ENERGY MODELING AND COMPUTATIONS IN THE BUILDING ENVELOPE

Alexander V. Dimitrov

~ ~~r~Fr~~i~Zr~up 'e/ Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

Contents

teface .............. _.-„.„ .. - ... „.-.„- .... "";-·„-~ ..... . .. „ ••••• , ........ „ ... ,„u .... ~.-. ... . . .... ............... . „.xi Author .. „„ ....... „ ......... „.„„ ...... ,„._„.„.„ ... „.-.„ .. „„„„„„ .. „ .. ;-..„„„.„ .. „ .... „„„„„ ... xiii

1. Introduction: The Buildings' Envelope-A Component of the Building Energy System.„„„„„„„.„ .. „ ... „ ...• „ .... „„ ...• „.„„„„"„.„ .... „ .......• „. l 1.1 Systematic Approach Applied to Buildings .. „.„.„„„„„„„„„„„ .. „„„1 1.2 Envelope System (Envelope) and Energy Functions Design „„„.„. 3 1.3 Summary Analysis of the Building-Surrounding Energy

Interactions .......... - ......... „ ... - ........ „ ..........•..........•............................... 11

2. Physics of Energy Conversions in the Building Envelope at Microscopic Level .„„.„„_„.„.„ .. „ ...... „„„ .. „„ .... „.„ ..•.. „ .• „„„„„„.„„.„ ........ 13 2.1 Idealized Physical Model of the Building Envelope as an

Energy-Exchanging Medium (Review of the Literature from Microscopic Point of View) „„„ .. „„„„„ .. „.„„„„„„„„„.„„.„„ .. „„ ....... 16

2.2 Conclusions and Generalizations Based on the Survey of Literature Published in the Field „ ... „ .... „.„.„.„„ ... „„.„„„„„„„„ .. „„ 30

2.3 Design of a Hypothetical Physical Model of Phonon Generation in Solids: Scatter of Solar Radiation within the Solid .... „ ... „.„ .. „„ .. „ .... „ .. „ .... „ .... „ ..... „ ..• „.„ ..... „ .... „ .... „ .. „ .. „ ..... 32 2.3.1 Interna! Ionization and Polarization Running in

Solids (Formation of Temporary Electrodynamic Dipole ) .. „„„„ .... „„„ .. „„„„ .. „ .. „„„„ .. „„ .. „„ .. „ •• „„ .. „„„„„ ... „.32

2.3.2 Hypothetical Mechanism of Energy Transfer in the Building Envelope Components „„„„„ „„ .. „ .. „„„ .... „„„„ „„ 36 2.3.2.1 Physical Pattern of Energy Transfer within

the Envelope Components „ .. „„„ .. „„„.„„ .. „„ ... „ .. 36 2.3.3 Hypothetical Model of Energy Transfer through

Solid Building Components: A Model of Lagging Temperature Gradient ... „.„ .. „„ .......... „ .. „ .... „ .... „ ................. 41 2.3.3.1 Model of Lagging Temperature Gradient.„„„„ . .48

2.4 Micro- Macroscopic Assessment of the State of the Building Envelope .„ .. „.„ ... „ .... „„„„„ ... „„.i.„.„„„„,.„ .. „ .... „ .. „ .. „ .. „ .. „„ .. „„„„„. 51 2.4.1 Microscopic Canonical Ensemble: Collective

Macroscopic State.„r•„•i·•·i„.„.„„ .............•........ „ ............ „ ...... 51

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2.4.2 Introduced Macroscopic State Parameters of the Building Envelope Considered as a Physical Medium of the Electrothermodynamic System ................ 53 2.4.2.l Temperature Field and Gradient of the

Lagrange Multiplier ... „ .. . . . .....•.• . . . .. „ .•.....•..•......•.... 53 2.4.2.2 Pressure Field .........•......... - ..................................... 58 2.4.2.3 Field of the Electric Potential: Potential

Function and Gradient of the Electric Potential ..................... „ .. ................ ........ ..• „ ....... ... 61

2.4.2.4 Entropy: A Characteristic of Degeneration of the Heat Charges (Phonons) within the Envelope Control Volume .... „ . ...••. ..... „ ......... „ . . .. . . 66

2.4.3 Conclusions on the General Methodological Approaches to the Study of an Electrothermomechanical System ....................................... 73

3. Design of a Model of Energy Exchange Running between the Building Envelope and the Surroundings: Free Energy Potential .„„„ ....... „ ............... „„ ...... „.„„ .. - .•..............•................. „ ............... 75 3.1 Energy-Exchange Models of the Building Envelope ..................... 75 3.2 Work Done in the Building Envelope and Energy-Exchange

Models .... „ ............ „ ......................................... „ . ........ „ ..... „ .... „„ ..•.••.... 81 3.2.1 Law of Conservation of the Energy Interactions

between the Envelope Components and the Building Surroundings .................. „ ......... h„ .•....••.•....••.• .•..••.••........ „ .... 82

3.2.2 Special Cases of Energy Interactions ...... „ ............... „ ........• 86 3.2.2.l Energy Model of Transfer of Entropy and

Electric Charges ......... „„ •••. „. „. „. „„ „ ........ „ .•.......... 86 3.2.2.2 Energy Model of Entropy Transfer with or

without Mass Transfer .... „ ...• „ ...•......•.•...... . . .....•...• 88 3.3 Specification of the Structure of the Free Energy

in the Components of the Building Envelope (Electrothermodynamic Potential of the System) ..... „ .... „ .........•...• 89 3.3. l Finding the Structure of the Free Energy Function ....... ... 92

3.3.1.1 Links between Entropy and the System Basic Parameters .. „ ..•. „ ... ....•.... „„ .... „ ...... .. „ ...•. „ .. .. 95

3.4 Distribution of the Free Energy within the Building Envelope ............................................•.•.........•.............................. 97 3.4.1 State Parameters Subject to Determination via the

Free Energy Function „ ... „ .. „„ .. „„ .. .. .. „.„ .... „ .... „ ..... „„„ ... „„ 99

4. Definition of the Macroscopic Characteristics of Transfer ................ 101 4.1 General Law of Transfer ................................................................... 106 4.2 Physical Picture of the Transmission Phenomena ....................... 108 4.3 Conclusions ................................................................................... „ ... 111

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5. Numerical Study of Transfer in Building Envelope Components ................ „ ....................•... „ ....................... _ ...... ............... 113 5.1 Method of the Differential Relations „.„„.„„.„„„„„„„„„„„ .... „„„ 113 5.2 Method of the Integral Forms „„ .. „ ..... „ ..... „ .. „„ .. „ „ ....... „„„„ ..... „. 119 5.3 Weighted Residuals Methodology Employed to Assess the

ETS Free Energy Function „ ..... „ ....... „„.„„ ... „ ........ „ ... „. „.„„ „„„ .... 122 5.3.1 Basic Stages of the Application of WRM in

Evaluating Transport within the Envelope „„.„„„.„„„„„ 125 5.3.1.1 One-Dimensional Simple Finite Element .. „„„. 140 5.3.1.2 Two-Dimensional Simple Finite Element in

Cartesian Coordinates .... „.„„ .. „ .... „ ..... „„ .. „„„„. 140 5.3.1.3 Two-Oimensional Simple Finite Element in

Cylindrical Coordinates ..... „ ..... „„ .... „.„ ............. 141 5.3.1.4 Three-Dimensional Simple Finite Element ...... 141

5.3.2 Modeling of Transfer in a Finite Element Using a Matrix Equation (Galerkin Method) ... „ ... „ ....................... 142

5.3.3 Steady Transfer in One-Dimensional Finite Element .. „. 146 5.3.3.1 Integral Form of the Balance of Energy

Transfer through One-Dimensional Finite Element ....... „ ... „ .. „ .......... „ .................... „ .............. 147

5.3.3.2 Modified Matrix Equation of lD Transfer „.„„. 150 5.3.3.3 Transfer through lD Simple Finite Element

Presented in Cylindrical Coordinates „„.„„„„ .. 155 5.3.4 Steady Transfer in a 2D Finite Element..„„ .. „„„ .. „„ .... „„. 160

5.3.4.1 Equation of a 2D Simple Finite Element in Cartesian Coordinates „.„„„ ......... „„„ ... „„.„„ ... „ 161

5.3.4.2 Design of Transfer Equation in Cylindrical Coordinates regarding a Three-Noded 2D Finite Element .„„ .... „ .. „ .. „„„„ ...... „„„ .................. 166

5.3.5 Transfer through a 3D Simple Finite Element „„.„„.„„.„ 170 5.3.5.1 Design of the Matrix Equation of Transfer

in Cartesian Coordinates .. „„„„„„.„.„ .. „.„„ ....... 170

6. Initial and Boundary Conditions of a Solid Wall Element..„ .. „ .... „ .. 175 6.1 Effects of the Environmental Air on the Building Envelope„„„ 175

6.1.1 Mass Transfer from the Building Envelope (Wall Dehumidification, Drying) „„„„„„.„„„.„ .... „.„ .... „„.„„ ... „ .. „ 176 6.1.1.1 Processes Running at a Cold Wall (TA~ Tw;) .. „„177 6.1.1.2 Processes Running at a Cold Wall (Tw <TA) „„„178

6.2 Various Initial and Boundary Conditions of Solid Structural Elements „ ...... -.„„.„.„.„ ........... „.„„.-.„ .. „„„.„ ..... „„ .. „„„„„„ ......... „. 179

6.3 Design of Boundary Conditions of Solid Structural Elements„ .... 182 6.3.1 Boundary Conditions of Convective Transfer

Directed to the Wall lnternal Surface „ .. „ .•••... „ ........... „.„183 6.3.2 Boundary Conditions at the Wall External Surface„ .. „„185

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7. Engineering Methods of Estimating the Effect of the Surroundings on the Building Envelope: Control of the Heat Transfer through the Building Envelope (Arrangement of the Thermal Resistances within a Structure Consisting of Solid Wall Elements) .................................................................... „ ..... „ ..... 191 7.1 Calculation of the Thermal Resistance of Solid Structural

Elements .. „ ....... „ ............................... „ ..... „ ...... „ .... „ .. „ .. ...... .......... „ .. 194 7.2 Solar Shading Devices (Shield) Calculation .......... „„„ ... „„.„„.„„.203 7.3 Modeling of Heat Exchange between a Solar Shading

Device, a Window, and the Surroundings .„ ...... „ ......... „ .............. 208 7.3.1 Mathematical ModeL .............. „„ ........ „ ...... „ .................. „ .. 212

7.4 Design of Minimal-Admissible Light-Transmitting Envelope Apertures Using the Coefficient of Daylight (CDL) „ ..... „„ .. „ ...... 213 7.4.1 Energy and Visual Comfort „ ....... „.„.„„„„„.„„ .. „.„„„„ .... 213 7.4.2 Calculation of the Coefficient of Daylight (CDL) ...... „„ .. 218

7.5 Method of Reducing the Tribute of the Construction and the Thermal Bridges to the Energy Inefficiency .„ ...... „.„.„ ............. „. 223 7.5.1 Characteristics of Heat Transfer through Solid

Inhomogeneous Multilayer Walls ...... „ .... „„ ................... „ 224 7.5.2 Method Described Step by Step „ ........ „ .. „.„ ................. „ .. 227 7.5.3 Description of the Energy Standard of the

Construction (EEa,11111) • .,.., ••• „-„ .. „ ..... „ ....•..••. ~„ .......... „.„ ..... 227 7.5.4 Employment of the Energy Standard to Assess How

the Building Structure Affects the Energy Efficiency„„„229 7.6 Assessment of Leaks in the Building Envelope and the

Air-Conditioning Systems .„ ........ „.„„ ........ „ ....... „ .......................... 233 7.6.1 Measuring Equipment of the Method "Delta-Q" „ ... „ .... 234 7.6.2 Modified Balance Equation of Leaks in Air Ducts,

Air-Conditioning Station, and Envelope„ ... „ ........ „„ ... „ .. 236 7.6.3 Delta-Q Procedure: Data Collection and

Manipulation„ ............•.. „.„ .. „„ ............................ „ ........... 238 7.6.4 Normalization of the Collected Data „.„ .... „ ... „„„„„„ .. „„ 241

7.7 Mathematical Model of the Environmental Sustainability of Buildings .. „ ................ „.„ ................. „„„ ...................... „ .. „ ............... „. 244 7.7.1 General Structure of the Model .............. „ ..... .................... 244 7.7.2 Selection of an Ecological Standard: Table of

Correspondence ..... „ .............................. „ ..... „ .................. „. 248 7.7.3 Comparison of Systems Rating the Ecological

Sustainability in Conformity with the General Criteria .................................. „ ... „ „ ... „ „ „ .................. „ ........ 255

7.8 Conclusion.„ ............................ „„ .............. „„ ................. -.„ ............... 258 Acknowledgments ...... „ ................................ „ .... „ ...... „ .. „ ...... „.„„ ........... „. 262

Contents ix

8. Applications (Solved Tasks and Tables) „ .. „„ ..... „ . . . . . „ . ..... ... . .. .... ...... . .. . 263 8.1 Matrix of Conductivity [KO>] ...................... ... ......... .... .. .............. ... ... 263 8.2 Matrix of Surface Properties [f(ll] .... ............................................ ... 264 8.3 Generalized Matrix of the Element Conductivity

[GO>] = [K(1l] + [f(ll] .. .. ............ .............................................................. 265 8.4 Vector of a Load due to Recuperation Sources {f 21>} .•.•••.•.•••.. ••• .• 265 8.5 Vector of a Load due to Convection to the Surrounding

Matter {f 21> ) •••••••••• ••• ••• ••••••••••• •••• ••••• •• ••• •... . . .•• •••••••••• •••• •• •• .•• •. •• •••• •• •••••• • 266

8.6 Vector of a Load due to a Direct Flux {ff,, } ................................... 266 8.6.1 Design and Solution of the Matrix Equation ................... 267

References .............. ........................................................... .. ... ......... .... ......... ....... 293

Index ........ .. ......................... ............ ........................................................... .. ...... .. . 305