.5

Table 5.1

Table 5.2

Table 5.3

Table 6.1

Table 6.2

Table 6.3

Table A.1

Table A.2

Table A.3

Table A.4

Table A.5

List of Illustrations

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

Figure 1.8

Figure 1.9

Figure 1.10

Figure 1.11

Figure 1.12

Figure 1.13

Figure 1.14

Figure 1.15

Figure 1.16

Figure 1.17

Figure 1.18

Figure 1.19

Figure 1.20

Figure 1.21

Figure 1.22

Figure 1.23

Figure 1.24

Figure 1.25

Figure 1.26

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 3.10

Figure 3.11

Figure 3.12

Figure 3.13

Figure 3.14

Figure 3.15

Figure 3.16

Figure 3.17

Figure 3.18

Figure 3.19

Figure 3.20

Figure 3.21

Figure 3.22

Figure 3.23

Figure 3.24

Figure 3.25

Figure 3.26

Figure 3.27

Figure 3.28

Figure 3.29

Figure 3.30

Figure 3.31

Figure 3.32

Figure 3.33

Figure 3.34

Figure 3.35

Figure 3.36

Figure 3.37

Figure 3.38

Figure 3.39

Figure 3.40

Figure 3.41

Figure 3.42

Figure 3.43

Figure 3.44

Figure 3.45

Figure 3.46

Figure 3.47

Figure 3.48

Figure 3.49

Figure 3.50

Figure 3.51

Figure 3.52

Figure 3.53

Figure 3.54

Figure 3.55

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.11

Figure 4.12

Figure 4.13

Figure 4.14

Figure 4.15

Figure 4.16

Figure 4.17

Figure 4.18

Figure 4.19

Figure 4.20

Figure 4.21

Figure 4.22

Figure 4.23

Figure 4.24

Figure 4.25

Figure 4.26

Figure 4.27

Figure 4.28

Figure 4.29

Figure 4.30

Figure 4.31

Figure 4.32

Figure 4.33

Figure 4.34

Figure 4.35

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 6.1

Figure 6.2

Figure 6.3

Guide

Cover

Table of Contents

Begin Reading

Chapter 1

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Applied Building Physics

Ambient Conditions, Building Performance and Material Properties

Second Edition

Hugo Hens

All books published by Ernst & Sohn are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

2. completely revised Edition

Print ISBN: 978-3-433-03147-6

oBook ISBN: 978-3-433-60711-4

ePDF ISBN: 978-3-433-60712-1

ePub ISBN: 978-3-433-60714-5

eMobi ISBN: 978-3-433-60723-7

Dedication

To my wife, children and grandchildren

In remembrance of Professor A. de Grave who introduced Building Physics as a new discipline at the University of Leuven (KULeuven) Belgium in 1952

Preface

Until the first energy crisis of 1973, building physics was a rather dormant field within building engineering, with seemingly limited applicability. While soil mechanics, structural mechanics, building materials, building construction and HVAC were perceived as essential, designers sought advice on room acoustics, moisture tolerance, summer comfort or lighting only when really necesary or when problems arose. Energy was even not a concern, while thermal comfort and indoor environmental quality were presumed to be guaranteed thanks to infiltration, window operation and the heating and cooling system installed. The energy crises of the 1970s, persisting moisture problems, complaints about sick buildings, thermal, visual and olfactory discomfort and the move towards more sustainability changed it all. Societal pressure to diminish energy consumption in buildings without degrading usability activated the notion of performance based design and construction. As a result, today, building physics – and its potential to quantify related performance requirements – is at the forefront of building innovation.

As with all engineering sciences, building physics is orientated towards application, which is why, after the first volume on the fundamentals, this second volume examines performance metrics and requirements as the basis for sound building engineering. Choices have been made, among others to limit the text to the heat, air and moisture performances. Subjects treated are: the outdoor and indoor ambient conditions, the performance concept, performance at the building level, performance metrics at the building enclosure level and the heat-air-moisture material properties of building, insulation and finishing materials. The book reflects 38 years of teaching architectural, building and civil engineers, bolstered by close to 50 years' experience in research and consultancy. Where needed, information from international sources was used, which is why each chapter ends with an extended reading list.

The book uses SI units. Undergraduate and graduate students in architectural and building engineering should benefit, but also mechanical engineers studying HVAC and practising building engineers, who want to refresh their knowledge. The level of discussion presumes that the reader has a sound knowledge of the fundamentals treated in the first volume, along with a background in building materials and building construction.

Acknowledgements

The book reflects the work of many people, not just the author. Therefore, I would like to thank the thousands of students I have had during my 38 years of teaching. They have given me the opportunity to optimize the content. Also, were I not standing on the shoulders of those who precede me, this book would not be what it is. Although I started my career as a structural engineer, my predecessor, Professor Antoine de Grave, planted the seeds that fed my interest in building physics. The late Bob Vos of TNO, the Netherlands, and Helmut Künzel of the Fraunhofer Institut für Bauphysik, Germany, showed the importance of experimental work and field testing for understanding building performance, while Lars Erik Nevander of Lund University, Sweden, taught that solving problems does not always require complex modelling, mainly because reality in building construction is always much more complex than any model could simulate.

During my four decades at the Laboratory of Building Physics, several researchers and PhD students have been involved. I am very grateful to Gerrit Vermeir, Staf Roels, Dirk Saelens and Hans Janssen, colleagues at the university; also to Jan Carmeliet, professor at the ETH, Zürich; Piet Standaert, principal at Physibel Engineering; Jan Lecompte; Filip Descamps, principal at Daidalos Engineering and part-time professor at the Free University Brussels (VUB); Arnold Janssens, professor at the University of Ghent (UG); Rongjin Zheng, associate professor at Zhejiang University, China; Bert Blocken, full professor at the Technical University Eindhoven (TU/e); Griet Verbeeck, associate professor at the University of Hasselt; and Wout Parys, all of whom contributed through their work. The experiences gained as a structural engineer and building site supervisor at the start of my career, as building assessor over the years, as researcher and operating agent of four Annexes of the IEA, Executive Committee on Energy in Buildings and Communities forced me to rethink my engineering-based performance approach time and again. The many ideas I exchanged and received in Canada and the USA from Kumar Kumaran, the late Paul Fazio, Bill Brown, William B. Rose, Joe Lstiburek and Anton Ten Wolde were also of great help.

Finally, I thank my family, my wife Lieve, who manages to live with a busy engineering professor, my three children who had to live with that busy father and my many grandchildren who do not know that their grandfather is still busy.

Leuven, January 2016

Hugo S.L.C. Hens

0Introduction

0.1 Subject of the Book

This is the second volume in a series of four books:

– Building Physics: Heat, Air and Moisture

–

Applied Building Physics: Boundary Conditions, Building Performance and Material Properties

– Performance Based Building Design: from below grade construction to cavity walls

– Performance Based Building Design: from timber-framed construction to partition walls.

Subjects discussed in this volume are: outdoor and indoor ambient conditions, performance concept, performance at the urban, building and building envelope level and the heat–air–moisture material properties. The book figures as a hinge between ‘Building Physics: Heat, Air and Moisture’ and the two volumes on ‘Performance Based Building Design’. Although it does not deal with acoustics and lighting in detail, they form an integral part of the performance arrays and are mentioned as and when necessary.

The outdoor and indoor ambient conditions and related design approaches are highlighted in Chapter 1. Chapter 2 advances the performance concept with its hierarchical structure, going from the urban environment across the building and building assemblies down to the layer and material level. In Chapter 3, the main heat, air and moisture linked performances at the building level are discussed, while Chapter 4 analyses related metrics of importance for a well-performing building envelope and fabric. Chapter 5 deals with timber-framed walls as an exemplary case, and Chapter 6 lists the main heat, air and moisture material property values needed to predict the response of building assemblies.

A performance approach helps designers, consulting engineers and contractors to better ensure building quality. Of course, physical integrity is not the only factor adding value to buildings. Functionality, spatial quality and aesthetics – aspects belonging to the architect's responsibility – are of equal importance, though they should not cause us to neglect the importance of an overall outstanding building performance.

0.2 Building Physics Vs. Applied Building Physics

Readers who would like to know more about the engineering field ‘building physics’, its importance and history, should consult the first volume, ‘Building Physics: Heat, Air and Moisture’. It might seem that adding the term ‘applied’ to this second volume is unnecessary – building physics is, by definition, applied. Rather, the word stresses the focus of this book: entirely directed towards its use in building design and construction.

0.3 Units and Symbols

The book uses the SI system (internationally mandated since 1977). Its base units are the metre (m), the kilogram (kg), the second (s), the kelvin (K), the ampere (A) and the candela. Derived units of importance when studying applied building physics are:

Force:

newton (N);

1 N = 1 kg·m·s

−2

Pressure:

pascal (Pa);

1 Pa = 1 N/m

= 1 kg·m

−1

·s

−2

Energy:

joule (J);

1 J = 1 N·m = 1 kg·m

·s

−2

Power:

watt (W);

1 W = 1 J·s

−1

= 1 kg·m

·s

−3

For symbols, the ISO-standards (International Standardization Organization) are followed. If a quantity is not included, the CIB-W40 recommendations (International Council for Building Research, Studies and Documentation, Working Group ‘Heat and Moisture Transfer in Buildings’) and the list edited by Annex 24 of the IEA EBC (International Energy Agency, Executive Committee on Energy in Buildings and Communities) apply.

Table 0.1 List with symbols and quantities

Symbol

Meaning

SI units

Acceleration

m/s

Thermal diffusivity

Thermal effusivity

W/(m

·K·s

0.5

)

Specific heat capacity

J/(kg·K)

Concentration

kg/m

, g/m

Emissivity

—

Specific free energy

J/kg

Temperature ratio

—

Specific free enthalpy

J/kg

Acceleration by gravity

m/s

Mass flux

kg/(m

·s)

Height

Specific enthalpy

J/kg

Surface film coefficient for heat transfer

W/(m

·K)

Mass related permeability (mass could be moisture, air, salt…)

Length

Specific enthalpy of evaporation or melting

J/kg

Mass

Ventilation rate

−1

, h

−1

Partial pressure

Heat flux

W/m

Radius

Specific entropy

J/(kg·K)

Time

Specific latent energy

J/kg

Velocity

m/s

Moisture content

kg/m

Cartesian coordinates

Water sorption coefficient

kg/(m

·s

0.5

)

Area

Water penetration coefficient

m/s

0.5

Diffusion coefficient

Moisture diffusivity

Irradiation

W/m

Free energy

Free enthalpy

Mass flow (mass = vapour, water, air, salt)

kg/s

Enthalpy

Radiation intensity

J/rad

Thermal moisture diffusion coefficient

kg/(m·s·K)

Mass permeance

s/m

Force

Luminosity

W/m

Emittance

W/m

Power

Thermal permeance

W/(m

·K)

Total pressure

Heat

Thermal resistance

·K/W

Gas constant

J/(kg·K)

Entropy

J/K

Saturation degree

—

Absolute temperature

Period (of a vibration or a wave)

s, days,…

Latent energy

Thermal transmittance

W/(m

·K)

Volume

Air resistance

m/s

Moisture ratio

kg/kg

Diffusion resistance

m/s

Thermal expansion coefficient

−1

Absorptivity

—

Surface film coefficient for diffusion

s/m

Volumetric thermal expansion coefficient

−1

Dynamic viscosity

N·s/m

Temperature

°C

Thermal conductivity

W/(m·K)

Vapour resistance factor

—

Kinematic viscosity

Density

kg/m

Reflectivity

—

Surface tension

N/m

Transmissivity

—

Relative humidity

—

Angle

rad

Specific moisture capacity

kg/kg per unit of moisture potential

Porosity

—

Volumetric moisture ratio

Heat flow

Table 0.2 List with suffixes and notations

Symbol

Meaning

Symbol

Meaning

Indices

Air

Moisture, maximal

Capillary, convection

Operative

Outside, outdoors

Radiant, radiation

Hygroscopic

sat

Saturation

Inside, indoors

Surface, area, suction

Critical

Water vapour

, SO

Chemical symbol for gasses

Water

Relative humidity

Notation

Meaning

[], bold,

Matrix, array, value of a complex number

dash (ex..:

)

Vector

1Outdoor and Indoor Ambient Conditions

1.1 Overview

In building physics, the outdoor and indoor ambient conditions play a role comparable to the loads in structural engineering, which is why the term ‘ambient loads’ is often used. Their knowledge is essential to make correct design decisions. The components that shape them are:

Outdoors

Indoors

Air temperature (also called dry bulb temperature)

Radiant temperature

Relative humidity

(Partial water) vapour pressure

Solar radiation

Under-cooling

Wind

Air speed

Rain and snow

Air pressure

a,e

Air pressure

a,i

In the paragraphs that follow, these components are discussed separately. Bear in mind though that the greater the decoupling between the outdoor and indoor temperatures, and sometimes the relative humidities, the stricter will be the envelope and HVAC performance requirements. Otherwise, much more energy will be needed to maintain those differences.

Predicting future outdoor conditions is hardly possible. Not only are most components measured in only a few locations but the future is never the same as the past. Unfortunately, climate does not obey the paradigm ‘the longer the data chain available, the better the forecast’. Moreover, global warming is affecting everything, see Figure 1.1.

Figure 1.1 Increase in the world's average annual temperature between 1850 and 2014.

A typical way of bypassing the problem is by using reference values and reference years for each performance check that needs climate data, such as the heating and cooling load, end energy consumption, overheating, moisture tolerance and other durability issues.

Much of the data illustrating the facts and trends discussed in the following paragraphs comes from the weather station at Uccle, Belgium (50° 51′ north, 4° 21′ east). This is because of the large number of observations available, which allowed the synthesis of the weather there over the past century.

1.2 Outdoors

Geographical location defines, to a large extent, the outdoor climate: northern or southern latitude, proximity of the sea, presence of a warm or cold sea current and height above sea level. Of course, microclimatic factors also intervene. The urban heat island effect means that air temperature in city centres is higher, relative humidity lower and solar radiation less intense than in the countryside. Table 1.1 lists the monthly mean dry bulb temperature measured in a thermometer hut for the period 1901–1930 at Uccle and Sint Joost. Both weather stations are situated in the Brussels region, though the Uccle one overlooks a green area, while the Sint Joost one is in the city centre.

Table 1.1 Monthly mean dry bulb temperature at Uccle and Sint Joost, Brussels region, for the period 1901–1930 (°C)

Location

Month

Uccle

2.7

3.1

5.5

8.2

12.8

14.9

16.8

16.4

14.0

10.0

5.2

3.7

Sint Joost

3.8

4.2

6.8

9.4

14.6

16.7

18.7

18.0

15.4

11.2

6.4

4.7

The outdoor climate further shows periodic fluctuations, linked to the earth's inclination and its elliptic orbit around the sun, the year and its succession of winter, spring, summer and autumn, and the wet and dry seasons in the equatorial band. Then there is the sequence of high and low pressure fronts; in temperate and cold climates, high brings warmth in summer and cold in winter, low gives cool and wet in summer and fresh and wet in winter. Finally, there is the effect of day and night, a consequence of the earth's rotation around its axis.

Design focuses on annual cycles, daily cycles and daily averages, but the meteorological references are 30-year averages, for the 20–21st century: 1901–1930, 1931–1960, 1961–1990, 1991–2020, 2021–2050…These vary due to long-term climate changes as induced by solar activity and global warming, but the data is also affected by relocation of weather stations, more accurate measuring devices and the way averages are calculated. Up to 1930, the ‘daily mean temperature’ was the average of that day's minimum and maximum, as logged by a minimum/maximum mercury thermometer. Today, the air temperature at many weather stations is logged at 10′ intervals, and the daily mean is calculated as the average of these 144 values.

1.2.1 Air Temperature

Knowing the air temperature helps in estimating the heating and cooling load and the related annual end energy consumption with the loads fixing the size and cost of the HVAC system needed and the end energy used being part of the annual costs. From day to day the air temperature also participates in the heat, air and moisture stresses that enclosures endure, while high values increase the indoor overheating risk. Measurement takes place in a thermometer hut in open field, 1.5 m above grade. The accuracy imposed by the World Meteorological Organization is ±0.5 °C. Table 1.2 covers over 30 years of averaged monthly means for several weather stations across Europe and North America. All look well represented by an annual mean and single harmonic, although adding a second harmonic gives a better fit:

Table 1.2 Monthly mean air temperatures for several locations (°C)

Location

Month

Uccle (B)

2.7

3.1

5.5

8.2

12.8

14.9

16.8

16.4

14.0

10.0

5.2

3.7

Den Bilt (NL)

1.3

2.4

4.3

8.1

12.1

15.3

16.1

14.2

10.7

5.5

1.2

Aberdeen (UK)

2.5

2.7

4.5

6.8

9.0

12.1

13.7

13.3

11.9

9.3

5.3

3.7

Eskdalemuir (UK)

1.8

1.9

3.9

5.8

8.9

11.8

13.1

12.9

10.9

8.5

4.3

2.7

Kew (UK)

4.7

4.8

6.8

9.0

12.6

15.6

17.5

17.1

14.8

11.6

7.5

5.6

Kiruna (S)

−12.2

−12.4

−8.9

−3.5

2.7

9.2

12.9

10.5

5.1

−1.5

−6.8

−10.1

Malmö (S)

−0.5

−0.7

1.4

6.0

11.0

15.0

17.2

16.7

13.5

8.9

4.9

2.0

Västerås (S)

−4.1

−1.4

4.1

10.1

14.6

17.2

15.8

11.3

6.3

1.9

−1.0

Lulea (S)

−11.4

−10.0

−5.6

−0.1

6.1

12.8

15.3

13.6

8.2

2.9

−4.0

−8.9

Oslo (N)

−4.2

−4.1

−0.2

4.6

10.8

15.0

16.5

15.2

10.8

6.1

0.8

−2.6

München (D)

−1.5

−0.4

3.4

8.1

11.9

15.6

17.5

16.7

13.9

8.8

3.6

−0.2

Potsdam (D)

−0.7

−0.3

3.5

8.0

13.1

16.6

18.1

17.5

13.8

9.2

4.1

0.9

Roma (I)

7.6

9.0

11.3

13.9

18.0

22.3

25.2

24.7

21.5

16.8

12.1

8.9

Catania (I)

10.0

10.4

12.0

14.0

18.0

22.0

25.2

25.6

23.2

18.4

15.2

11.6

Torino (I)

1.6

3.5

7.6

10.8

15.4

19.0

22.3

21.6

17.9

12.3

6.2

2.4

Bratislava (Sk)

−2.0

0.0

4.3

9.6

14.2

17.8

19.3

18.9

15.3

10.0

4.2

0.1

Copenhagen (Dk)

−0.7

−0.8

1.8

5.7

11.1

15.1

16.2

16.0

12.7

9.0

4.7

1.1

Montreal

−9.9

−8.5

−2.4

5.7

13.1

18.4

21.1

19.5

14.6

8.5

1.8

−6.5

New York

0.6

2.2

6.1

11.7

17.2

22.2

25.0

24.4

20.0

13.9

8.9

3.3

Chicago

−5.6

−3.3

2.8

9.4

15.0

20.6

23.3

22.2

18.3

11.7

4.4

−2.8

Los Angeles

15.0

14.9

20.3

17.3

18.8

20.7

22.9

23.5

22.8

20.3

16.9

14.2

Single harmonic

(1.1)θe=θ¯e+A1,1sin2πt365.25+B1,1cos2πt365.25

Two harmonics

(1.2)θe=θ¯e+A2,1sin2πt365.25+B2,1cos2πt365.25+A2,2sin4πt365.25+B2,2cos4πt365.25

In both formulas, θ¯e is the annual mean and t time. For three of the locations listed, the two-harmonic equation gives (°C, see Figure 1.2):

2,1

2,2

Uccle

9.8

−2.4

−7.4

0.45

−0.1

Kiruna

−1.2

−4.2

−11.6

1.2

0.5

Catania

17.2

−4.1

−6.6

0.8

0.2

Figure 1.2 Air temperature: annual course, single and two harmonics.

For Uccle the average difference between the monthly mean daily minimums and maximums (θe,max,day − θe,min,day) during the period 1931 − 1960 looked as (°C):

5.6

6.6

7.9

9.3

10.7

10.8

10.6

10.1

9.8

8.0

6.2

5.2

A combination with the annual course could give (time in hours):

(1.3)θe=θ¯e+θˆecos2πt−h18766+12Δθ¯e,dag+Δθˆe,dagcos2πt−h28766sin2πt−h324

with:

dag

(°C)

dag

(°C)

(

)

(

)

(

)

8.4

2.8

456

−42

an equation, assuming that the daily values fluctuate harmonically. This is not the case. The gap between the daily minimum and maximum swings considerably, without even a hint of a harmonic course. To give an example, in Leuven, Belgium, that gap for January and July 1973 was purely random, with averages of 4.0 °C and 8.9 °C and standard deviation percentages 60 in January and 39 in July.

A question is whether the air temperature recorded during the past decades in any weather station reflects global warming? For that, the data recorded between 1997 and 2013 at the outskirts of Leuven were tabulated. Figure 1.3 shows the annual means and the monthly minima and maxima measured.

Figure 1.3 Leuven weather station (Belgium): air temperature between 1996 and 2013: annual mean (left) and average, minimum and maximum monthly mean (right).

The least square straight line through the annual means equals:

θ¯e,ann=11.1−0.034×year

With an of average 11.1 °C and a slightly negative slope, the expected increase seems absent. Not so at Uccle, 30 km west of Leuven. There the overall mean between 1901 and 1930 was 9.8 °C, that is 1.4 °C lower than measured at Leuven from 1997 to 2013. Between 1952 and 1971 that mean remained 9.8 °C but since then the moving 20-year mean has increased slowly, with the highest values noted between 1992 and 2011.

1.2.2 Solar Radiation

Solar radiation means free heat gains. These lower the energy used for heating but may create cooling needs, as too many gains increase the overheating risk. The sun further lifts the outside surface temperature of irradiated envelope assemblies. Although this enhances drying, it also activates solar-driven vapour flow to the inside of moisture stored in rain buffering outer layers, whereas the associated drop in relative humidity aggravates hygrothermal stress in thin outer finishes.

The sun is a 5762 K hot black body, 150 000 000 km from the earth. Due to the large distance, the rays approach the earth in parallel. Above the atmosphere the solar spectrum follows the thin line in Figure 1.4, while the total irradiation is approximately:

(1.4)EST=5.67TS1004rSDSE2=5.67×57.644×0.695·1061.496·1082=1332W/m2

with rs the solar radius and DSE the distance between sun and earth, both in km.

Figure 1.4 Solar spectrums before (thin) and after passing the atmosphere (thicker line).

This 1332 W/m2 represents the average solar constant (ESTo), that is the mean radiation per square metre that the earth would receive perpendicular to the beam if there were no atmosphere. The related energy flow is thinly spread. Burning 1 litre of fuel gives 4.4 × 107 J, but collecting the same amount from the sun just above the atmosphere on a square metre perpendicular to the beam would take 9 hours of constant irradiation. This thinness explains why collecting solar energy for heat or electricity production requires such large surface areas. A more exact calculation of the solar constant accounts for the annual variation in distance between earth and sun and the annual cycle in solar activity (d the number of days from December 31/January 1 at midnight):

(1.5)ESTo=13731+0.03344cos2π365.25d−2.75(W/m2)

What fixes the solar position at the sky is either the azimuth (as) and solar height (hs) or the time angle (ω) and declination (δ), that is the angle between the Tropics of Capricorn or Cancer, where the solar height reaches 90°, zenith position, and the equator plane, see Figure 1.5. The first two describe the sun's movement as seen locally, the second two relate it to the equator.

Figure 1.5 Solar angles.

The time angle (ω) goes from 180° at 0 a.m. through 0° at noon to −180° at 12 p.m. One hour therefore corresponds to 15°. The declination (δ) in radians is given by:

(1.6)δ=arcsin−sinπ18023.45cos2π365.25d+10

where ±23.45 is the latitude of the Tropics in degrees. Solar height in radians at any moment equals:

(1.7)hs=max0,π/2−arccoscosφcosδcosω+sinφsinδ

The maximum value (hs,max) in degrees or radians follows from:

(1.8)Degrees: hs.max=90−φ°+δ°Radians: hs,max=π/2−φ+δ

with φ latitude, positive for the northern, negative for the southern hemisphere. The addition (°) means values in degrees celsius.

1.2.2.1 Beam Radiation

During its passage through the atmosphere, selective absorption by ozone, oxygen, hydrogen, carbon dioxide and methane interferes with the solar beam and changes its spectrum, while scattering disperses a part of it. The longer the distance traversed through the atmosphere, the more the radiation is affected, as represented by the air factor m, which is the ratio between the real distance traversed to sea level through the atmosphere, with the sun at height hs and the distance traversed to any location at and above sea level, assuming that the sun stands in zenith position there (Figure 1.6).

Figure 1.6L the distance traversed through the atmosphere to sea level, z height of a location in km, Lo the distance traversed to z for the sun in zenith position.

For a location z km above sea level the air factor can be written as (all formulas below with solar height in radians):

(1.9)m=LLo=1−0.1zsinhs+0.15hs+3.885−1.253

Beam radiation on a surface perpendicular to the solar rays then becomes:

ESD,n=ESToexp−mdRTAtm

where TAtm is atmospheric turbidity and dR the optic factor, a measure for the scatter per unit of distance traversed:

(1.10)dR=1.4899−2.1099coshs+0.6322cos2hs+0.0253cos3hs−1.0022sinhs+1.0077sin2hs−0.2606sin3hs

On a clear day with average air pollution, atmospheric turbidity is given by:

TAtm=3.372+3.037hs−0.296cos0.5236mo

With minimal air pollution, it becomes:

TAtm=2.730+1.549hs−0.198cos0.5236mo

In both formulas mo is the month, 1 for January, 12 for December.

Beam radiation on a tilted surface, whose normal forms an angle χ with the solar rays, is calculated as (Figure 1.7):

(1.11)ESD,s=max0,ESD,ncosχ

with the zero to be applied before sunrise and after sunset and:

(1.12)cosχ=sinδsinφcosss−sinδcosφsinsscosas+cosδcosφcossscosω+cosδsinφsinsscosascosω+cosδsinsssinassinω

Here ss is the surface's slope, 0° when horizontal, 90° (π/2) when vertical, between 0 and 90° when tilted to the sun, between 0 and −90° (−π/2) when tilted away from the sun, and as the surface's azimuth (south 0°, east 90°, north 180°, west −90°).

Figure 1.7 Direct radiation on a surface with slope ss.

For a horizontal plane facing the sun the formula reduces to:

cosχh=sinδsinφ+cosδcosφcosω

For vertical planes facing the sun it becomes:

Southcosχv,south=−sinδcosφ+cosδsinφcosωWestcosχv,west=−cosδsinωNorthcosχv,north=−sinδcosφ−cosδsinφcosωEastcosχv,east=cosδsinω

Where the beam radiation on a horizontal surface is known (ESD,h), its value on any tilted surface (ESD,s) follows from:

(1.13)ESD,s=max0,ESD,hcosχs/cosχh

Beam radiation seems to be predictable, but the big unknown is the atmospheric turbidity (TAtm). Cloudiness, air pollution and relative humidity all intervene, but their impact is very complex and varies from day to day.

1.2.2.2 Diffuse Radiation

Whether the sky is blue or cloudy, diffuse solar radiation reaches the earth from sunrise to sunset. At the earth's surface, it's as if the rays come from all directions. The simplest model considers the sky as a uniformly radiating vault. Any surface, whose slope forms an angle with the horizontal, sees part of it. As a black body at constant temperature, each point on the vault has equal luminosity, turning the surface's view factor into:

(1.14)Fs,sk=1+cosss/2

If ESd,h is the diffuse radiation on a horizontal surface, tilted it becomes:

(1.15)ESd,s=ESd,h1+cosss/2

Better approximating reality is the sky as a vault with the highest luminosity at the solar disk and the lowest at the horizon. With the position of any point P on that vault characterized by its azimuth aP and height hP, luminosity there writes as L(aP,hP). The angle Γ between the normal on a surface with slope ss and the line from its centre to this point P now equals:

cosΓ=sinsscoshPcosas−aP+cossssinhP

Diffuse radiation on a tilted surface therefore becomes:

(1.16)ESd,s=KD∬aP,hPLaP,hPcoshPcosΓdhPdaP

with KD=1+0.03344cos0.017202d−2.75, 0≤aP≤2π, 0≤hP≤π/2, cosΓ≥0 and:

(1.17)LaP,hP=Lsd0.91+10exp−3ε+0.45cos2ε1−exp−0.32cosechP0.273850.91+10exp−3π2−hS+0.45sin2hS︸f

where Lsd is the luminosity at the solar disk and ɛ the angle between the line from the surface's centre to P and the normal on the vault in P, which coincides with the solar beam there:

cosε=coshScoshPcosaS−aP+sinhScoshP

Entering this formula and the multiplier from Eq. (1.17) in Eq. (1.16), results in:

ESd,s=KDLzenith∬aP,hPfcoshPcosΓdhPdaP

The luminosity at the solar disk then equals:

Lsd=0.8785hs°−0.01322hs°2+0.003434hs°3+0.44347+0.0364TAtm

with TAtm atmospheric turbidity and hs(°) solar height in degrees. On a monthly basis, this set of formulas is simplified to:

ESd,s=ESd,hfmo1+cosss/2

with fmo a multiplier that corrects the monthly diffuse radiation, calculated according to (1.15) for the luminosity at the solar disk effect. For Uccle, fmo takes the values given in Table 1.3.

Table 1.3 Uccle, multiplier fmo for the total monthly diffuse radiation

Azimuth →

Slope ↓

0 S

22.5

67.5

90 E,W

112.5

135

157.5

180 N

1.00

22.5

1.03

1.02

1.01

1.00

0.99

0.98

0.97

0.96

1.05

1.04

1.03

1.01

0.99

0.96

0.94

0.92

67.5

1.06

1.05

1.03

0.99

0.94

0.90

0.86

0.84

0.83

1.06

1.04

1.00

0.94

0.87

0.81

0.76

0.73

0.71

112.5

0.98

0.97

0.92

0.85

0.76

0.68

0.63

0.60

135

0.80

0.78

0.74

0.67

0.59

0.53

0.49

0.47

157.5

0.58

0.56

0.51

0.48

0.46

0.43

0.41

0.40

0.34

180

0.00

1.2.2.3 Reflected Radiation

Surfaces on earth reflect part of the beam and diffuse radiation received. To calculate the intensity, all surroundings are considered to be acting as one horizontal plane with reflectivity 0.2, called the albedo. Every surface then receives reflected radiation proportional to the view factor with that horizontal plane (Fse):

(1.18)ESr,s=0.2ESD,h+ESd,hFse=0.2ESD,h+ESd,h1−cosss/2

Reflected radiation on a horizontal surface facing the sky (ss = 0) looks to be zero though in reality this is not by definition the case. A low-sloped roof for example gets radiation reflected from surrounding higher buildings. Also, an albedo of 0.2 is too simplistic. White snow gives a higher value.

1.2.2.4 Total Radiation

Beam, diffuse and reflected irradiation together give the total solar radiation that a surface receives. The appendix contains tables with values for Uccle, while Table 1.4 here summarizes the average, minimum and maximum monthly totals on a horizontal surface measured there, together with the monthly mean cloudiness, calculated as one minus the ratio between the measured and clear sky total on a horizontal surface. Table 1.5 in turn lists the monthly totals on a horizontal surface for several locations across Europe, while Figure 1.8 shows the annual totals with the ratio between least and most sunny location approaching a value of 2.

Table 1.4Monthly total solar irradiation on a horizontal surface (MJ/(m2.month)) and cloudiness at Uccle, average, maximum and minimum values for 1958–1975

Total solar radiation

Mean

129

247

356

500

538

510

439

327

197

Min.

104

177

263

406

431

408

366

279

145

Max.

188

311

485

589

640

651

497

444

274

112

Average cloudiness

Mean

0.47

0.44

0.42

0.36

0.35

0.38

0.34

0.39

0.49

0.50

Min.

0.55

0.58

0.57

0.48

0.51

0.48

0.44

0.55

0.62

0.63

Max.

0.31

0.19

0.27

0.20

0.25

0.22

0.21

0.30

0.11

0.15

0.33

0.30

Table 1.5 Monthly total solar irradiation on a horizontal surface for several locations in Europe (MJ/(m2.month))

Location

Month

Den Bilt (NL)

132

249

381

522

555

509

458

316

193

Eskdalemuir (UK)

112

209

345

458

490

445

370

244

143

Kew (UK)

115

244

355

496

516

501

434

311

182

Lulea (S)

182

358

528

612

589

418

211

Oslo (N)

110

268

441

616

689

624

490

391

153

Potsdam (D)

104

137

238

332

498

557

562

412

267

174

Roma (I)

182

247

404

521

670

700

750

654

498

343

205

166

Torino (I)

171

212

343

474

538

573

621

579

422

281

181

148

Bratislava (Sk)

159

300

464

597

635

624

544

389

233

101

Copenhagen (Dk)

114

244

407

579

622

576

479

308

159

Figure 1.8 Annual solar radiation on a horizontal surface.

How sunny locations are is important when questions are raised such as where to promote photovoltaic cells (PV) as renewable. Within Europe, PV is good in Portugal, Spain, Southern France, Southern Italy and Greece, but of only moderate benefit in the north-west and Scandinavia.

1.2.3 Longwave Radiation

Longwave radiation gives extra heat loss as it can chill the outer surface and the layers outside of the insulation to temperatures below those of outdoors, even below the dew point outdoors. Under-cooling, as it is called, turns the outdoor air into a moisture source rather than a drying medium with a visible result being condensation on the outer surface of insulating glass, EIFS-stucco and tiled or slated well-insulated pitched roofs (Figure 1.9).

Figure 1.9 Rime formation on a well-insulated pitched roof due to under-cooling.

Under-cooling reflects the longwave balance between the atmosphere, represented by the celestial vault, the terrestrial plane and the surface considered, with the vault acting as a selective radiant body, absorbing all incoming radiation but emitting only a fraction. Calculation assumes a vault at air temperature with emissivity below 1, absorptivity 1 and reflectivity 0. Several formulas quantify its emissivity. To give a few (pe in Pa, θe in °C):

Clear sky

Cloudy sky

(1)

sky

0.75

−

0.32

⋅

−

0.051

1000

(4)

sky

−

0.84

(2)

sky

0.52

0.065

1000

(3)

sky

1.24

1000

273.15

Clear sky emissivity thus drops with air temperature but increases with partial water vapour pressure outdoors as water vapour in fact acts as a strong greenhouse gas. In the cloudy sky formula, c stands for the cloudiness factor, 0 for clear, steps 0.125 for hardly covered to more covered and 1 for a covered sky. According to Figure 1.10(a) left, the formulas (1) and (2) apparently give a different emissivity, whereas Figure 1.10(b), illustrating formula (3), suggests that (1) applies to lower and (2) to somewhat higher temperatures outdoors.

Figure 1.10 Sky emissivity, left according to the clear sky formulas (1) and (2), right according to the clear sky formula (3).

The following two equations for the black body emittance of the surface considered and the terrestrial plane describe the ‘celestial vault/surface/terrestrial plane’ radiant system:

Mb,s=1+ρL,sεL,sFs,t+Fs,skyMs′−ρL,sεL,sFs,tMt′+Fs,skyMsky′Mb,t=1+ρL,tεL,tFt,s+Ft,skyMt′−ρL,tεL,tFt,sMs′+Ft,skyMsky′

In both, the suffix s stands for the surface, the suffix t for the terrestrial plane, the suffix sky for the celestial vault, Msky′ for the radiosity of the celestial vault and Fs,t, Fs,sky,…for the view factors between these radiant bodies. As that plane and celestial vault surround the surface, the sum Fs,t + Fs,sky is 1. The same holds for the view factor between the terrestrial plane and the celestial vault. In fact, the one between that plane and the surface is so small that using zero does not falsify the second equation. Celestial vault radiosity thus simplifies to:

Msky′=εL,skyMb,sky,θe

turning the two equations into:

(1.19)Mb,s=1εL,sMs′−ρL,sεL,sFs,tMt′+Fs,skyεL,skyMb,sky,θe

(1.20)Mb,t=1εL,tMt′−ρL,tεL,skyMb,sky,θe

The radiant heat flow rate at the surface is now:

qR=qRs,t+qRs,sky=εL,sρL,sMb,s−Ms′=εL,sFs,tMb,s−εL,tMb,t+εL,sFs,skyMb,s−ρL,envFs,tFs,t+1εL,skyMb,sky,θe

Assuming the terrestrial plane to be a black body at outdoor air temperature further simplifies the formula:

(1.21)qR=εL,sCbFs,t+Fs,skyTse1004−Fs,t+Fs,skyεL,skyTe1004

Linearization by replacing the celestial vault by a black body at temperature

θsk,e=θe−23.8−0.2025θe1−0.87c

gives:

(1.22)qR=εL,sCbFs,tFTs,t+Fs,skyFTs,skyθse−θe+23.8−0.2025θe1−0.87cFs,skyFTs,sky

a result that fits with expression (1.21) for a sky emissivity somewhat higher than in Figure 1.10(b). Combining (1.22) with the convective heat exchanged quantifies under-cooling:

(1.23)qce+qRe=hce+εL,sCbFs,tFTs,t+Fs,skyFTs,skyθse−θe+εL,sCbFs,skyFTs,sky23.8−0.2025θe1−0.87c

qT+qce+qRe=0

where qT is the heat flow rate by transmission to or from the exterior surface. Figure 1.11 shows calculated data for a low-slope roof with thermal transmittance 0.2 W/(m2.K), a membrane with longwave emissivity 0.9 and very low thermal inertia. Parameters are the air temperature and wind speed. The outside surface temperature can drop substantially below ambient.

Figure 1.11 Lightweight low-sloped roof, U = 0.2 W/(m2.K), membrane with eL = 0.9: under-cooling represented by θe − θse.

1.2.4 Relative Humidity and (Partial Water) Vapour Pressure

Both relative humidity (ϕe) and (partial water) vapour pressure (pe) impact the moisture tolerance of building enclosures and buildings in a straightforward way. Table 1.6 summarizes monthly means for several locations across Europe.

Table 1.6 Monthly mean relative humidity (%) and vapour pressure (Pa, bold) for several locations all over Europe

Location

Month

Uccle (B)

89.6

89.0

84.0

78.5

77.8

78.9

79.9

79.8

84.2

88.3

91.2

92.7

663

681

757

854

1151

1334

1529

1489

1346

1084

806

780

Aberdeen (UK)

81.5

80.3

74.9

72.3

75.0

78.5

74.1

79.1

80.6

81.6

78.1

77.1

596

631

714

860

1107

1161

1207

1122

955

695

614

Catania (I)

66.5

72.4

68.8

69.8

71.2

70.0

62.0

68.6

69.4

69.6

68.5

65.9

816

912

964

1114

1469

1849

1985

2252

1972

1471

1183

900

Den Bilt (NL)

86.1

82.1

76.0

75.9

72.9

72.7

77.1

78.9

80.7

84.4

85.5

86.8

578

596

631

811

1028

1263

1411

1443

1306

1086

772

587

Kiruna (S)

83.0

82.0

77.0

71.0

64.0

61.0

68.0

72.0

77.0

81.0

85.0

177

171

221

324

476

710

1011

914

676

436

292

219

Malmö (S)

87.0

86.0

83.0

76.0

73.0

74.0

78.0

77.0

82.0

85.0

87.0

89.0

510

496

561

711

958

1262

1531

1464

1269

969

753

627

Munich (G)

83.7

81.9

76.8

72.3

74.9

76.8

74.2

76.1

79.2

82.9

83.5

85.7

451

484

598

780

1043

1361

1483

1446

1267

938

660

515

Rome (I)

76.1

71.3

66.5

69.1

71.4

71.3

61.6

68.5

72.3

74.1

78.1

79.4

794

764

816

1048

1400

1795

1881

2042

1776

1346

1124

874

Västerås (S)

84.0

82.0

74.0

66.0

62.0

65.0

69.0

74.0

81.0

83.0

86.0

364

355

402

540

766

1081

1354

1328

1085

793

602

483

On average, relative humidity hardly changes between winter and summer. Vapour pressure, however, does. In temperate climates the inverse often holds between day and night: large differences in relative humidity and fairly constant vapour pressures. A sudden temperature rise lowers the relative humidity while a sudden drop may push it up to a misty 100%. During rainy weather the wet bulb temperature closely follows the raindrop temperature. When it is as warm as the air, relative humidity will near 100%. Also, the environment strongly influences relative humidity and vapour pressure, with higher values in forests and river valleys than in cities. Again, the annual variation is often written in terms of a Fourier series with one harmonic, though, as Figure 1.12illustrates, deviation from the monthly averages can be significant:

(1.24)ϕe=ϕ¯e+ϕˆecos2πt−d365.25pe=p¯e+pˆecos2πt−d365.25

with:

Relative humidity (

), %

Vapour pressure (

), Pa

Quality of the fit

Average

Amplitude

Days

Average

Amplitude

Days

Kiruna

75.5

11.1

346

469

380

209

±,

−

Roma

71.6

5.3

342

1305

627

214

−,

Figure 1.12 Monthly mean relative humidity and vapour pressure in Kiruna (Sweden), a cold climate, and in Rome (Italy), a rather warm climate – harmonic fit.

1.2.5 Wind

Wind impacts the hygrothermal response of building enclosures. A higher speed hastens the initial drying period but lowers the sol-air temperature and counteracts under-cooling. The thermal transmittance of single glass is increased as wind speed increases. Also infiltration, exfiltration and wind washing of poorly mounted insulation layers becomes more importance. Wind combined with precipitation gives wind-driven rain. Wind also governs comfort conditions outdoors. High speeds exert unpleasant dynamic forces on people, chills them and makes it harder to open and close doors.

1.2.5.1 Wind Speed

In meteorology, wind speed is seen as a horizontal vector, whose amplitude and direction are measured in the open field at a height of 10 m. The average per 3 seconds is referred to as the immediate, and the average per 10 minutes as the mean speed. The spectrum shows various harmonics, while the vector changes direction constantly. Locally, the environment impacts the amplitude and direction. Venturi effects in small passages increase speed, while alongside buildings eddies develop and the windward and leeward side see zones of still air created.

As following formula shows, due to the friction that terrain roughness causes, wind speed increases from 0 m/s at grade up to a fixed value in the 500–2000 m thick atmospheric boundary layer in contact with the earth:

(1.25)vh=v10Klnh/n

v10 being the average wind speed in flat open terrain, 10 metres above grade, vh average wind speed h metres above grade, n terrain roughness and K a friction-related factor:

Terrain upwind

Open sea

0.128

0.0002

Coastal plain

0.166

0.005

Flat grassland, runway area at airports

0.190

0.03

Farmland with low crops

0.209

0.10

Farmland with tall crops, vineyards

0.225

0.25

Open landscape with larger obstacles, forests

0.237

0.50

Old forests, homogeneous villages and cities

0.251

1.00

City centres with high-rises, industrial developments

≥0.265

≥2

Figure 1.13 and Table 1.7 show the annual distribution of the wind vector over all directions at Uccle. For almost half the year the wind comes from the west through south-west to south. Of course, these distributions differ between locations.

Figure 1.13 Typical wind rose for Uccle, Belgium.

Table 1.7 Uccle, ‰ of the time wind comes from the different directions (monthly means, 1931–1960)

Orientation

Month

NNE

103

ENE

ESE

SSE

100

109

SSW

120

109

118

105

132

163

130

113

105

103

131

152

104

124

142

147

WSW

125

115

100

120

145

103

119

125

109

121

WNW

NNW

1.2.5.2 Wind Pressure

The fact that wind exerts a pressure against any obstacle follows from Bernoulli's law. Without friction the sum of kinetic and potential energy in a moving fluid must remain constant. In a horizontal flow, potential energy is linked to pressure. When an obstacle stops the flow, all kinetic becomes potential, which gives the following as pressure (pw in Pa):

(1.26)pw=ρavw2/2

with ρa the air density in kg/m3 (≈1.2 kg/m3) and vw the wind speed in m/s. Yet, since no obstacle stretches to infinity, the flow is only impeded and redirected. That makes wind pressure on buildings different from the stop-the-flow value, a fact accounted for by the pressure coefficient (Cp):

(1.27)pw=ρaCpvw2/2

where vw is a reference wind speed measured at the nearest weather station or at 1 m above the roof ridge. Field measurements, wind tunnel experiments and CFD have shown that pressure coefficients change depending on the reference and the up- and downwind environment. On buildings, their value varies from place to place, being highest at the edges and upper corners, lowest down in the middle. At the wind side, values are positive, at the rear side and sides parallel or nearly parallel to the wind negative. Values are found in the literature, see Table 1.8.

Table 8.1 Wind pressure coefficients. Exposed building, up to three storeys, rectangular floor plan, length-to-width ratio 2 to 1 (reference speed: local, at building height)

Location

Wind angle

135

180

225

270

315

Face 1

(Wind side)

0.5

0.25

−0.5

−0.8

−0.7

−0.8

−0.5

0.25

Face 2

(Rear side)

−0.7

−0.8

−0.5

0.25

0.5

0.25

−0.5

−0.8

Face 3

(Side wall)

−0.9

0.2

0.6

0.2

−0.9

−0.6

−0.35

−0.6

Face 4

(Side wall)

−0.9

−0.6

−0.35

−0.6

−0.9

0.2

0.6

0.2

Roof Pitches

Wind side

−0.7

−0.8

−0.7

−0.8

−0.7

<10°

Rear side

−0.7

−0.8

−0.7

−0.8

−0.7

Average

−0.7

−0.8

−0.7

−0.8

−0.7

Pitches

Wind side

−0.7

−0.6

−0.5

−0.6

−0.7

10–30°

Rear side

−0.5

−0.6

−0.7

−0.6

Average

−0.6

−0.65

−0.7

−0.65

−0.6

−0.65

−0.7

−0.65

Pitches

Wind side

0.25

−0.6

−0.9

−0.8

−0.9

−0.6

>30°

Rear side

−0.8

−0.9

−0.6

0.25

−0.6

−0.9

Average

−0.28

−0.45

−0.6

−0.45

−0.28

−0.45

−0.6

−0.45

1.2.6 Precipitation and Wind-Driven Rain

In humid climates, rain is the largest moisture load on buildings. The term ‘wind-driven’ applies to the horizontal component, and ‘precipitation’ to the vertical one. While in windless weather the horizontal component remains zero, higher wind speeds increase it. Horizontal and angled outside surfaces collect rain under all circumstances whereas vertical surfaces are struck by wind-driven rain only, albeit that they also suffer from run-off coming from angled and sometimes horizontal surfaces. In countries where outside wall buffering ensures rain-tightness, wind-driven rain to some extent impacts end energy use for heating and cooling.

1.2.6.1 Precipitation

Precipitation is as variable as the wind. Table 1.9 and Figure 1.14 give mean durations (hours) and amounts per month for Uccle. As with wind speed, no annual cycle appears, though slightly more rain falls in summer. The absolute maxima noted between 1956 and 1970 were: 4 l/m2 in 1 minute, 15 l/m2 in 10 minutes and 42.8 l/m2 in 1 hour.

Table 1.9 Precipitation: duration and amounts per month, means for Uccle (1961–1970)

Precipitation

Month

Duration (h)

53.6

57.3

51.9

51.5

41.9

36.0

42.9

38.8

36.5

52.5

67.3

72.7

Amount (l/m

)

57.4

61.4

56.8

63.6

63.1

74.9

92.3

78.6

54.6

74.5

76.5

84.5

Figure 1.14 Precipitation: monthly amounts and duration for 1961–1970 at Uccle (averages, maxima and minima).

Showers are characterized by a droplet distribution Fd,precip. According to Best (1950), the relation with rain intensity is:

(1.28)Fd,precip=1−exp−d1.3gr,h0.2322.25

with d the droplet size in m and gr,h the precipitation in l/(m2.h). In windless weather, droplets have a final speed (d droplet size in mm, see also Figure 1.15) given by:

(1.29)v∞=−0.166033+4.91844d−0.888016d2+0.054888d3

Depending on the mean droplet size, following terms describe precipitation:

Mean droplet size, mm

Precipitation

0.25

Drizzle

0.50

Normal

0.75

Strong

1.00

Heavy

1.50

Downpour

Figure 1.15 Final vertical speed of a raindrop in windless weather.

1.2.6.2 Wind-Driven Rain

The drag force that wind exerts inclines droplet trajectories. Final tilt angle depends on droplet size, wind direction compared to horizontal and speed increase with height. A constant horizontal speed keeps the inclined droplet trajectories straight. Wind-driven rain intensity (gr,v in kg/(m2.s)) then becomes:

(1.30)gr,v=0.222vwgr,h0.88

with gr,h the precipitation in kg/(m2.s). This equation is simplified to:

(1.31)gr,v=0.2vwgr,h