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A simplified building energy simulation tool: material and environmental properties effects on HVAC performance
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A simplified building energy simulation tool: material and environmental properties effects on HVAC performance
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1
A SIMPLIFIED BUILDING ENERGY SIMULATION TOOL:
MATERIAL AND ENVIRONMENTAL PROPERTIES EFFECTS ON HVAC PERFORMANCE
By
Chenchuan Qian
______________________________________________________________________________
A Thesis Presented to the
FACULTY OF THE USC SCHOOL OF ARCHITECTURE
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF BUILDING SCIENCE
August 2016
Copyright 2016 Chenchuan Qian
2
COMMITTEE
Karen Kensek (Chair)
Assistant Professor
USC School of Architecture
Kensek@usc.edu
Marc Schiler
Professor
USC School of Architecture
Marcs@usc.edu
Douglas Noble
Associate Professor
USC School of Architecture
Dnoble@usc.edu
3
ACKNOWLEDGEMENT
I would like first and foremost to acknowledge and give thanks to Professor Karen Kensek for her
involvement in this research. Thank you for providing guidance in every possible way. The thesis is
impossible to be accomplished without your assistance.
I would also like to acknowledge Professor Paul Ronney for his boundless technical support. Your
knowledge on thermodynamic field facilitates the creation of the tool. Your guidance enlightens me to
make modifications and improvements for the tool.
I would also like to thank Professor Marc Schiler for his technical support. I am gratefully indebted to your
very valuable comments on this thesis. Your guidance improves the logic rigor of the thesis.
I would also like to thank Professor Douglas Noble for the many roles he played, each one integral to the
success of this thesis. Thank you for keeping me aware and disciplined throughout the entire 2 years of the
thesis.
Last but not least, I would like to thank Haoyu Feng for technical support of coding and tool development.
The Excel tool cannot be running smoothly without your assistance.
Author
Chenchuan Qian
4
Table of Contents
Abstract .................................................................................................................................................. 6
Hypothesis .............................................................................................................................................. 6
List of Figures ........................................................................................................................................ 7
List of Tables ....................................................................................................................................... 11
Chapter 1: Introduction ................................................................................................................. 14
1.1. Thermal mass material and time lag in climates with high diurnal swings .......................... 16
1.2. Thermal mass, thermal time lag, and their applications ........................................................ 20
1.3. Energy simulation tool design............................................................................................... 24
1.4. Conclusion ............................................................................................................................ 30
Chapter 2: Background ................................................................................................................. 31
2.1. Scope of work ....................................................................................................................... 31
2.2. Heat transfer principles, thermal time lag and related properties in exterior walls............... 31
2.3. Energy modeling engines comparison and features .............................................................. 37
Chapter 3: Methodology ................................................................................................................ 42
3.1. Scope of work ....................................................................................................................... 42
3.2. Formulation ........................................................................................................................... 43
3.2.1. Parameter introduction .................................................................................................. 43
3.2.2. Heat transfer equations .................................................................................................. 44
3.2.3. Forward Finite Element method (FFE) and heat transfer model .................................. 46
3.2.4. Thermal lag calculation ................................................................................................. 48
3.3. Excel tool development ......................................................................................................... 50
3.3.1. Excel worksheet introduction ........................................................................................ 51
3.3.2. Parameter input ............................................................................................................. 56
3.3.3. Weather profile ............................................................................................................. 60
3.3.4. Parameter output ........................................................................................................... 61
3.3.5. Calculation and Macros ................................................................................................ 64
3.4. Conclusion ............................................................................................................................ 68
5
Chapter 4: Results and Discussion ................................................................................................ 72
4.1. Scope of work ....................................................................................................................... 72
4.2. Test of thermal time lag and various parameters .................................................................. 73
4.2.1. Material properties effects on thermal time lag ............................................................ 73
4.2.2. Validation of thermal time lag ...................................................................................... 77
4.2.3. Boundary conditions affect thermal time lag ................................................................ 81
4.2.4. Conclusion and discussion of material and environmental factors influence on thermal time
lag 88
4.3. Material and environment parameters effect on heating and cooling system energy performance
89
4.3.1. Thermal time lag and material properties effects on energy performance .................... 91
4.3.2. Climate effects on energy performance ........................................................................ 99
4.3.3. HVAC setting temperature effects on energy performance ........................................ 108
4.3.4. Environmental factors effects on energy performance ............................................... 115
4.3.5. Energy performance conclusion and discussion ......................................................... 119
4.4. Economic evaluation ........................................................................................................... 121
4.4.1. Economic value varies with different types of heating system ................................... 122
4.4.2. Economic value varies with different material cost .................................................... 128
4.4.3. Economic evaluation discussion ................................................................................. 137
Chapter 5: Conclusions and future work ................................................................................... 139
Bibliography ...................................................................................................................................... 144
Appendix ............................................................................................................................................ 146
a. Excel Macros .......................................................................................................................... 146
b. Weather data ........................................................................................................................... 151
c. Heater types ............................................................................................................................ 154
d. Material specifications and prices ........................................................................................... 158
6
Abstract
Construction material choice and environmental parameters have shown significant influence on building
energy performance. The current building energy simulator, EnergyPlus (Crawley et al, 2015) and DOE-2
(James J. Hirsch & Associates, 2012), focus on calculations of HVAC system energy load with user
customizations. Although the heat transfer calculation algorithms of both engines are comprehensive for
the energy simulation purpose, it is difficult to make experimental tests on specific parameters such as
thermal time lag and climate zone effects. A tool is required to be developed to study specific material
and environmental parameters‘ influence on building energy performance. The tool ought to have the
ability of simple building information modeling with user customization and showing building energy
performance results according to target material or environment parameter. In order to study the material
energy performance, the tool also needs to improve the features upon EnergyPlus and DOE-2 such as
input data configuration, exterior wall boundary conditions, weather data (time steps), HVAC operation
loop etc.
A prototype tool has been developed. The current version of the tool has several simplifications and
differences compared with EnergyPlus and DOE-2. It has the ability to perform monthly/annual energy
simulation for a cubic room with user customization. The tool is based on Excel visual basic applications
(VBA), which codes the exterior wall heat transfer mechanism and environment properties. The Excel
tool calculates two dimensional heat transfer using forward finite element (FFE) method. The time step is
120 seconds, which is smaller and more accurate than EnergyPlus (1-60 minutes) and DOE-2 (1 hour
fixed-). Various tests have been conducted to study different material and environment parameters effects
on building energy performance and to explore the potential usage and further development of this tool.
Hypothesis
The synergy between construction material and environment parameters has complicated effects on
building energy performance. This effect also varies with climate zones and other local conditions. It is
possible to create a simplified tool that shows the results of energy use when changing single or multiple
target parameters.
7
List of Figures
Figure 1.1 Thermal time lag between wall and environment temperature (From the Excel tool) ........ 17
Figure 1.2 Thermal mass material (concrete block) in climate with large temperature swing ............. 18
Figure 1.3 Thermal mass material in constant hot climate .................................................................. 19
Figure 1.4 Thermal mass material in constant cold climate .................................................................. 19
Figure 1.5 Indoor temperature on June 20
th
in Fairbanks, Alaska (Stevens, 2012) .............................. 20
Figure 1.6 Trombe wall avoiding summer overheat (Autodesk Sustainability workshop, 2015)......... 22
Figure 1.7 Night flush cooling and solar chimney (Autodesk Sustainability workshop, 2015) ........... 22
Figure 1.8 high thermal lag wall (Blue – outside, red – wall, purple – inside) ..................................... 23
Figure 1.9 low thermal lag wall (Blue – outside, red – wall, purple – inside) ...................................... 24
Figure 1.10 sine wave temperature ....................................................................................................... 26
Figure 1.11 constant temperature .......................................................................................................... 26
Figure 1.12 Theoretical periodic temperature (For instance, specific laboratory condition) ................ 26
Figure 1.13 actual temperature data ...................................................................................................... 27
Figure 1.14 Annual solar radiation and temperature data (Miami year 2012) (NOAA, 2015) ............. 27
Figure 1.15 temperature curves when use ideal HVAC system (Blue – outside, red – wall, purple – inside)
.............................................................................................................................................................. 28
Figure 1.16 HVAC control loop ........................................................................................................... 29
Figure 2.1 critical thickness and energy saving in Ryiadh using concrete wall with insulations ......... 32
Figure 2.2 Indoor temperature on June 20
th
in Fairbanks, Alaska (Stevens, 2012) .............................. 33
Figure 2.3 time lag and decrement factor of different wall configurations (Ibrahim, 2013) ................ 34
Figure 2.4 temperature curves of interior temperature for 2 cm wallboard without PCM (Solid black line), 2
cm wallboard with PCM (dash line), semi-infinite thickness of concrete (dotted line), exterior temperature
(grey line) (Richardson, 2008) .............................................................................................................. 35
Figure 2.5 list of thermal time lag with different material and thickness (Asan, 2008)........................ 36
Figure 2.6 radiation heat transfer results differences (Kunzel, 2002) ................................................... 37
Figure 2.7 peak heating and cooling loads for low-rise building (Simge Andolsun, 2008) ................. 38
Figure 2.8 program struction of EnergyPlus (EnergyPlus, 2016) ......................................................... 39
Figure 2.9 annual exterior wall convection coefficient in hourly scale (Dandan Zhu, 2012) ............... 40
Figure 2.10 Ecomat v1.0 ....................................................................................................................... 41
Figure 2.11 Opaque (Murray Milne, 1989) ........................................................................................... 41
Figure 3.1 scope of work ...................................................................................................................... 43
Figure 3.2 The wall is break down into ten pieces using FFE .............................................................. 46
Figure 3.3 outside boundary cell heat transfer ...................................................................................... 46
Figure 3.4 inside cells between boundaries heat transfer ...................................................................... 47
Figure 3.5 outside boundary cells heat transfer .................................................................................... 47
8
Figure 3.6 wall temperature profile transfers into Excel (Ronney, 2013) ............................................. 48
Figure 3.7 graphic results of the model................................................................................................. 48
Figure 3.8 thermal time lag on thermal mass material .......................................................................... 49
Figure 3.9‗Thermal time lag calculation‘ worksheet ............................................................................ 49
Figure 3.10 locate the time of highest wall temperature and environment temperature ....................... 50
Figure 3.11 HVAC system control loop ............................................................................................... 50
Figure 3.12‗Main‘ worksheet ................................................................................................................ 53
Figure 3.13 Part of ‗Heat transfer Celsius-scale‘ worksheet (part of 262,772 rows) ............................ 54
Figure 3.14 Part of ‗Heat transfer Kelvin-scale‘ worksheet (part of 262,772 rows) ............................. 54
Figure 3.15 ‗Thermal time lag calculation‘ worksheet ......................................................................... 55
Figure 3.16‗Material Chart‘ worksheet ................................................................................................. 56
Figure 3.17‗Material input‘ section ...................................................................................................... 56
Figure 3.18 Harmonic / sine wave temperature profile ......................................................................... 57
Figure 3.19‗Thermal lag input‘ section ................................................................................................. 57
Figure 3.20‗Environment input‘ section ............................................................................................... 58
Figure 3.21 HVAC control loop ........................................................................................................... 58
Figure 3.22‗Indoor setting‘ section ....................................................................................................... 58
Figure 3.23 ‗Solar radiation‘ section ..................................................................................................... 59
Figure 3.24 ‗HVAC & Room input‘ section ......................................................................................... 60
Figure 3.25 thermal time lag value and graphic result .......................................................................... 62
Figure 3.26 energy consumption output ............................................................................................... 63
Figure 3.27 temperature curves of June 21st, 2014, Miami (Climate zone 1) ...................................... 63
Figure 3.28 Annual HVAC load (using actual weather data) ............................................................... 64
Figure 3.29 Excel Visual Basic Editor (VBE) ...................................................................................... 64
Figure 3.30 Macros to transfer regular annual weather data into 120-second scale data (Appendix A)65
Figure 3.31 Macros to inject 120-second scale weather profile into Excel model (Appendix A) ........ 66
Figure 3.32 Macro launch bottom on ‗Main‘ worksheet (see Appendix A) ......................................... 66
Figure 3.33 temperature profiles (Celsius) in ‗Heat transfer calculation‘ worksheet ........................... 67
Figure 3.34 applying control loop in ‗Heat transfer calculation‘ worksheet ........................................ 67
Figure 3.35 eQuest model ..................................................................................................................... 70
Figure 3.36 DesignBuilder model ......................................................................................................... 70
Figure 4.1 thickness (meter) affects thermal time lag (hours) .............................................................. 75
Figure 4.2 conductivity (W/mK) affects thermal time lag (hours) ....................................................... 76
Figure 4.3 density (Kg/m3) affects thermal time lag (hours) ................................................................ 76
Figure 4.4 specific heat (J/kgK) affects thermal time lag (hours) ......................................................... 77
Figure 4.5 outdoor maximum temperature (Celsius) affects thermal time lag (hours) ......................... 84
9
Figure 4.6 outdoor minimum temperature (Celsius) affects thermal time lag (hours) ......................... 85
Figure 4.7 different temperature range (Celsius) affects thermal time lag (hours) ............................... 86
Figure 4.8 different outdoor temperature swing (Celsius) affects thermal time lag (hours) ................. 87
Figure 4.9 solar radiation (Watt) affects thermal time lag (hours)........................................................ 88
Figure 4.10 annual HVAC energy consumption ................................................................................... 90
Figure 4.11 Annual cooling capacity (kWh) in different thermal time lag ........................................... 94
Figure 4.12 Annual heating capacity (kWh) in different thermal time lag ........................................... 95
Figure 4.13 Annual total capacity (kWh) in different thermal time lag ................................................ 96
Figure 4.14 Annual capacity (kWh) with different thickness (Meter) .................................................. 97
Figure 4.15 Annual capacity (kWh) with different conductivity (W/(mK)) ......................................... 98
Figure 4.16 Annual capacity (kWh) with different density (kg/m3)..................................................... 98
Figure 4.17 Annual capacity (kWh) with different specific heat (J/(kgK)) .......................................... 99
Figure 4.18 Annual capacity (kWh) with different specific heat (J/(kgK)) ........................................ 101
Figure 4.19 annual temperature data of Seattle (climate zone 4) ........................................................ 102
Figure 4.20 annual temperature data of Fargo (climate zone 7) ......................................................... 102
Figure 4.21 annual temperature data of Phoenix (climate zone 2)...................................................... 102
Figure 4.22 annual temperature data of Los Angeles (climate zone 3)............................................... 103
Figure 4.23 heating load (kWh) of different material types in seven climate zones ........................... 104
Figure 4.24, total load (kWh) of different material types in seven climate zones .............................. 105
Figure 4.25 thermal lag (hours) in different climates effect on annual cooling load (kWh)............... 106
Figure 4.26 thermal lag (hours) in different climates effect on annual heating load (kWh) ............... 107
Figure 4.27 thermal lag (hours) in different climates effect on annual total load (kWh) ................... 107
Figure 4.28 cooling load (kWh) in different cities by change indoor temperature setting (Celsius) .. 109
Figure 4.29 heating load (kWh) in different cities by change indoor temperature setting (Celsius) .. 110
Figure 4.30 total load (kWh) in different cities by change indoor temperature setting (Celsius) ....... 111
Figure 4.31 annual load (kWh) by changing air conditioner offset temperature (Celsius) in Los Angles112
Figure 4.32 annual cooling load (kWh) in different climate zones ..................................................... 113
Figure 4.33 annual heating load (kWh) in different climate zones ..................................................... 114
Figure 4.34 annual total load (kWh) in different climate zones ......................................................... 115
Figure 4.35 energy load (kWh) by changing emissivity ..................................................................... 116
Figure 4.36 energy load (kWh) by changing environment radiant temperature (Celsius) .................. 117
Figure 4.37 air convection factor (W/(m2•K)) in different wind speed m/s ....................................... 118
Figure 4.38 energy load (kWh) by changing outside convection factor h (W/(m2•K)) ...................... 118
Figure 4.39 annual heating energy cost (USD) for different heating systems .................................... 125
Figure 4.40 annual total energy cost (USD) for different heating systems ......................................... 126
Figure 4.41 annual heating cost (USD) for different heating systems ................................................ 127
10
Figure 4.42 annual total energy cost (USD) for different heating systems ......................................... 128
Figure 4.43 material cost in different thickness (meter) ..................................................................... 130
Figure 4.44 annual total load (kWh) in different thickness (meter) .................................................... 132
Figure 4.45 annual energy source cost (USD) in different thickness (meter) ..................................... 132
Figure 4.46 annual total cost (USD), including material and energy cost .......................................... 133
Figure 4.47 total cost for five years (USD), including material and energy cost ................................ 134
Figure 4.48 total cost for ten years (USD), including material and energy cost ................................. 134
Figure 4.49 cement annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter) .................................................................................................................. 136
Figure 4.50 concrete block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter) .................................................................................................................. 136
Figure 4.51 brick block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter) .................................................................................................................. 136
Figure 4.52 wood block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter) .................................................................................................................. 137
Figure 4.53 plastic board annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter) .................................................................................................................. 137
Figure 0.1 weather data of Miami ....................................................................................................... 151
Figure 0.2 weather data of Phoenix .................................................................................................... 151
Figure 0.3 weather data of Los Angeles ............................................................................................. 151
Figure 0.4 weather data of Seattle ....................................................................................................... 152
Figure 0.5 weather data of Pittsburgh ................................................................................................. 152
Figure 0.6 weather data of Minneapolis .............................................................................................. 152
Figure 0.7 weather data of Fargo ........................................................................................................ 153
11
List of Tables
Table 1.1 common construction material thermal properties ................................................................ 21
Table 2.1 comparison between EnergyPlus and DOE-2 (Dandan Zhu, 2012) ..................................... 39
Table 3.1 important parameters description (Atkins, 2013) ................................................................. 44
Table 3.2 Excel worksheets summary ................................................................................................... 52
Table 3.3 selected US cities in seven different climate zones .............................................................. 60
Table 4.1 base case boundary condition ............................................................................................... 74
Table 4.2 test material types ................................................................................................................. 74
Table 4.3 thickness (meter) affects thermal time lag (hours) ................................................................ 74
Table 4.4 conductivity (W/mK) affects thermal time lag (hours) ......................................................... 75
Table 4.5 density (Kg/m3) affects thermal time lag (hours) ................................................................. 76
Table 4.6 specific heat (J/kgK) affects thermal time lag (hours) .......................................................... 77
Table 4.7 boundary conditions in researches and tool .......................................................................... 78
Table 4.8 validation with Xing Jin‘s (2011) results of thermal time lag .............................................. 79
Table 4.9 validation with Asan‘s(2011) results of thermal time lag (0.2meter) ................................... 80
Table 4.10 validation with Asan‘s(2011) results of thermal time lag (0.3 meter) ................................ 81
Table 4.11 boundary condition settings from different thermal time lag tests ..................................... 82
Table 4.12 validation with different boundary condition ...................................................................... 82
Table 4.13 base case boundary condition ............................................................................................. 83
Table 4.14 test material types ............................................................................................................... 83
Table 4.15 outdoor maximum temperature (Celsius) affects thermal time lag (hours) ........................ 84
Table 4.16 outdoor minimum temperature (Celsius) affects thermal time lag (hours) ......................... 84
Table 4.17 indoor temperature (Celsius) affects thermal time lag (hours) ........................................... 85
Table 4.18 different temperature range (Celsius) affects thermal time lag (hours) .............................. 86
Table 4.19 different outdoor temperature swing (Celsius) affects thermal time lag (hours) ................ 87
Table 4.20 solar radiation (Watt) affects thermal time lag (hours) ....................................................... 87
Table 4.21 base model environment setting .......................................................................................... 90
Table 4.22 base model cooling and heating system .............................................................................. 91
Table 4.23 base model HVAC setting .................................................................................................. 91
Table 4.24 base model room setting ..................................................................................................... 91
Table 4.25 tested material properties .................................................................................................... 92
Table 4.26 material thickness in different thermal time lag .................................................................. 93
Table 4.27 Annual cooling capacity (kWh) in different thermal time lag ............................................ 93
Table 4.28 Annual heating capacity (kWh) in different thermal time lag ............................................ 95
Table 4.29 Annual total capacity (kWh) in different thermal time lag ................................................. 96
Table 4.30 Annual capacity (kWh) with different thickness (Meter) ................................................... 97
12
Table 4.31 Annual capacity (kWh) with different conductivity (W/(mK)) .......................................... 97
Table 4.32Annual capacity (kWh) with different density (kg/m3) ....................................................... 98
Table 4.33 Annual capacity (kWh) with different specific heat (J/(kgK)) ........................................... 99
Table 4.34 representative city in each climate zone ........................................................................... 100
Table 4.35 test material properties ...................................................................................................... 100
Table 4.36 cooling load of different material types (8 hours lag) in seven climate zones .................. 101
Table 4.37 heating load (kWh) of different material types in seven climate zones ............................ 103
Table 4.38 total load (kWh) of different material types in seven climate zones ................................. 104
Table 4.39 thermal lag (hours) in different climates effect on annual cooling load (kWh) ................ 106
Table 4.40 thermal lag (hours) in different climates effect on annual heating load (kWh) ................ 106
Table 4.41 thermal lag (hours) in different climates effect on annual total load (kWh) ..................... 107
Table 4.42 cooling load (kWh) in different cities by change indoor temperature setting (Celsius) ... 109
Table 4.43 heating load (kWh) in different cities by change indoor temperature setting (Celsius) ... 109
Table 4.44 total load (kWh) in different cities by change indoor temperature setting (Celsius) ........ 111
Table 4.45 annual load (kWh) by changing air conditioner offset temperature (Celsius) in Los Angles112
Table 4.46 annual cooling load (kWh) in different climate zones ...................................................... 113
Table 4.47 annual heating load (kWh) in different climate zones ...................................................... 114
Table 4.48 annual total load (kWh) in different climate zones ........................................................... 115
Table 4.49 energy load (kWh) by changing emissivity ...................................................................... 116
Table 4.50 energy load (kWh) by changing environment radiant temperature (Celsius) ................... 117
Table 4.51 energy load (kWh) by changing outside convection factor h (W/(m2•K)) ....................... 118
Table 4.52 cost of electricity and natural gas (USD) in Los Angeles area in October 2015 .............. 122
Table 4.53 specifications of different heaters (Appendix C) .............................................................. 123
Table 4.54 base model setting ............................................................................................................. 124
Table 4.55 test material properties ...................................................................................................... 124
Table 4.56 annual heating load (kWh) for different heating systems ................................................. 124
Table 4.57 annual heating energy cost (USD) for different heating systems ..................................... 125
Table 4.58 annual cooling load (kWh) and cost (USD) ...................................................................... 125
Table 4.59 annual total load (kWh) for different heating systems ...................................................... 125
Table 4.60 annual total energy cost (USD) for different heating systems .......................................... 125
Table 4.61 annual heating load (kWh) for different heating systems ................................................. 126
Table 4.62 annual heating cost (USD) for different heating systems ................................................. 127
Table 4.63 annual cooling load (kWh) and cost (USD) ...................................................................... 127
Table 4.64 annual total load (kWh) for different heating systems ...................................................... 127
Table 4.65 annual total energy cost (USD) for different heating systems .......................................... 127
Table 4.66 test material properties ...................................................................................................... 129
13
Table 4.67 base model setting ............................................................................................................. 129
Table 4.68 material weight (Ton) in different thickness (meter) ........................................................ 130
Table 4.69 material volume (m3) in different thickness (meter) ........................................................ 130
Table 4.70 material cost in different thickness (meter) ....................................................................... 130
Table 4.71 annual cooling load (kWh) in different thickness (meter) ................................................ 131
Table 4.72 annual heating load (kWh) in different thickness (meter) ................................................ 131
Table 4.73 annual total load (kWh) in different thickness (meter) ..................................................... 131
Table 4.74 annual energy source cost (USD) in different thickness (meter) ...................................... 132
Table 4.75 annual total cost (USD), including material and energy cost............................................ 133
Table 4.76 total cost for five years (USD), including material and energy cost ................................. 133
Table 4.77 total cost for ten years (USD), including material and energy cost .................................. 134
Table 5.1 comparison between EnergyPlus DOE-2 and Excel tool .................................................... 140
Table 5.2 material and boundary parameters effects on thermal time lag .......................................... 141
Table 5.3 material and environmental parameters effects on heating and cooling system load ......... 142
Table 0.1 validation with Xing jin‘s (2011) results of thermal time lag (0.24 meter) ........................ 148
Table 0.2 validation with Asan‘s(2011) results of thermal time lag (0.2meter) ................................. 149
Table 0.3 validation with Asan‘s(2011) results of thermal time lag (0.3 meter) ................................ 150
14
Chapter 1: Introduction
Building energy simulation programs have been developed since the 1960s (IBPSA, 2016). With the rise of
the computer, HVAC companies started to use computer coding to calculate the dynamic heat flows in
buildings (IBPSA, 2016). In 1970s, the U.S. department of defense (DOD) created the building loads
analysis and system thermodynamics (BLAST) engine (IBPSA, 2016). Meanwhile, the US Department of
Energy (DOE) developed DOE-2 (James J. Hirsch & Associates, 2012) from Cal-ERDA
(https://publications.lbl.gov/islandora/object/ir%3A1053020)
(https://www.google.com/search?q=cal+ERDA&oq=cal+ERDA&aqs=chrome..69i57.5476j0j4&sourceid
=chrome&ie=UTF-8). Both BLAST and DOE-2 developed rapidly from late 1970s to early 1980s. In late
1990s, EnergyPlus was developed, claiming a more powerful tool combining the features from BLAST and
DOE-2 (James J. Hirsch & Associates, 2012). Currently, various derivative energy modeling programs use
EnergyPlus and DOE-2 as simulation engines, including DesignBuilder (EnergyPlus), eQUEST (DOE-2),
EnergyPro (EnergyPlus), BEopt (EnergyPlus), etc. These programs can handle comprehensive building
information modeling and energy simulation at the same time. They can also use building information
directly from architecture design programs such as AutoCAD and Revit (Autodesk, 2016). These building
energy simulation programs aim at creating a building information model that is close to the actual
conditions with maximum user customizations.
As the current building energy modeling programs target real building conditions, a building energy
simulation tool is required to be developed targeting theoretical/lab conditions that is more flexible of
changes for various research objectives and can focus on specific material or environment parameters such
as thermal time lag. The theoretical conditions include various lab environments such as adiabatic models,
extreme environment conditions (Antarctic, space buildings), sealed model with no infiltration heat losses,
etc. To design such tool also helps gain better understanding of building heat transfer and energy system by
formulating and coding the heat transfer mechanism. It also helps study and evaluate thermal mass material
effects on building energy performance in modern building design.
1.1. Introduction of thermal mass material
Thermal mass is a property of an object. The mass difference determines its ability to retain and release heat
over time. It did not take too long for cavemen to discover the temperature difference between outside and
few yards inside the cave. The temperature stayed relatively constant throughout a year. Initially in wall
material history, the nomadic time, the houses or shelter were made of grass and simple cloth. The
tent/shelter has very little heat capacity and some heat resistance, depending on construction. Then around
Neolithic periods (10,200 BC), people started to use mud brick and adobe to build houses, such as in the
15
Mesopotamian area, where people built wall mosaics of glazed brick (Bradtmueller, 2014). Egypt (around
2,600 BC) used rough, low grade limestone to build pyramids and other important monuments.
Common thermal mass materials include water, concrete, brick/adobe, earth/mud, stone masonry, and logs
(Kosny, 2001). Water is not a common construction material, but it has been applied to some domestic
technologies. For instance, due to its high heat capacity (4200 J/(kgK)), water can be used as thermal mass
material for buildings. One of the first roofpond buildings, Skytherm house in Atascadero, California (Hay,
1973), uses water as heat absorber on the roof. The roofpond is able to provide both radiation heating and
cooling to the adjacent space, by using sliding insulation on the roof. The 16-story Ingalls building in
Cincinnati, Ohio, is the first skyscraper constructed with reinforced concrete (2400kg/m3) in year 1903. It
uses purely reinforced concrete on floors, wall, beams and stairs. The construction contains no other metal
structures except the one in the reinforced concrete. Moreover, a large number of historical monuments are
made of masonry, including the White House, the U.S. Capitol and many buildings in Washington D.C..
They are both constructed with quia creek sandstone, which is easy to shape and has good durability and
high thermal mass (USGS, 2014).
Thermal mass materials are widely used in construction worldwide. Concrete is a popular residential
material in most of the world and is also commonly used for commercial construction (Amanda Partridge,
2012). Innovations were made such as phase-change materials (increasing its heat capacity during phase
change) and biological material (such as green roof, which increases its thermal resistance as wall/roof)
have shown the ability of increasing material‘s thermal capacity (Richardson, 2008). For example, the
School of Art, Design and Media at Nanyang Technological University in Singapore has a green roof
structure (Payne, 2010). Phase change materials (PCM) such as water-based ice and gel packs are used for
storage proposes to maintain 0 degree temperature change. (Sharma, 2009). Buildings constructions using
PCM contained in microscopically small polymer (such as paraffin-based PCM) benefits their energy
consumption. . In the US, states like California have their unique energy codes to regulate the baseline of
thermal resistance in wall/window/ roof for both residential and commercial buildings (California Energy
Commission, 2015). They include factors for high mass construction. Overall, thermal mass material is
indeed one of the most efficient passive strategies to save energy output in buildings. Its efficiency depends
on directly controlling the energy flow between inside and outside space (Atkins, 2013). It affects a
building‘s heat gain/loss, HVAC load, as well as passive systems design such as natural ventilation. In the
thermodynamic engineering domain, heat flows within thermal mass material have been analyzed using
mathematical models, from hourly coefficients to complete finite element method analysis. Among various
parameters, thermal time lag between outside space and material temperature plays a significant role on
controlling the efficiency of thermal mass strategy (Asan, 2005).
16
Thermal time lag can cause different energy performance in different climate types; this also varies with the
thermal performance of different types of material. The overall heat transfer performance of thermal mass
material depends on material and environmental parameters. For instance, even some heavy-weight
material such as concrete/masonry could cause negative effects in a humid climate zone with constantly
hot/cold weather (Asan, 2005). The importance of the study of thermal time lag is to understand the
thermodynamic performance of wall/roof/window, exploring the optimization of wall/roof material
combination in a certain type of climate, as well as discussing the validity of the conventional concept that
using heavy-weight material can contribute to building energy saving.
1.1.1. Thermal mass material and time lag in climates with high diurnal swings
High thermal mass material is energy efficient in high diurnal swing climate types (Ulgen, K. 2002). For
example, in Phoenix (Climate zone 2, Hot-dry), Arizona, masonry remains a popular construction material
type through the 20th century. Some of the well-known buildings are made of masonry, including the Luhrs
Tower (concrete, built in 1929), US Bank Center (concrete, built in 1976, second highest building in
Phoenix), and Arizona State Capitol (masonry and concrete, built in 1912). High thermal mass material is
also widely used in Los Angeles, California (Climate zone 3, high diurnal swing, dry) although limited
somewhat by seismic conditions. Large numbers of buildings are constructed with concrete and masonry,
including Los Angeles City Hall (concrete and masonry, built in 1928), and Capitol Records Building
(concrete, built in 1956).
Thermal mass materials are building materials with relatively high mass and density that effectively
absorb and slowly release heat flux to reduce indoor temperature variation. The principle of heat gain (Q)
has a direct relationship to the mass of the object (m), specific heat of the material (c), and the difference in
the starting and ending temperature (delta T) (Eq. 1.1).
Equation 1.1
Where, (Joule) is the heat energy absorbed/released, m (kg) is the mass, c (J/kg.K) is the heat capacity,
(Kelvin) is the before and after temperature variation of the target object
The equation shows that the material‘s ability of absorbing heat energy depends on mass, heat capacity, and
temperature difference. Accordingly, a heavier material is able to store more energy than a light material.
Absorbing the same amount of energy, heavier materials can maintain more constant temperature then
light-weight materials. For example, in an ideal building model, with perfectly sealed envelope, one with
heavier material is able to maintain more constant inside space temperature than light-weight material. The
application of thermal mass material can lead to energy saving in many possible ways.
17
In climates with high diurnal swings, massive building envelopes such as masonry, concrete, and earth can
be utilized as one of the simplest ways of reducing building heating and cooling loads. Very often such
savings can be achieved in the design stage of the building and on a relatively low-cost basis (Sun, C., 2013).
Such reductions in building envelope heat losses combined with optimized material configuration and the
proper amount of thermal insulation in the building envelope help to reduce the building cooling and
heating energy demands and building related CO2 emission into the atmosphere. Thermal mass effects
occur in buildings containing walls, floors, and ceilings made of heavy material such as logs, masonry, and
concrete (Atkins, 2013).
Thermal time lag is the duration of heat flux transferring from outside surface of exterior wall to the inside.
It can be calculated as the time difference for the heat to move through the wall. It is another measurement
of wall heat transfer ability other than R-value (thermal resistance of a wall). The thermal mass wall acts as
a heat sink to retain heat during the day and release heat during the night (Fig. 1.1). Depending on the
temperature difference between the wall and outside air and also the wall and the inside air, the release of
heat could go either direction; in fact, it is possible that the heat is going both directions at once from the
wall. For the heat flow in hot/dry climates with high diurnal swings, generally the sun heats up the wall
during the day, the heat ―moves‖ towards the interior, and the wall releases its heat back to both the exterior
and interior at night. In building applications, putting on night time exterior insulation on the wall can keep
the heat moving towards inside the building where it can be used to raise the temperature of the inside space
(Asan, 2005).
The lag shows a gap between wall/roof and environment temperature, which can be utilized to control
energy flows for the interior of the building. Thermal time lag varies with material and environmental
properties.
Figure 1.1 Thermal time lag between wall and environment temperature (From the Excel tool)
Thermal lag
18
An effective thermal time lag can properly set the temperature difference between wall and outside space.
The temperature difference can provide energy towards surrounding spaces in respect of thermal comfort.
Meanwhile, the amount of energy flow requires it to be controlled in order to minimize unnecessary heat
flow transfer into the building, often by adjusting the thickness of the wall.
Thermal mass material has a high sensitivity to different climate types. For example, architects building in
hot and dry climates can use favorable high diurnal swings (caused partially by low humidity) as an
opportunity to lower energy consumption in their buildings due to the dynamic heat conduction of the
faç ade (Asan, 1998). In contrast, thermal mass material in constantly humid hot/cold climates, has less
effect on building energy savings and can sometimes increase burden on energy consumption. Overall, the
ability of material‘s energy sustainability depends on how effectively the it absorbs and releases the heat
flux between indoor and outdoor space. The time-diversity of absorbing/releasing heat is crucial to save
energy in thermal mass material (Atkins, 2013).
When the outside temperature has a large swing, thermal mass material is able to maintain inside space
despite outside temperature variation. The lag between outside and wall temperature creates the
temperature difference, which leads to heat flows through each other (Fig. 1.2). A 12 hour time lag provides
positive energy flow towards the inside space to maintain thermal comfort and release the burden on HVAC
system (Atkins, 2013).
When the outside temperature is constantly hot/cold outside the comfortable zone, the uncontrolled
material continuously absorbs/releases heat to the inside space. Instead of conditioning inside space, the
walls and the roof may be a burden on the HVAC system throughout the year. Therefore, the HVAC system
Figure 1.2 Thermal mass material (concrete block) in climate with large temperature swing
19
requires to constantly removing those heat flows to maintain indoor thermal comfort. Compared to regular
construction material, thermal mass has the least advantage in this specific case.
Applying thermal mass in a cold climate in Alaska (climate zone 6, 7 and 8, Figure 1.5) shows that
increasing the thermal mass decreases the risk of overheating in summer, but does not affect the annual heat
demand overall (Stevens 2012), . The research built a model in DOE-2 energy simulation program, with
actual weather data gathered from weather station. The model compares a typical Alaskan residence using
heavyweight floor and lightweight floor. The result shows using high thermal mass improves the indoor air
temperature by reducing the peak temperature in non-heating season. It also improves the comfort level of
the house in all three climate types using Predicted Mean Vote (PMV), which is a thermal comfort model
that represents the mean response from a large group of people. Therefore, high thermal mass material in
Alaska is not an effective strategy to reduce heating demand, because in cold climates thermal mass
Figure 1.3 Thermal mass material in constant hot climate
Figure 1.4 Thermal mass material in constant cold climate
20
material cannot take advantage of the spare heat from daily temperature swing (Stevens 2012). The
exception is the use of high mass materials in sun spaces. Different wall temperature curves are compared,
including ICF, log, fiberglass and concrete (Figure 1.5).
Figure 1.5 Indoor temperature on June 20
th
in Fairbanks, Alaska (Stevens, 2012)
1.1.2. Thermal mass, thermal time lag, and their applications
Many new buildings choose material appearance or other criteria over strictly energy performance, using
light-weight material with low thermal resistance, such as glass and metal. Due to high conductivity and
low thermal mass, these material types usually transfers large amount of energy flow towards building,
seriously puts a burden on building energy system, and contributes negative effect on energy crisis (Ozel,
2012) (Table 1.1)
21
Table 1.1 common construction material thermal properties (Tony Atkins, 2013)
The application of thermal time lag has been widely used in passive system for natural ventilation. Natural
ventilation occurs due to atmospheric pressure difference (Liddament, 1994). Thermal time lag causes
partial temperature difference in building structure, basing on material‘s ability to restore heat. Trombe wall
is a passive energy saving strategy using winter sunlight heating up the internal space (Torcellini, 2004).
The structure contains outside transparent layer, operable vents, layer of air and internal thermal mass layer.
During the day, the vents are open so that both the room air and the internal space are heated (Figure 1.6).
During the night, the vents are shut to prevent heat loss through air convection (Figure 1.6). Meanwhile, the
outside transparent layer blocks the long-wave radiation escaping the structure. Buildings can also use
overlays to avoid overheating during summer (Figure 1.6). The temperature difference leads to air
movement that drives air from the gap between the wall and the glazing into the building. Similarly, a night
flush strategy uses the higher temperature of the indoors to drive cool night air into the building. Similarly,
a solar chimney uses indoor air with higher temperature that is heated by sunlight and drives cool fresh air
into the building (Figure 1.7) (Atkins, 2013). These passive energy saving systems utilize the thermal
storage ability of thermal mass material to provide sufficient heat on demand.
Building materials Thermal conductivityDensity Specific heat
[W/(mK)] (kg/m3) [J/(kgK)]
Cement layer 0.36 700 1050
Concrete block 0.51 1400 1000
Brick block 0.62 1800 840
Gypsum plastering 0.42 1200 837
Granite (red) block 2.9 2650 900
Marble (white) block 2 2500 880
Sandstone block 1.83 2200 712
Clay layer 0.85 1900 837
Asphalt sheet 1.2 2300 1700
Steel slab 50 7800 502
Aluminum slab 210 2700 880
Cork board 0.04 160 1888
Wood block 0.16 800 2093
Plastic board 0.5 1050 837
Rubber board 0.3 1600 200
P.V.C board 0.16 1379 1004
Asbestos sheet 0.16 2500 1050
Formaldehyde board 0.03 30 1674
Thermalite board 0.19 753 837
Fiberglass 300 1000 0.06
Siporex board 0.12 550 1004
Polyurethane board 0.03 30 837
Light plaster 0.16 600 1000
Dense plaster 0.5 1300 1000
22
Figure 1.6 Trombe wall system (Autodesk Sustainability workshop, 2015)
Figure 1.7 Night flush cooling and solar chimney (Autodesk Sustainability workshop, 2015)
There are several ways to increase the thermal resistance of building envelopes by changing the material
properties, such as material types and thickness. The building envelope system requires thermal mass
material to store more energy from the environment. Thicker wall with dense material performs as a
thermal barrier to block heat energy from transferring into building. Thermal insulation, such as wool, an
air gap or foams, although they do not have high thermal capacity, will reduce the conductivity of wall/roof
and indirectly reduce the thermal lag. Due to the high thermal resistance (R-value) of thermal insulation, the
heat flux is more difficult to get through the exterior wall.
Using multilayer wall construction can increase its thermal resistance and increase ability to store heat. The
sequence of layers should be carefully selected, in case condensation occurs when the temperature of
specific layer drops below dew point (Tony Atkins, Marcel Escudier, 2013). There should always be a
vapor barrier on the warmer side. From the angle of heat transfer, the sequence can also lead to different
thermal lag and change the thermal performance of the wall/roof. In recent years, innovative envelope
23
systems have been designed such as hydro-wall, which contains a large percentage of water with high
thermal capacity (Rael-Sanfratello, 2015). The water has much higher thermal capacity than conventional
structure material, therefore can store more heat.
The differences of material with high or low thermal time lag are displayed in the temperature curves
(figure 1.8 and figure 1.9). The wall temperature curve varies with material and environmental properties.
A denser and thicker wall can perform as a heat sink, which is able to restore large amount of heat. The
curve shows the wall with bigger thermal lag has lower temperature fluctuation (Fig. 1.7). In comparison,
the wall with smaller thermal time lag has relatively higher temperature fluctuation (Fig. 1.8). The energy
performance of a wall system still depends on other environment properties, and it is more complex in
reality with cost and appearance concerns. For instance, material with smaller thermal lag may adjust better
in mild climates, since the demand on heating and cooling is low. Dense material such as wood and
masonry sometimes can be high in cost. These hypotheses can be further investigated in the mathematical
model.
Figure 1.8 high thermal lag wall (Blue – outside, red – wall, purple – inside)
0
5
10
15
20
25
30
35
0.0
Temperature (Celcius)
One day
24
Figure 1.9 low thermal lag wall (Blue – outside, red – wall, purple – inside)
Note, Figure 1.8 and 1.9 are simplified situations assuming the indoor temperature is controlled constantly
at 25 Celsius.
Buildings must be designed so that they experience both times of net energy gain and net loss, a necessary
condition for energy savings (Childs, 2009). Further savings can be made through adjusting cooling and
heating system settings. Not only can this be optimized to especially save cooling energy, but could also
reduce peak loads (extremely important for power plant sizing and construction), save money by utilizing
time-based utility pricing, and balance the daily use of the mechanical equipment (―part-load performance‖)
(James E, 1990). Even for a single interior temperature set point, thermal lag can reduce the use of energy in
a space by absorbing heat energy and reducing the temperature fluctuation.
1.2. Energy simulation tool design
Building a mathematical heat transfer model is useful to investigate the parameter relationship within the
thermal mass material. Thermal time lag is a dependent parameter of several material and environmental
parameters. The value of thermal lag is affected by material factors such as thickness density, conductivity,
and thermal capacity, as well as other environment factors such as humidity and atmospheric pressure
(Simge Andolsun, 2008). However, most current energy simulation software does not have the feature to
study thermal time lag and related properties in details (for research purpose), except for some small scale
add-ons such as Ecomat (AUREA Consulting Sustainable Architecture & Engineering ltd, 2014) and
Opaque (Murray Milne, 1989). The current large energy simulation engines for buildings are EnergyPlus
(EnergyPlus, 2015) and DOE-2 (James J. Hirsch & Associates, 2012). Although neither of them focus
0
5
10
15
20
25
30
35
0.0
Temperature (Celcius)
One Day
Envirnment Temp
25
specifically on thermal time lag, the concept of energy modeling and heat transfer calculation mechanism
can be applied into this project.
EnergyPlus, the latest authorized energy simulating engine, has the ability to calculate the heat transfer
mechanisms with exterior walls. It is sponsored by both US Department of Defense (USDOD) and US
Department of Energy (USDOE) (Crawley et al, 1998). The developer claimed EnergyPlus derives most
features from DOE-2 (James J. Hirsch & Associates, 2012) and BLAST (BLAST Support Office, 1992).
For load calculation method, EnergyPlus uses heat balance approach (same as BLAST), while DOE-2 uses
room weighting factor approach. The solution algorithms from EnergyPlus, including heat transfer
calculation and HVAC load calculation, shows differences of results comparing with DOE-2. Simulating
experiments show the total building load in EnergyPlus is 11% lower than that in DOE-2, with detailed
modeling including internal facilities, people, and infiltration heat loss (Simge Andolsun, 2008). Another
research on heat transfer through slab-on-grade floor type in low-rise buildings, shows the EnergyPlus has
25% higher in cooling load and 27% lower in heating load than DOE-2 (Simge Andolsun, 2010).
Apparently, the weighting factor approach simplified the internal wall convection coefficient by combining
radiation and convection coefficient, as well as using the temperature of the adjacent room from a former
time step (Dandan Zhu, 2012). The research indicates that users should be cautious when using DOE-2 in
multiple room building with different conditioning environment in each room.
Time step is a byproduct when calculating heat transfer equations; it represents the duration between
former and later heat transfer calculation steps. The time step is also another issue that requires to be
solved in this project. According to the time step of EnergyPlus (up to 1 minute) and DOE-2 (1 hour,
fixed), the time step has significant effect on the accuracy of the results. EnergyPlus introduced a detailed
time step system with accuracy up to 1 minute (Drury B. Crawley, 2010). This feature is applied into
various heat transfer calculations including surface convection coefficients and long/short-wave radiation
heat exchange. These data all calculated at a 1 minute scale. The weather data including temperature and
solar radiation collected from local weather stations can be translated into minutes or hourly scale in the
program (Dandan Zhu, 2012). In order to design a comprehensive tool that can handle tests on thermal
mass material properties, both input, output data, and design platform will be carefully selected. The
calculation algorithms will be design according to the thermal mass material properties.
Exterior temperature profile
The fact that the mass of a roof or the walls has a large effect on thermal time lag, and the use and layering
of different materials can be used to adjust the time lag appropriately has been confirmed by other studies.
(Sambou, 1990). However, just designing a building with the appropriate time lag for a specific roof/wall
26
construction is not sufficient to guarantee energy savings. In addition to the interior conduction through the
wall, the outside boundary conditions (including temperature profile, solar radiation, and emissivity of the
surface), and interior conditions (including temperature set points) are important.
There are many possible conditions on both the outside or inside space. On outside space node, theoretical
or actual weather data can be applied in the model depending on the requirement. For different research
purposes, there are several types of outside/inside temperature curves, including sine wave, constant,
periodical and actual data.
Figure 1.10 sine wave temperature
Figure 1.11 constant temperature
Figure 1.12 Theoretical periodic temperature (For instance, specific laboratory condition)
27
Figure 1.13 actual temperature data
The weather data includes the parameter that has influence on thermal performance, so temperature and
solar radiation will be used in the model. Both the sine curve and actual temperature profiles will be
included in the tool. The sine temperature wave is frequently used to represent the daily temperature curve.
It simplifies the randomness into a mathematical equation, so it can be easier to build into the thermal
performance model. Many experiments use a sine temperature wave as outside temperature condition that
requires merely diurnal maximum and minimum temperature. The sine wave is also essential to calculate
the thermal time lag (the calculation of thermal lag will be discussed in later section). On the other hand, the
actual temperature/solar radiation data are gathered from weather stations. It represents the actual condition
of outside space, giving a relatively precise environmental model. With the actual temperature/solar
radiation data, the model is able to simulate more complex and practical situation. Since annual
temperature/ solar radiation is provided from weather stations, annual performance can also be simulated
using the actual weather data. Furthermore, outside space condition can be categorized into different
climate zones for further research purposes.
Figure 1.14 Annual solar radiation and temperature data (Miami year 2012) (NOAA, 2015)
HVAC system with constant internal temperature
It is necessary to determine the internal temperature control method for a HVAC system. DOE-2
introduces the weighting factor approach, which assumes the conditioned room has constant internal
28
temperature. Namely when the HVAC system works in an ideal condition, working at infinite working rate,
it is keeping the internal temperature constant in spite of the outside condition. The heat flow from the wall
will be instantaneously neutralized by HVAC system during the entire time. This ideal condition
maximizes the energy consumption of air conditioning and heating systems since the system is working
continuously. Meanwhile, the convection and radiation heat exchange is operating between wall and indoor
air. Therefore, the heat flow is either performing cooling or heating. The HVAC is working all the time
because the room requires constant temperature. The wall cools the room in the area left of point A, heating
between point A and B, and again cooling in the area right of point B. This assumption is helpful to
understand wall performance under such circumstance; however, is not application for practical model
because in reality no HVAC system can achieve such infinite working rate. In practice, there is a
temperature range allowance.
Figure 1.15 temperature curves when use ideal HVAC system (Blue – outside, red – wall, purple – inside)
The ideal working rate HVAC system generates a simpler model with constant inside temperature. It
assumes the internal temperature is always equal to the HVAC setting temperature the entire time. This
requires the air conditioner has extreme sensitive sensor, which is not possible in real situatiosn. This model
helps with the study of theoretical model or ideal HVAC system. It also has advantage of providing
explanation of the operation principle of the model. This model can also be practically used in building with
large internal space. Since it is easier to control indoor temperature with sufficient air conditioner capacity
in large space, which can be considered constant all the time, it can be even applied to this theoretical model
0
5
10
15
20
25
30
35
Temperature (Celcius)
One day
A B
29
HVAC system with typical control loop
By adding a controller into an air conditioner, it improves the air conditioner performance with a control
loop that can be set by the user. The internal temperature is fluctuating, and the controller is continuously
sending the signal to the HVAC system. In spite of the setting temperature on the thermostat, the room
temperature will be fluctuated because of the control loop. The room temperature is controlled between
Tin- Limit and Tin + Limit, where Tin represents the set temperature inside and Limit the temperature range
allowance set by controller configuration. Once the room temperature reaches the setting temperature, the
HVAC stops working until the room temperature exceed the limits. The cooling mode will activate when
the room temperature exceeds Tin + Limit, and the heating mode will activate when the room temperature
drops below Tin – Limit. This type of HVAC system can maintain the room temperature within the
comfortable zone and allows fluctuation of internal temperature and interval of HVAC system operation
(Fig. 1.16). For example, if the indoor setting temperature is 70°F and the Limit temperature is 3°F, the
actual indoor temperature under such control loop will bouncing between 73°F (70°F +3°F) and 67°F
(70°F-3°F).
Figure 1.16 HVAC control loop
This internal condition is more realistic, because no HVAC system can work in an infinite working rate.
The HVAC system stops operating when the internal temperature is within the limit. Meanwhile, thermal
mass wall/roof absorbs heat from internal space to reduce the pressure of HVAC system. Since the working
rate for HVAC system is constant, the duration of working hours decides the energy consumption of the
system. Therefore, it is worthy to explore the ability of thermal mass material reducing the operating hours
of the HVAC system in the model.
30
1.3. Conclusion
Building an accurate energy model is necessary to explore the relationship between energy consumption
and material properties. By using actually weather data can provide a more precise database for the model.
Different cities in different climate types can be selected using weather data from weather station. There are
many material and environmental parameters can be added into the model including boundary conditions,
solar absorption, humidity, etc. Additionally, by using heat transfer model, heat flow and temperature
curves can be observed in graphics. The thermodynamic process of heat transfer in walls/roofs can be
further analyzed.
31
Chapter 2: Background
2.1. Scope of work
This section primarily focuses on previous research projects on the following topics. The order of the
sections is based on the order of Excel simulation tool development. It will include research tests and
related results, followed by discussion of its potential to be used in Excel tool development.
Heat transfer principles, thermal mass material applications, and latest thermal time lag research
findings
Energy simulation tool development history and its details on heat transfer on exterior walls
2.2. Heat transfer principles, thermal time lag and related properties in exterior walls
Heat transfer with building
The development of an Excel tool requires knowledge of the basic principles of heat transfer. The energy
exchange between indoor and outdoor is through heat transfer. The heat transfer occurs at exterior wall
includes all three fundamental modes: conduction, convection, and radiation (Kusuda, 1977).
To be more specific, conduction heat transfer occurs in building includes exterior wall conduction, interior
mass conduction, conversion from heat gain/loss to cooling and heating load and ground heat loss (Kusuda,
1977). Heat convection occurs at the exterior surface depending on wind speed and surface conditions. It
also occurs in and through the cavity walls, infiltrations, indoor air movement due to temperature change
and within the porous insulating structure (Kusuda, 1977). Radiation heat transfer includes short-wave solar
radiation and long-wave emission (Kusuda, 1977).
Thermal mass material and thermal time lag
There is a lot of research on the topic of thermal mass material and its potential for energy saving. Topics in
different cities globally are studied with different material combinations. Both energy simulation tools
(such as Designbuilder, Energy Pro) and numerical heat transfer method are applied in various studies.
Research shows the heat flow through exterior walls have significant relationship with thermal mass
material and its thickness in Ryiadh, Saudi Arabia (Al-Sanea, 2011). The research uses a 1-dimensional
heat transfer model to study a concrete wall with insulations. It uses numerical heat transfer model, which is
able to simulate multi-layer wall. The results show the heat flow through wall has obvious drops with
increasing thickness in spring and autumn rather than winter and summer (Al-Sanea, 2011). The concrete
wall can improve the energy saving up to 95% (Figure 2.1) with critical thickness (Al-Sanea, 2011).
32
Figure 2.1 critical thickness and energy saving in Ryiadh using concrete wall with insulations
Dodoo again confirms that the energy saving advantage of thermal mass material could be relatively low in
mild cold and cold climates such as Nordic area (Northern Europe) and Alaska (United States). According
to a research in Vä xjö , Sweden (Dodoo, 2011), the heating energy saving (only heating required in Vä xjö )
due to thermal mass material is small and varies with location and building types. The research tests
concrete and wooden wall in a 4-storey building with three energy phases, including production, operation
and end-of-life phase (Dodoo, 2011). This includes the construction, transportation and recovery energy of
the material life-cycle energy consumption. The energy simulation program used in the test is VIP+, which
is developed by Strusoft (strusoft.com). The result shows the annual heating demand reduced 0.5-2.4% by
using the thermal mass material (Dodoo, 2011). Another research shows in Alaska, although thermal mass
reduced the over-heating risk in summer, it does not have significant effect on heating demand in most of
the year (Stevens, 2012). The research uses IDA Indoor Climate and Energy (IDA ICE) as its energy
modeling program. The result gives one-day indoor temperature curves difference between several material
types on June 20
th
(Figure 2.2).
33
Figure 2.2 Indoor temperature on June 20
th
in Fairbanks, Alaska (Stevens, 2012)
Thermal mass material works well with high thermal resistance insulation (Ibrahim, 2013). Research
conducts energy simulations with EnergyPlus on different wall configurations, including with innovative
thermal insulation material ‗Parex‘ which has higher thermal resistance than the conventional insulation.
The study shows not only thermal insulation increases the thermal resistance (R-value) of the thermal mass
wall, but it increases the thermal time lag by 1 hour (Ibrahim, 2013). The result also gives thermal time lag
and decrement factor values (Figure 2.3) in order to compare with each other.
34
Figure 2.3 time lag and decrement factor of different wall configurations (Ibrahim, 2013)
As noted earlier, phase change material (PCM) has been developed and been a controversial passive energy
saving strategy in building design (Richardson, 2008). The fact that PCM is able to absorb large amount of
energy during phase change progress makes it extremely efficient on thermal storage as thermal mass
material (Richardson, 2008). The test result (Figure 2.4) shows the indoor temperature difference with and
without PCM (Richardson, 2008). PCM also has its limits come to building passive energy strategies.
Previous applications of PCM for building uses have the issue of high material price, duration of
phase-change ability, corrosiveness and leaking of PCM causing structure damage (Kosny, 2015).
Innovations in last decades have improved the practicability of PCM material. The integration between
insulation and PCM, PCM-enhanced cellulose and PCM in bended fiberglass shows capability of heat
storage in buildings (Kosny, 2006, 2007, and 2010).
http://www.cse.fraunhofer.org/building-energy-efficiency/background
35
Figure 2.4 temperature curves of interior temperature for 2 cm wallboard without PCM (Solid black line), 2 cm
wallboard with PCM (dash line), semi-infinite thickness of concrete (dotted line), exterior temperature (grey line)
(Richardson, 2008)
The research also indicates a new approach that the ideal exterior wall configurations can be calculated
backwards based on known indoor thermal comfort conditions (Zeng, 2010). The ideal specific heat of
external wall, which requires the least air conditioning, can be calculated using numerical method with
known indoor condition (Zeng, 2010). The model in the research is an office room with one side southern
external wall. The test location includes 7 different cities in mainland China with different climate types.
Based on ideal specific heat of external wall system, the other wall configurations vary with different
climate types (Zeng, 2010). However, the research is based on adiabatic mathematical model and other
‗experimental conditions.‘ In reality, the heat transfer between outdoor and indoor environment will be
much more complicated. Other climate types should be tested in further studies.
Thermal time lag and decrement factor
Research shows the thermal time lag is affected by multiple factors. A detailed thermal time lag
calculation is described in research (Asan, 2008), which requires exterior temperature data and other
boundary conditions. The test results are also verified by another research (Xing Jin, 2011) using the same
approach. Both tests use theoretical sine curve weather profile and constant boundary condition. The
result gives a thermal time lag list of construction material with different thickness (Figure 2.5). Another
research shows the thermal time lag and decrement factor are affected by position of the insulation layer
(K.J.Kontoleon, 2006). This indicates the possibility of insulation layer position effect on total building
energy load. Another research suggests using single-layer formation wall for the building usage of
36
specific time intervals, while using multi-layer walls for buildings with frequent usage density (Ulgen, K,
2002)
Figure 2.5 list of thermal time lag with different material and thickness (Asan, 2008)
Boundary conditions
Research indicates the long-wave emission has been ignored in numbers of previous researches (Kehrer,
2002). The conventional exterior wall heat transfer analysis often uses a simpler model that ignores the
long-wave radiation from surrounding environment. A more accurate radiation model (Based on WUFI, a
radiation heat transfer simulation tool) was built with emissive heat transfer (Kunzel, 2002). It shows the
exterior wall condition is affected by long-wave emission, evaporation and condensation heat transfer
(Kunzel, 2002). This is affected by surrounding objects and exterior air humidity level. There are several
tests of radiation heat transfer using WUFI. The results (Figure 2.6) shows the temperature curves of the
exterior wall is sensitive to boundary conditions, which requires further investigation of material types and
weather data (Kunzel, 2002). The results show the temperature of water content in oriented strand board
(OSB), which is the test material. It indicates the difference of results in three ways, simplified model, no
solar radiation model and complete radiation balance model. The difference of the temperature curves can
be observed.
37
Figure 2.6 radiation heat transfer results differences (Kunzel, 2002)
Short wave solar radiation is the main heat gain of exterior walls (Duffin, 1984). The heat gain from solar
radiation highly depends on the absorption coefficient, as well as time lag and decrement factor. The
research results (Duffin, 1984) show that an absorption factor has significant effect on time lag, decrement
factors and temperature variations. Specifically, increasing solar absorptivity up to 0.2 causes the time lag
decreasing, while decreasing the solar absorptivity leads to decreasing of minimum temperature
peaks
, and leads to the increasing of temperature swing on both side of the surface. In conclusion,
changing surface color (emissivity) can be a quite profitable passive solution for energy saving. The solar
absorptivity is important to solar heat gain from outside, therefore, is crucial factor of energy consumption
of the entire building. It is necessary to include solar absorptivity in the Excel tool to examine exterior wall
energy performance.
2.3. Energy modeling engines comparison and features
DOE-2, BLAST and EnergyPlus
EnergyPlus, DOE-2, and BLAST are the three popular and authorized building energy simulation engines
supported by the federal government. They provide heat transfer and energy solution algorithms for
buildings, and had been widely used throughout the world (Lawrie, 1998). BLAST (BLAST Support Office,
1992) was sponsored by US Department of Defense (USDOD). DOE-2 (James J. Hirsch & Associates,
2012) was once sponsored by US Department of Energy (USDOE) before EnergyPlus came out.
EnergyPlus (Crawley et al, 2004) was the latest energy simulation engine sponsored by USDOE and
USDOD, claiming a more powerful tool combining the features from BLAST and DOE-2. There are
38
various derivative energy modeling programs that use the above simulation engines, including
DesignBuilder (EnergyPlus), eQUEST (DOE-2), EnergyPro (EnergyPlus), BEopt (EnergyPlus) etc.
As a new generation of building energy simulating engine, EnergyPlus has its differences with DOE-2 and
BLAST. The heat transfer solution algorithms are fixed among energy simulation engines, which cause the
differences in solution algorithms and results. Various researches show the simulation results differences
using these engines. Simulating experiments show the total building load in EnergyPlus is 11% lower than
that in DOE-2, with detailed modeling including internal facilities, people and infiltration heat loss (Figure
2.7, Simge Andolsun, 2008). Another research on heat transfer through slab-on-grade floor type in low-rise
buildings, shows the EnergyPlus has 25% higher in cooling load and 27% lower in heating load than DOE-2
(Simge Andolsun, 2010).
Figure 2.7 peak heating and cooling loads for low-rise building (Simge Andolsun, 2008)
The differences in simulation results lead to further research on solution algorithms for the listed engines.
The developer of EnergyPlus claimed that the new generation energy simulation engine not only derives the
advantages from DOE-2 and BLAST, but also added new features including customization input and
reporting system (Drury B. Crawley, 1998). For load calculation method, EnergyPlus uses heat balance
approach (same as BLAST), while DOE-2 uses room weighting factor approach (Figure 2.8). Research
shows the weighting factor approach is simplified calculation of heat flux exchange among rooms (Dandan
Zhu, 2012). The weighting factor approach simplified the internal wall convection coefficient by
combining radiation and convection coefficient, as well as using the temperature of adjacent room from a
former time step (Dandan Zhu, 2012). The research indicates that users should be cautious when using
39
DOE-2 in multiple room building with different conditioning environment in each room. For comparison
among EnergyPlus and DOE-2, research made a list for some key opponents (Table 2.1).
Features DOE-2 EnergyPlus
Inputs Text, BDL Text, IDF/IDD
Extensive
Outputs Summary & hourly reports Extensive summary & detailed
reports with user specified time steps
Algorithms Surface heat balance: Response
Factor, CTF; Zone Weighting
Factors
Surface heat balance; Zone air heat
balance
Time Step 1 hour, fixed 1 to 60 minutes Hourly
Weather Data 1 hour, fixed 1 to 60 minutes Hourly
User customization User functions EMS (Energy Management System),
External Interface, FMI (Functional
Mockup Interface)
Language Fortran Fortran
Table 2.1 comparison between EnergyPlus and DOE-2 (Dandan Zhu, 2012)
Figure 2.8 program struction of EnergyPlus (EnergyPlus, 2016)
Time step and weather data
EnergyPlus also introduce a detailed time step system with accuracy up to 1 minute (Drury B. Crawley,
2010). This feature is applied into various heat transfer calculations including surface convection
coefficients (figure 2.9) and long/short-wave radiation heat exchange. These data all calculated in a 1
40
minute scale. The weather data including temperature and solar radiation collected from local weather
station can be transferred into minutes or hourly scale in the program (Dandan Zhu, 2012). For all the
listed simulation engines, the direct solar radiation is calculated with latitude and solar angles. Hence the
solar radiation level varies with global locations. However, none of the listed simulation engines uses
wind speed data that is tranfered into hourly file to specify different exterior convection coefficients.
Figure 2.9 annual exterior wall convection coefficient in hourly scale (Dandan Zhu, 2012)
Thermal time lag related add-ons
There are several programs that have the function of calculating thermal time lag of exterior wall, for
example, Ecomat and DesignBuilder (DesignBuilder, 2014), which both belong to AUREA Consulting
Sustainable Architecture & Engineering ltd (2014). Ecomat was developed by German camposin 2009
(http://ecoeficiente.es/ecomates/, 2016). It is a small-scale program that works as an add-on for Ecotect
(Autodesk, 2014). It only has the function of calculating the thermal time lag using material information
from Ecotect. DesignBuilder as a well-developed energy modeling program, displays the material thermal
time lag only in the material information tab. Another older program is called Opaque (Murray Milne,
1989), which displays construction details of wall or roof sections. It shows the temperature drop from
exterior surface to the interior surface and calculates U-value, thermal lag and decrement factor.
41
Figure 2.10 Ecomat v1.0
Figure 2.11 Opaque (Murray Milne, 1989)
Energy performance of a building is affected by synergy from various material and environment
properties. Construction material, thermal insulation, climates, thermal lag etc. all has different influence
on energy performance. The current energy modeling programs, EnergyPlus and DOE-2, has their
differences and limits that can be found in various aspects, such as calculation of multiple room,
temperature data accuracy etc. Few programs have the feature to calculate material‘s thermal time lag
except for some small scale add-ons. As thermal time lag is one of the important features in thermal mass
material. For the further tool development in this research, one needs to make use of the heat transfer
calculation method from the existing energy modeling programs, as well as to develop useful functions to
study effects from various material and environment parameters.
42
Chapter 3: Methodology
3.1. Scope of work
The first stage (figure 3.1) of studying thermal mass material was to review background literature about the
effect of different time lags in materials and existing tools and prepare to build the simulation model.
During this stage, relevant concepts of thermal lag and thermal mass material were clarified. The heat
transfer processes in wall/roof was comprehensively studied including understanding equations of
conduction, convection, and radiation. Relevant material and environment parameters were studied, as well
as learning the conventional method of calculating thermal time lag by solving the heat transfer equations.
During this stage, exploration and comparison of different software had also been accomplished.
The second stage (figure 3.1) was the development of Excel software tool. After exploration of different
heat transfer models, it was eligible to set up the model in Excel program. However, at the beginning stages,
there were several issues with the simulation model that require to be solved, including time step, applying
HVAC control loop, importing of weather data, and using macros for calculation. The Excel file size was
reduced and usability improved by using macros. Aside from tool‘s function, the model was required to
build with user friendly interface to provide more opportunities to explore its potential more conveniently.
After the development is accomplished, validation of results was demanded to examine the correctness of
the simulation model. The results including thermal lag and energy consumption will be compared with
other sources. It was also explore different research directions for the model.
43
Figure 3.1 scope of work
3.2. Formulation and concept
The simulation model of thermal mass material follows the law of heat transfer. Conduction, convection
and radiation heat transfer occurs in particle level of selected material. Different parameters of material and
environment have various influences on thermal mass material‘s energy performance. This section will
introduce the model principle with heat transfer equations and relevant concepts.
3.2.1. Parameter introduction
There are various amounts of parameters using in the simulation model, including material and
environmental parameters. Some of the parameters have crucial effect on the energy performance of
thermal mass material. Some are required in the construction of the model. Most of the parameters exist in
heat transfer equations. Hence it is important to understand the function of each parameter (Table 3.1).
44
Parameter Symbol Unit Description
Density kg/m3 Material‘s mass on certain amount of volume. Dense
material such as concrete weighs more than light material
such as plastic with the same volume.
Heat capacity
J/(kgK) Material‘s ability to absorb heat. High heat capacity
material such as water release large amount of heat
reducing its temperature.
Conductivity W/(mK) Material‘s ability to transfer heat through conduction.
Material with high conductivity, such as metal, transfer
faster than material with low conductivity, such as wood.
Convection factor W/(m2•K) Material‘s ability to transfer heat through convection. The
factor mainly controlled by particle movement speed.
Higher air increases the convection factor.
Time step Second Time is a required parameter used to calculate
temperature within walls. This factor is used in
calculation worksheet in the model.
Emissivity N/A Material‘s ability to emissive radiant energy. Emissivity
has high correlation with material surface condition such
as surface color.
Solar absorption
factor
N/A Material‘s ability to absorb solar radiation. Higher value
of this factor means the material has stronger ability to
absorb solar radiation
Environment
radiant
temperature
Tradout Celsius Radiant temperature from the surrounding environment.
Table 3.1 important parameters description (Atkins, 2013)
3.2.2. Heat transfer equations
The energy flow phenomenon in wall/roof can be transferred into heat transfer equations in thermodynamic
domain. According to Fourier‘s law, one-dimension heat transfer through wall/roof can be written in
equation (Asan, 2012):
Equation 3.1
The boundary conditions are:
Equation 3.2
Equation 3.3
45
Where he, hi are the convection factor of outside and inside, respectively
are the boundary
temperature difference of inside and outside,
are the radiation heat gain from outside and inside.
In this heat transfer equation, there are three different types of heat transfer. They are conduction,
convection, and radiation. In thermal mass material, the material and environmental properties has
significant influence on these three types of heat transfer modes. The energy flow of wall/roof is also
affected by different material and environment properties.
Conduction: Conduction heat transfer is the direct microscopic exchange of kinetic energy of particles
through the boundary between two systems (Atkins, 2013) In this project, conduction heat transfer happens
in the cells within the wall.
Equation 3.4
Where, is conductivity; cross area; is thickness; is change in temperature
Convection: Heat convection occurs when flow of a fluid carries heat along with the flow of matter. The
convection mainly occurs on the boundary of the wall when the surface is contacting with the surrounding
air. The heat transfer on the inside and outside surface is convection heat transfer (Atkins, 2013).
Equation 3.5
Where, is convection factor; cross area; is change in temperature
Radiation: Radiation heat transfer is the transfer of energy by photons in waves. The radiation mainly
happens on the boundary of the wall. On the outside surface, radiation energy source includes short-wave
solar radiation, long-wave surrounding objects radiation. and the emissivity from the wall. On the inside
surface, the radiation source includes the emissivity of inside wall surface and radiation from inside objects
(Atkins, 2013).
Equation 3.6
Where, is emissivity; cross area; is Stephan Boltzmann constant; T
H
and T
L
are the high and low
temperatures
All three types of heat transfer affect energy flow within a wall. The conduction occurs within the wall,
while radiation and convection only affect boundary surface. Boundary condition is critical in heat transfer
of wall/roof, because the outside temperature and inside temperature are uncontrollable factors and have
huge effect on energy flow (Atkins, 2013). On boundary surface of wall/roof, radiation effect varies with
climate types and other factors, while convection effect is mainly controlled by air movement.
46
3.2.3. Forward Finite Element method (FFE) and heat transfer model
The Forward Finite Element (FFE) method is the mathematical method of connecting many small
subdomains into a larger domain (Asan, 2012). FFE is one of the numerical methods to solve heat transfer
equations. The accuracy of finite element method depends on how many elements (subdomain) it breaks
from the main object. As in this simulation model, the wall can be divided into several small pieces. Each
small piece has its own thermal condition and temperature profiles and is affected by adjacent element
(other cells and environment).
On the boundary surface of wall, the temperature and heat transfer is a little different from the cells within.
The model shows 10 different cells from outside to inside (Fig. 3.2). The outside boundary cell 1 is affected
by outside temperature through heat convection, solar radiation and surrounding objects. However, cell 1
only has conductions effect with cell 2. Similarly, cell 10 from the inside surface is affected by inside
temperature through convection and radiation from inside sources. Cell 2 to cell 8 only has conduction heat
transfer with each other.
Figure 3.2 The wall is break down into ten pieces using FFE
The calculation of cell 1 includes solar radiation, convection and conduction with outside and cell 2 (Fig.
3.3).
Figure 3.3 outside boundary cell heat transfer
47
The calculation of cell 2 to 9 only has conduction heat transfer with each other because they are not contact
with surrounding environment (Fig. 3.4).
Figure 3.4 inside cells between boundaries heat transfer
Cell 10 is the inside boundary cell. It has conduction heat transfer with cell 9, radiation with inside objects
and convection heat transfer with inside environment (Fig. 3.5).
Figure 3.5 outside boundary cells heat transfer
By using FFE, the wall can be translated into small cells and quantified into temperature profiles. The
model can be transferred into Excel. Each cell in Excel represents a small piece of wall/roof. The value of
each cell is the temperature of that piece of wall on a certain time. Each piece is affected by adjacent
elements by conduction, convection and radiation. The temperature profile can fluctuate dramatically with
changing of surrounding environment. A 0.2 meter thick wall is divided into 10 cells (Figure 3.6). The
number in each cell represents the temperature (Kelvin) of that cell. Each row represents 1 time step, which
is 125 seconds in this case. The table can be transferred into 3D charts (Figure 3.7)
48
Figure 3.6 wall temperature profile transfers into Excel (Ronney, 2013)
Figure 3.7 graphic results of the model
One difference from the physical model is that the Excel model has many rows (Figure 3.6). Each row
represents different time step. The combination of all rows creates a continuous heat transfer model in
respect of time. The time step is important in this model because parameters varies with time, such as
temperature, wind speed, solar radiation etc. Control of the time step in this model can provide eligible
potentials to explore different parameter‘s influence on results.
3.2.4. Thermal lag calculation
Thermal time lag is the difference of peak temperature between outside space and wall/roof (Figure 3.8). It
is a value varies with material and environment properties. This includes material thickness, conductivity,
Time -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
0 398 398 398 398 398 398 398 398 398 398 398
125 391.75 398 398 398 398 398 398 398 398 398 387.4971906
250 387.84375 396.046875 398 398 398 398 398 398 398 394.717872 381.6546072
375 384.791992 394.09375 397.389648 398 398 398 398 398 396.974335 391.661267 377.3541955
500 382.274292 392.2169189 396.550415 397.8092651 398 398 398 397.67948 395.634521 388.850641 373.9778044
625 380.11422 390.4640656 395.589588 397.4754791 397.9403954 398 397.899837 397.140593 394.153608 386.322842 371.192232
750 378.216408 388.8314645 394.577203 397.0314245 397.8137355 397.950073 397.693874 396.444424 392.639927 384.041641 368.8246963
875 376.520088 387.3098027 393.548604 396.5089526 397.6118687 397.827405 397.383483 395.645972 391.141868 381.97331 366.7681142
1000 374.984368 385.8876421 392.524088 395.9285049 397.3345626 397.621324 396.979237 394.781412 389.684226 380.086861 364.9524309
1125 373.580118 384.5542582 391.514079 395.3040175 396.9847827 397.331059 396.493069 393.875361 388.27792 378.356528 363.3289462
1250 372.28578 383.2997834 390.523491 394.6449008 396.5677549 396.960976 395.936907 392.944194 386.926685 376.760844 361.862433
1375 371.084795 382.1153157 389.554023 393.957852 396.0897445 396.518073 395.321706 391.998946 385.630331 375.281916 360.5264918
1500 369.964033 380.9928738 388.605623 393.2478718 395.5573807 396.010355 394.657208 391.047116 384.386643 373.904726 359.3007516
1625 368.912794 379.9253452 387.677342 392.5188907 394.9772138 395.445942 393.951913 390.093872 383.192442 372.616583 358.1690969
1750 367.922166 378.9064217 386.767827 391.7741326 394.3554655 394.83258 393.213159 389.142813 382.044183 371.4067 357.1185128
1875 366.984611 377.930531 385.875608 391.0163286 393.6978974 394.177413 392.447245 388.196474 380.938291 370.265855 356.1383092
2000 366.093673 376.9927676 384.999247 390.2478438 393.0097557 393.486887 391.659557 387.256658 379.871337 369.186133 355.2195851
49
specific heat, density, exterior temperature, solar radiation etc. The value of the thermal time lag can be
calculated by solving the heat transfer equations.
Figure 3.8 thermal time lag on thermal mass material
In this heat transfer model, thermal time lag will be calculated in an Excel spreadsheet. By using heat
transfer model in Excel (Ronney, 2013), thermal time lag value can be achieve by locating the time of
highest tempeture on wall and environment. According to FFE, each Excel cell represents temperaure of
relavent wall pieces. On boundary layers, a highest temperature of a day will be located by using Excel
commands. The outside environmental temperature will also be located using the same method. The value
of thermal time lag will achieve by calculating time step differnce between the peak tempeature of outside
surface and surrounding environment (Figure 3.9).
Figure 3.9‗Thermal time lag calculation‘ worksheet
Time(s) Environment temp Tin -0.0915 -0.0732 -0.0549 -0.0366 -0.0183 0 0.0183 0.0366 0.0549 0.0732 0.0915
0 10 23 273 273 273 273 273 273 273 273 273 273 273
20 10.00003 23 273.1489 273 273 273 273 273 273 273 273 273 273
40 10.00007 23 273.2918 273.0036 273 273 273 273 273 273 273 273 273
60 10.00013 23 273.4289 273.0106 273.0001 273 273 273 273 273 273 273 273
80 10.00022 23 273.5606 273.0206 273.0003 273 273 273 273 273 273 273 273
100 10.00033 23 273.6873 273.0333 273.0008 273 273 273 273 273 273 273 273
120 10.00045 23 273.8091 273.0485 273.0016 273 273 273 273 273 273 273 273
140 10.0006 23 273.9263 273.066 273.0027 273.0001 273 273 273 273 273 273 273
160 10.00077 23 274.0392 273.0855 273.0042 273.0001 273 273 273 273 273 273 273
180 10.00096 23 274.148 273.1069 273.0061 273.0002 273 273 273 273 273 273 273
200 10.00118 23 274.2529 273.1299 273.0084 273.0004 273 273 273 273 273 273 273
220 10.00141 23 274.3541 273.1545 273.0112 273.0006 273 273 273 273 273 273 273
240 10.00166 23 274.4518 273.1803 273.0144 273.0008 273 273 273 273 273 273 273
260 10.00194 23 274.5462 273.2074 273.0182 273.0011 273.0001 273 273 273 273 273 273
280 10.00224 23 274.6374 273.2356 273.0224 273.0015 273.0001 273 273 273 273 273 273
300 10.00255 23 274.7256 273.2647 273.0271 273.002 273.0001 273 273 273 273 273 273
320 10.00289 23 274.8109 273.2946 273.0323 273.0026 273.0002 273 273 273 273 273 273
340 10.00325 23 274.8935 273.3253 273.038 273.0032 273.0002 273 273 273 273 273 273
360 10.00363 23 274.9735 273.3567 273.0442 273.004 273.0003 273 273 273 273 273 273
Thermal lag
Peak Temperature
50
Figure 3.10 locate the time of highest wall temperature and environment temperature
3.2.5. Internal temperature control loop
The Excel tool uses typical HVAC control loop for internal temperature setting which involves internal
setting temperature and controller temperature offset. The internal setting temperature is the temperature
setting displaying on the room thermostat for a typical HVAC system. The controller temperature offset
determines the upper and lower limit telling a cooling/heating system when to work. The room temperature
is controlled between Tin- Limit and Tin + Limit, where Tin represents the set temperature inside and Limit
the temperature range allowance set by controller configuration. Once the room temperature reaches the
setting temperature, the HVAC stops working until the room temperature exceed the limits. The cooling
mode will activate when the room temperature exceeds Tin + Limit, and the heating mode will activate
when the room temperature drops below Tin – Limit. This type of HVAC system can maintain the room
temperature within the comfortable zone and allows fluctuation of internal temperature and interval of
HVAC system operation (Fig. 3.11).
Figure 3.11 HVAC system control loop
3.3. Excel tool development
The heat transfer model of wall/roof was created in Excel. It allows calculation of large amount of data with
simple operation. Excel can simultaneously display input, calculating data with results, diagrams, and
graphics. It is also able to display data in desired order while in separated zones. It allows different
Maximum Temp Row Time
292.2249 12226 244480
30 10807 216100
Time lag calculatuon
51
calculation to be detached in various spreadsheets, so that the calculation of different parameters not be
mixed in complicity. Excel for the Windows version also has a macro function.. Excel programming, the
writing of macros, allows interaction of data outside the software, so the weather data and other parameters
from other sources will be able to inject into Excel with simple in-program command. Based on previous
work of heat transfer model in Excel (Ronney, 2013), this new numeric wall/roof heat transfer model was
created in Excel.
An Excel based thermal time lag energy simulation tool was developed to simulate heat transfer of
wall/roof in different climate zones. The tool was designed with user friendly interface with input, results
zones, and several calculation worksheets. The model was based upon forward finite element method and
calculates one-dimensional heat transfer through multilayer walls/roofs. The outside boundary surface
applies actual weather data including temperature and solar radiation in different climate zones.
Environmental and physical parameters were added into the model depends on their effects on energy flow,
including emissivity (color), reflectance (surface condition, vein), orientation, window/door area etc. The
model was designed close to the actual condition of a residential house.
The results section shows wall/roof‘s thermal time lag and monthly/annually energy consumption in both
numbers and graphics with input parameters. The results vary with different climate information. The tool
allows adjusting wall/roof material properties including layers, thickness, specific heat and conductivity.
With various input data, it is possible for this model to explore the low-energy wall in any climate zone.
3.3.1. Excel worksheet introduction
The model was built in Excel with five separate worksheets. The ‗Main’ worksheet shows input and output
data, containing graphic results, thermal time lag, calculation bottom and various material and environment
parameters. The worksheet is divided into input section and output section. This worksheet is connected
with other calculation worksheet, including ‗Heat transfer calculation’ worksheet and ‗Thermal time lag
calculation’ worksheet. Some of the common material information can be copy and paste from the
‗Material chart‘ worksheet. The ‗Material chart’ was developed into a parameter information collector,
which contains useful parameters that can be added into the model.
The ‗Main‘ worksheet intends to be the most useful tab to investigate when using this Excel-based
simulation model.
52
Excel Worksheets
Main
(Input/output)
Heat transfer calculation Thermal lag
Calculation
Material chart
Celsius Kelvin
Table 3.2 Excel worksheets summary
The ‗Main‘ worksheet is divided into input section and output section. In the input section, there are six
different branches that can affect the results, including material, thermal lag, environment, indoor controller
setting, radiation and HVAC input. Each branch has its unique influence on the calculation of the model.
Various amounts of input combination leads to different results depend on the research purposes. In the
result section, there are thermal time lag and annually energy output. The thermal lag results also shows in
as a sign wave, which is the simplified temperature curve to simulate daily temperature swing. As it is
difficult to find the actual peak temperature in actual exterior temperature data from weather station. The
energy output, the most important result, also shows in graphic result area, which can be further added
depends on research purposes. Users can accomplish entire simulation processes in this worksheet without
reviewing the other worksheets.
53
Figure 3.12‗Main‘ worksheet
Excel worksheet tabs
Layer MaterialWidth (m) Conductivity Density Specific heat Dx
Outside Default 0.183 0.62 1800 0.0183
Layer 2 Wood 0.16 800 0
Layer 3 Concrete 0.51 1500 0
Layer 4 Brick 0.62 1800 0
Inside 0
Cool Heat total Cool Heat Cool Heat
Jan -434.3 1.9 436.2 53.8 223.6 80.7 447.2
Feb -526.2 2.8 529.0 83.1 179.3 124.6 358.5
Mar -752.3 5.3 757.6 166.0 161.9 249.1 323.8
Apr -947.0 10.4 957.4 277.4 96.9 416.2 193.8
May -1146.9 15.5 1162.4 375.4 59.8 563.1 119.5
Jun -1217.5 17.4 1234.8 419.5 38.1 629.2 76.1
Jul -1290.8 18.1 1308.9 449.0 36.5 673.5 73.0
Aug -1475.2 18.4 1493.6 516.3 14.6 774.5 29.1
Sep -1313.9 15.9 1329.7 407.1 23.6 610.7 47.1
Oct -1007.5 9.1 1016.6 230.2 78.5 345.3 157.1
Nov -578.9 3.0 581.9 86.8 158.9 130.2 317.8
Dec -230.4 0.9 231.3 18.5 264.3 27.8 528.7
Grand -10920.8 118.5 11039.33 3083.1 1335.9 4624.7 2671.8
Wall temperature 6/16 to
6/26
Roof/wall area
May 12th
50
1.8 Roon height H m
Environment input
Time gap
Symbol
Tmax
Tmin
23
20.0
Tradout
As
Celsius
N/A
Name Unit
Emissivity(color) Epsilon
Celsius
Radiation
Stefan Constant Sigma N/A
Surrounding Radiant temp
Solar Absorption
Name Symbol Unit
Convection inside W/(m2•K) hin
Initial condition (Mid-point) Tini
Heating efficiency
HVAC cool
HVAC heat
Cooling efficiency N/A
Name Value
Period P
80%
5.6703E-08
Value
8.7
Indoor setting
Name Symbol Unit
Value
Second 86400
Symbol Unit
Cool Watt
Temperature limit DeltaT Celsius 3
Heating rate Heat Watt
Cooling rate 1500
Pa J/C.kg 1000
rhoa kg/m3 1.3
Energy consumption
0
0.2
HVAC input
Symbol
Air heat capacity
Air density
Room input
Conditioned area
Calculation
Time gap 2
Room volume
Monthly heating load
50
Area m2
2000
Value
W/(m2•K) 18.6
DeltaTau2
June 21st
N/A
Monthly Cooling load
Grand HVAC load
(kWh)
7296.5
HVAC (hour)
HVAC load
527.9
483.1
572.9
610.0
682.6
705.3
746.5
803.6
657.8
502.4
448.0
556.5
HVAC Control loop
28380
7.88
Second
Hour
Thermal time lag
Theoretical Energy consume (kWh/m2)
Second
Watt 20
2.09E+03
1.10E+03
8.40E+02
7297
Unit
Celsius
Celsius
HVAC load (kWh)
m2
Watt
Watt
m3 90
Aroof
100%
1500
2000
η1
η2
Pc
Ph
Vr
Material input
Thermal lag input
Name
Max Temperature
Min Temperature
8.40E+02
Solar radiation
Inside temp Tin Celsius
qsolar
This version only calculates the first layer
This section is only related with thermal
lag calculation
Value
30
10
20 DeltaTau
Convection Outside hout
second
May 12th
Monthly heating hour
Monthly cooling hour
120
100%
N/A
0
5
10
15
20
25
30
35
Temperature (Celcius)
Hours
Envirnment Temp Wall temp Tin
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly heating load (kWh)
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly heating load (kWh)
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling load (kWh)
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling hour
0.0
100.0
200.0
300.0
400.0
500.0
600.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly heating load (kWh)
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly heating load (kWh)
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling load (kWh)
0
100
200
300
400
500
600
700
800
900
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly load (kWh)
Room
temperature range:
Tin- Limit ≤ T(room) ≤
Tin+ Limit
HVAC
Status:
Stop working once
T(room)=Tin
Cooling -
Heating +
Cooling mode activated when, T(room) > Tin+ limit
Heating mode activated when, T(room) < Tin - limit
Get Data
Calculation 1
Calculation 2
0
10
20
30
40
50
60
Temperature (Celcius)
Inside
Mid-point
Outside
0.0
10.0
20.0
30.0
40.0
50.0
60.0
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
541
561
581
601
621
641
661
681
701
Temperature (Celcius)
Hours
Envirnment Temp Wall inside Wall ouside Wall middle
0.0
10.0
20.0
30.0
40.0
50.0
60.0
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
541
561
581
601
621
641
661
681
701
Temperature (Celcius)
Hours
Envirnment Temp Wall inside Wall ouside Wall middle
54
In the ‗Heat transfer calculation‘ work sheet, Excel cells are regarded as small pieces of a wall/roof in a
‗one-dimension‘ heat transfer model. The reason of separating into Celsius and Kelvin is based on the heat
transfer equation (equation 3.1 to 3.3), where the radiation heat transfer is required to be calculated in
Kelvin. However, in the calculation of HVAC energy consumption, Celsius has to be used instead of Kelvin.
The order of cells is based on forward finite element methods and heat transfer model from Prof. Paul
Ronney (2013). The input data from ‗Main‘ worksheet has significant influence in the calculation. The
results calculated from ‗Heat transfer‘ worksheet will inject into the ‗Energy consumption output‘ section
in the ‗Main‘ worksheet. This worksheet has strong ties with actual weather data (gathered from weather
station) that been transferred into ‗20-second‘ scale. Hence the amount is enormous, 262,772 rows to be
exact.
Figure 3.13 Part of ‗Heat transfer Celsius-scale‘ worksheet (part of 262,772 rows)
Figure 3.14 Part of ‗Heat transfer Kelvin-scale‘ worksheet (part of 262,772 rows)
Month Local Day LocalHour Local Time(s) -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
1 1 0 120 20 20 20 20 20 20 20 20 20 20 20
1 1 0 240 18.84 20 20 20 20 20 20 20 20 20 20.11
1 1 0 360 17.96 19.83 20 20 20 20 20 20 20 20.02 20.21
1 1 0 480 17.28 19.58 19.97 20 20 20 20 20 20 20.04 20.28
1 1 0 600 16.72 19.3 19.92 20 20 20 20 20 20.01 20.07 20.35
1 1 0 720 16.27 19.01 19.84 19.99 20 20 20 20 20.02 20.1 20.41
1 1 0 840 15.88 18.73 19.74 19.97 20 20 20 20 20.03 20.14 20.46
1 1 0 960 15.55 18.46 19.62 19.94 19.99 20 20 20.01 20.04 20.17 20.51
1 1 0 1080 15.26 18.2 19.5 19.9 19.99 20 20 20.01 20.05 20.2 20.55
1 1 0 1200 15 17.96 19.37 19.85 19.98 20 20 20.02 20.07 20.23 20.59
1 1 0 1320 14.77 17.73 19.23 19.8 19.96 19.99 20 20.02 20.08 20.26 20.63
1 1 0 1440 14.56 17.52 19.1 19.74 19.94 19.99 20 20.03 20.1 20.29 20.67
1 1 0 1560 14.38 17.32 18.96 19.68 19.92 19.99 20.01 20.04 20.12 20.32 20.7
1 1 0 1680 14.21 17.13 18.82 19.61 19.89 19.98 20.01 20.04 20.13 20.34 20.73
1 1 0 1800 14.05 16.95 18.69 19.53 19.86 19.97 20.01 20.05 20.15 20.37 20.76
1 1 0 1920 13.91 16.78 18.56 19.46 19.83 19.96 20.01 20.06 20.17 20.39 20.79
1 1 0 2040 13.77 16.62 18.43 19.38 19.8 19.95 20.01 20.07 20.19 20.42 20.81
1 1 0 2160 13.65 16.46 18.3 19.3 19.76 19.94 20.01 20.08 20.2 20.44 20.84
1 1 0 2280 13.53 16.32 18.18 19.22 19.72 19.92 20.01 20.09 20.22 20.47 20.86
1 1 0 2400 13.42 16.18 18.06 19.14 19.67 19.9 20.01 20.09 20.24 20.49 20.88
1 1 0 2520 13.32 16.05 17.94 19.06 19.63 19.88 20 20.1 20.25 20.51 20.9
1 1 0 2640 13.23 15.93 17.83 18.98 19.58 19.86 20 20.11 20.27 20.53 20.93
1 1 0 2760 13.14 15.81 17.72 18.9 19.54 19.84 20 20.12 20.28 20.55 20.95
1 1 0 2880 13.05 15.7 17.61 18.82 19.49 19.82 19.99 20.12 20.3 20.57 20.96
1 1 0 3000 12.97 15.59 17.51 18.74 19.44 19.8 19.99 20.13 20.31 20.59 20.98
1 1 0 3120 12.89 15.49 17.41 18.66 19.39 19.77 19.98 20.14 20.33 20.6 21
Time(s) -0.0915 -0.0732 -0.0549 -0.0366 -0.0183 0 0.0183 0.0366 0.0549 0.0732 0.0915
120 293 293 293 293 293 293 293 293 293 293 293
240 291.8362 293 293 293 293 293 293 293 293 293 293.1132
360 290.9601 292.829 293 293 293 293 293 293 293 293.0166 293.2055
480 290.2754 292.5795 292.9749 293 293 293 293 293 293.0024 293.0419 293.2832
600 289.7231 292.2991 292.9205 292.9963 293 293 293 293.0004 293.0079 293.0716 293.3502
720 289.2659 292.0119 292.8403 292.9857 292.9995 293 293.0001 293.0014 293.0161 293.1032 293.4093
840 288.8793 291.7301 292.74 292.9664 292.9975 292.9999 293.0002 293.0034 293.0268 293.1354 293.462
960 288.5466 291.4596 292.6248 292.9377 292.9933 292.9996 293.0007 293.0064 293.0393 293.1674 293.5098
1080 288.2562 291.2028 292.4996 292.8999 292.9861 292.9988 293.0013 293.0104 293.0533 293.1989 293.5535
1200 287.9996 290.9604 292.3679 292.8537 292.9753 292.9973 293.0023 293.0153 293.0684 293.2296 293.5937
1320 287.7707 290.7322 292.2325 292.8002 292.9607 292.9948 293.0035 293.0212 293.0843 293.2594 293.631
1440 287.5646 290.5175 292.0954 292.7404 292.9421 292.9911 293.0048 293.0279 293.1007 293.2883 293.6658
1560 287.3777 290.3154 291.9583 292.6752 292.9197 292.9859 293.0062 293.0352 293.1176 293.3162 293.6984
1680 287.2072 290.1252 291.8223 292.6058 292.8935 292.9791 293.0075 293.043 293.1347 293.3431 293.729
1800 287.0507 289.9458 291.6881 292.533 292.8638 292.9707 293.0085 293.0513 293.1518 293.3692 293.758
1920 286.9064 289.7764 291.5562 292.4574 292.8309 292.9606 293.0093 293.0598 293.169 293.3944 293.7855
55
In the ‗Thermal lag calculation‘ worksheet, the cells represent small pieces of wall/roof as in ‗Heat transfer‘
worksheet‘. However, instead of using actual weather data, it applies with a sine wave temperature profile.
It is much easier to find the peak temperature difference in a sine wave temperature curve than in actual
temperature curve. The data resource in this worksheet is ‗Thermal lag input‘ section in ‗Main‘ spreadsheet,
and it is separated calculation with heat transfer calculation. The result of thermal time lag has strong
correlation with energy output in the ‗Main‘ worksheet, but the ‗Thermal lag input‘ section has no effect on
‗Annual energy output‘ section.
Figure 3.15 ‗Thermal time lag calculation‘ worksheet
The ‗material chart‘ worksheet contains various material information, including conductivity, density and
specific heat. This section intends to provide some input information among common construction
materials, so that users can directly copy and paste material information from this worksheet to ‗Main‘
worksheet. This section can be further developed into a parameter library that provides useful data based on
input section.
Time(s) Environment temp Tin -0.0915 -0.0732 -0.0549 -0.0366 -0.0183 0 0.0183 0.0366 0.0549 0.0732 0.0915
0 10 23 273 273 273 273 273 273 273 273 273 273 273
20 10.00003 23 273.1489 273 273 273 273 273 273 273 273 273 273
40 10.00007 23 273.2918 273.0036 273 273 273 273 273 273 273 273 273
60 10.00013 23 273.4289 273.0106 273.0001 273 273 273 273 273 273 273 273
80 10.00022 23 273.5606 273.0206 273.0003 273 273 273 273 273 273 273 273
100 10.00033 23 273.6873 273.0333 273.0008 273 273 273 273 273 273 273 273
120 10.00045 23 273.8091 273.0485 273.0016 273 273 273 273 273 273 273 273
140 10.0006 23 273.9263 273.066 273.0027 273.0001 273 273 273 273 273 273 273
160 10.00077 23 274.0392 273.0855 273.0042 273.0001 273 273 273 273 273 273 273
180 10.00096 23 274.148 273.1069 273.0061 273.0002 273 273 273 273 273 273 273
200 10.00118 23 274.2529 273.1299 273.0084 273.0004 273 273 273 273 273 273 273
220 10.00141 23 274.3541 273.1545 273.0112 273.0006 273 273 273 273 273 273 273
240 10.00166 23 274.4518 273.1803 273.0144 273.0008 273 273 273 273 273 273 273
260 10.00194 23 274.5462 273.2074 273.0182 273.0011 273.0001 273 273 273 273 273 273
280 10.00224 23 274.6374 273.2356 273.0224 273.0015 273.0001 273 273 273 273 273 273
300 10.00255 23 274.7256 273.2647 273.0271 273.002 273.0001 273 273 273 273 273 273
320 10.00289 23 274.8109 273.2946 273.0323 273.0026 273.0002 273 273 273 273 273 273
340 10.00325 23 274.8935 273.3253 273.038 273.0032 273.0002 273 273 273 273 273 273
360 10.00363 23 274.9735 273.3567 273.0442 273.004 273.0003 273 273 273 273 273 273
380 10.00404 23 275.051 273.3886 273.0509 273.0049 273.0004 273 273 273 273 273 273
400 10.00446 23 275.1261 273.4211 273.058 273.0059 273.0005 273 273 273 273 273 273
420 10.00491 23 275.199 273.4539 273.0656 273.0071 273.0006 273 273 273 273 273 273
440 10.00537 23 275.2697 273.4872 273.0737 273.0083 273.0007 273.0001 273 273 273 273 273
460 10.00586 23 275.3384 273.5207 273.0822 273.0097 273.0009 273.0001 273 273 273 273 273
480 10.00637 23 275.4051 273.5545 273.0912 273.0113 273.0011 273.0001 273 273 273 273 273
56
Figure 3.16‗Material Chart‘ worksheet
3.3.2. Parameter input
In this ‗Main‘ worksheet, cells with red color are suggested to be input by users. Cells without color should
not be changed. The term ‗wall/roof‘ stands for the situation that certain data can be used in both wall and
roof.
The material input section contains material information of different layers in wall/roof. In this model, a
wall and the roof are the same, but have a different rotation; as a rotation of 0 degrees is a roof, that is what
is currently being shown (future work would add a rotation parameter) The model can currently only work
on single layer of wall/roof, but can be further developed into multiple layers. The material parameters
include thermal conductivity, density and specific heat. Dx is the length of each small piece of wall, and it is
auto-calculated by input value ‗Width‘ of wall/roof. Dx does not require to be input by users.
Figure 3.17‗Material input‘ section
Building materials Thermal conductivityDensity Specific heat
[W/(mK)] (kg/m3) [J/(kgK)]
Cement layer 0.36 700 1050
Concrete block 0.51 1400 1000
Brick block 0.62 1800 840
Gypsum plastering 0.42 1200 837
Granite (red) block 2.9 2650 900
Marble (white) block 2 2500 880
Sandstone block 1.83 2200 712
Clay layer 0.85 1900 837
Asphalt sheet 1.2 2300 1700
Steel slab 50 7800 502
Aluminum slab 210 2700 880
Cork board 0.04 160 1888
Wood block 0.16 800 2093
Plastic board 0.5 1050 837
Rubber board 0.3 1600 200
P.V.C board 0.16 1379 1004
Asbestos sheet 0.16 2500 1050
Formaldehyde board 0.03 30 1674
Thermalite board 0.19 753 837
Fiberglass 300 1000 0.06
Siporex board 0.12 550 1004
Polyurethane board 0.03 30 837
Light plaster 0.16 600 1000
Dense plaster 0.5 1300 1000
Layer MaterialWidth (m) Conductivity Density Specific heat Dx
Outside Default 0.183 0.62 1800 0.0183
Layer 2 Wood 0.16 800 0
Layer 3 Concrete 0.51 1500 0
Layer 4 Brick 0.62 1800 0
Inside 0
2.09E+03
1.10E+03
8.40E+02
7297
Material input
8.40E+02
This version only calculates the first layer
57
The ‗Thermal lag input‘ section is only input connected with ‗Thermal time lag calculation‘ worksheet. The
purpose of this section is to calculate the value of thermal time lag based on ‗Material input‘. As mentioned
in previous chapters, the calculation of thermal time lag uses harmonic temperature profile. The maximum
and minimum temperature can create a daily temperature profile. Solar radiation input has little effect on
thermal time lag, but added to improve the preciseness. Time gap is required when using the forward finite
element method. In this section, the time gap is changed by the user. The period is the total duration of the
time-lag simulation model in ‗Thermal time lag calculation‘ worksheet. It has been set to 86400 seconds,
and it also should not be changed by the user.
Figure 3.19‗Thermal lag input‘ section
The ‗Environment input‘ section currently contains convection factors of inside and outside. The
convection factor is mainly affected by air movement speed. Higher value of convection factor means
higher speed of surrounding wind. Although the cell is marked as red, it is not suggested to change the value.
The indoor air movement is usually very low, and 8.7 w/m2.k (wind speed is null) is a reasonable value
(Atkins, 2013). On the outside, even though the wind speed is higher, the furthermore changes of wind
speed has very little effect on convection factors. 18.6 w/m2.k (wind speed is below 5m/s) is an average
convection factor for outside (Ronney, 2013).
Time gap
Symbol
Tmax
Tmin
Period P Second 86400
Second
Watt 20
Unit
Celsius
Celsius
Thermal lag input
Name
Max Temperature
Min Temperature
Solar radiation qsolar
This section is only related with thermal
lag calculation
Value
30
10
20 DeltaTau
Figure 3.18 Harmonic / sine wave temperature profile
58
Figure 3.20‗Environment input‘ section
As the model is conditioned by HVAC system, it requires explicit control loop to complete the energy
circulation of the model. The ‗Indoor setting‘ section is based on HVAC control loop. The control loop is
set by ‗inside temperature setting‘ and ‗temperature limit‘. The ‗temperature limit‘ controls the upper and
lower limit of temperature setting. The ‗initial temperature‘ value is required to run this model, but it is not
suggested to be changed by users.
Figure 3.21 HVAC control loop
Figure 3.22‗Indoor setting‘ section
The ‗Solar radiation‘ section includes parameters related with solar radiation heat gain. This section is
connected with ‗Heat transfer‘ calculation worksheet. The emissivity is efficiently affected by the color of
the surface (Atkins, 2013). There is a chart of emissivity of different color of construction material in
‗Material chart‘ section. The Stefan constant is used to calculate radiation heat transfer (Atkins, 2013). The
surrounding radiant temperature is the radiant temperature from surrounding environment. The solar
Environment input
Name Symbol Unit
Convection inside W/(m2•K) hin 8.7
Value
W/(m2•K) 18.6 Convection Outside hout
Room
temperature range:
Tin- Limit ≤ T(room) ≤
Tin+ Limit
HVAC
Status:
Stop working once
T(room)=Tin
Cooling -
Heating +
Cooling mode activated when, T(room) > Tin+ limit
Heating mode activated when, T(room) < Tin - limit
Initial condition (Mid-point) Tini Celsius 20.0
Temperature limit DeltaT Celsius 3
Name Symbol Unit Value
Inside temp Tin Celsius 23
Indoor setting
59
absorption factor is the factor of surface‘s ability to absorb solar radiation. There is also a solar absorption
chart in the ‗Material chart‘ section.
Figure 3.23 ‗Solar radiation‘ section
In ‗HVAC & Room input‘ section, there are several parameters of HVAC system and geometric
information of the simulation room. In the HVAC part, input values include controller temperature offset
and cooling/heating coefficient of performance (COP). In the current version of the tool, instead of
inputting by users, the cooling and heating system capacities are automatically calculated by the tool based
on weather data. This is because a random value of heating or cooling capacity can cause error in the tool.
For example, the model sets up a heating system and its capacity to a small value in Fargo (Climate zone 7).
The heating capacity is not able to provide sufficient heat to the room, because the annual heating demand is
too large. A constant temperature drop will occur in this case, which generates unconvincing results. The
same situation also occurs in the previous version of DOE energy simulation engine. An insufficient
heating or cooling capacity unable to provide enough heat to the room will cause the indoor temperature
uncontrollably raising or dropping (Andolsun, S., 2008).
In the ‗Room geometric input‘ section, a standard room is built into the model with conditioned area, room
height and conditioned wall/roof surface area. Users can design a customized HVAC system and cubic
room. This section is connected with the ‗Heat transfer calculation‘ worksheet and directly affects the
‗Annual energy consumption‘ in the output section.
Tradout
As
Celsius
N/A
Name Unit
Emissivity(color) Epsilon
Radiation
Stefan Constant Sigma N/A
Surrounding Radiant temp
Solar Absorption
80%
5.6703E-08
Value
0
0.2
Symbol
N/A
60
Figure 3.24 ‗HVAC & Room input‘ section
3.3.3. Weather profile
One of the critical features in this heat transfer model is using actual weather data gathered from weather
station. By using actual weather data, different cities in different climate zones can be compared. It is useful
to research on geographic effects on thermal time lag and energy consumption. Currently, the data gathered
from weather station contains annual temperature and solar radiation level. A representative city will be
selected for each climate zone in US.
Climate zone 1 Miami
Climate zone 2 Phoenix
Climate zone 3 Los Angeles
Climate zone 4 Seattle
Climate zone 5 Pittsburgh
Climate zone 6 Minneapolis
Climate zone 7 Fargo
Table 3.3 selected US cities in seven different climate zones
Roof/wall area
50
2.5 Roon height H m
383
N/A
Name Value Symbol Unit
Cool Watt
Temperature offset DeltaT Celsius 3
Heating capacity Heat Watt
Cooling capacity
Pa J/C.kg 1000
rhoa kg/m3 1.3
HVAC input
Air heat capacity
Air density
Room input
Conditioned area
Room volume
120.71
Area m2
1495
N/A
m2
Watt
Watt
m3 125
Aroof
3.512
1837
5251
η1
η2
Pc
Ph
Vr
COP-heating
HVAC cool
HVAC heat
COP-cooling 4.8
61
The temperature and solar radiation profile gathered from weather station is in hourly scale. However, in
this heat transfer model the requirement of time step is 120 seconds. Therefore, the data will be transferred
into 120-second scale by using a custom Excel macro (see Appendix A).
3.3.4. Parameter output
The ‗Parameter output‘ section contains thermal time lag output and annual energy output. This section
shows the energy performance of the selected material in a certain climate type. Both statistic and graphic
results display in this zone. The results vary with different data from input section. This section is connected
with ‗thermal time lag calculation‘ worksheet and ‗Heat transfer calculation‘ worksheet. Currently the
graphic results intend to compare energy output with different independent factors. Some other useful
graphs can be added into this section bases on different research purposes.
The ‗Thermal time lag‘ result shows the thermal lag of selected material in hour-scale and second-scale.
Thermal time lag calculation is separated from heat transfer calculation (chapter 2.3.2). Thermal lag
calculation derives data from ‗Thermal lag input‘ section in ‗Main‘ worksheet. The calculation process
accomplishes in ‗Thermal time lag calculation‘ worksheet. In the graphic results, it shows temperature
curves in one-day duration. The blue line is environment temperature, which is in sine curve scale. The
purple line is indoor temperature, which has been set constant. The red line is temperature curve of
mid-point in wall/roof. The wall temperature curves vary with different material input data. In the current
version of this model, the thermal lag of selected material can only process material‘s thermal lag within 20
hours.
62
Figure 3.25 thermal time lag value and graphic result
The energy performance of the target wall system is expressed as HVAC energy consumption. The results
are in the energy consumption section of the spreadsheet. Both annual and monthly energy output has been
calculated. The result is divided into two parts, theoretical energy consumption and actual energy
consumption. In the theoretical section, the HVAC system is considering working on an infinite working
rate and keeping the indoor air temperature constant. The theoretical result can be used under several
research purposes, but it is not suitable for study on actual condition. The other part, actual energy
consumption, applies with HVAC control loop. The HVAC system not does work all the time. This is closer
to the actual condition and uses a ―limit‖ for the float allowed by the system. It has a certain amount of
cooling and heating hours during a year. The monthly/annual HVAC load result is based on heating/cooling
hours. The annual total energy consumption of actual condition is usually larger than of theoretical
condition. This is because the HVAC in actual condition does not work continuously throughout a year. The
thermal mass in wall/roof is able to restore energy during intermittent.
This section is connected and calculated by ‗Heat transfer‘ worksheet. It uses Excel macro functions (see
Appendix A) to inject actual weather data and other parameters from the input section. The macros derive
33320
9.26
Second
Hour
Thermal time lag
0
5
10
15
20
25
30
35
Temperature (Celcius)
Hours
Environment Temp Wall temp Tin
63
data from input section and extract results into the ‗Heat transfer‘ worksheet. In order to compare energy
consumption annually and monthly, several graphic results of energy consumption are shown (Fig. 5.25,
Fig. 5.26, Fig. 5.27). The graphic output includes temperature curves of single/multiple days and bar charts
of monthly heating/cooling load.
Figure 3.26 energy consumption output
Figure 3.27 temperature curves of June 21st, 2014, Miami (Climate zone 1)
Cool Heat total Cool Heat Cool Heat
Jan -434.3 1.9 436.2 53.8 223.6 80.7 447.2
Feb -526.2 2.8 529.0 83.1 179.3 124.6 358.5
Mar -752.3 5.3 757.6 166.0 161.9 249.1 323.8
Apr -947.0 10.4 957.4 277.4 96.9 416.2 193.8
May -1146.9 15.5 1162.4 375.4 59.8 563.1 119.5
Jun -1217.5 17.4 1234.8 419.5 38.1 629.2 76.1
Jul -1290.8 18.1 1308.9 449.0 36.5 673.5 73.0
Aug -1475.2 18.4 1493.6 516.3 14.6 774.5 29.1
Sep -1313.9 15.9 1329.7 407.1 23.6 610.7 47.1
Oct -1007.5 9.1 1016.6 230.2 78.5 345.3 157.1
Nov -578.9 3.0 581.9 86.8 158.9 130.2 317.8
Dec -230.4 0.9 231.3 18.5 264.3 27.8 528.7
Grand -10920.8 118.5 11039.33 3083.1 1335.9 4624.7 2671.8
Energy consumption
Grand HVAC load
(kWh)
7296.5
HVAC (hour)
527.9
483.1
572.9
610.0
682.6
705.3
746.5
803.6
657.8
502.4
448.0
556.5
Theoretical Energy consume (kWh/m2) HVAC load (kWh)
June 21st
0.0
10.0
20.0
30.0
40.0
50.0
60.0
1
21
41
61
81
101
121
141
161
181
201
221
241
261
281
301
321
341
361
381
401
421
441
461
481
501
521
541
561
581
601
621
641
661
681
701
Temperature (Celcius)
Time
Envirnment Temp Wall inside Wall ouside Wall middle
64
Figure 3.28 Annual HVAC load (using actual weather data)
3.3.5. Calculation and Macros
The macros made in this model are to import data from outside sources and make advanced batch
calculations. With macros, users can automate calculations for various tasks. Excel Macros are created in
Visual Basic Editor (VBE) in Excel program. It allows developers to create customized Excel Visual Basic
applications (VBA). Users can also develop, test and modify VBA procedures (macros) in Visual Basic
Editor in Excel (Microsoft, 2014). However, the macros do not run on the Macintosh version of Excel.
Figure 3.29 Excel Visual Basic Editor (VBE)
They are several tasks in this heat transfer model requires macros to be written with certain functions. One
of the main functions is to inject actual weather data from sources outside the model. The temperature and
solar radiation profile gathered from weather station is required to be transferred into 120-second scale.
HVAC load
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly heating load (kWh)
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly cooling load (kWh)
0
100
200
300
400
500
600
700
800
900
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Monthly load (kWh)
65
Hence it is 259,200 sets of temperature and solar radiation data in a year. Conventional way of using simple
equations and duplications in Excel will generate extremely large file size and even cause the software to
crash. This tremendous batch of dataset has to be processed by macros. After transferring the weather data
into 120-second scale, the data requires to be injected into the simulation model. This macro is important
because using actual weather data makes the model close to actual condition.
Figure 3.30 Macros to transfer regular annual weather data into 120-second scale data (Appendix A)
The macros written in this model also contains the function for advanced calculation. To calculate the
energy consumption of the model, it requires applying the HVAC control loop (chapter 1.3.2). This macro‘s
function is to calculate the working hours of HVAC system (cooling and heating) with injected weather
data. The results will be delivered to ‗Energy consumption‘ section in ‗Main‘ worksheet.
66
Figure 3.31 Macros to inject 120-second scale weather profile into Excel model (Appendix A)
Although the heat transfer calculation process is relatively complicated. Users do not require to process any
work on the calculation worksheet. The calculation will be automated by clicking the launch bottoms in
‗Main‘ worksheet. The macro will get data from weather profiles outside the model, and calculate the
results afterwards.
Figure 3.32 Macro launch bottom on ‗Main‘ worksheet (see Appendix A)
Using the heat transfer model (Ronney, 2013), a temperature profile from different part of wall/roof shows
in the Excel cells. All of heat transfer processes are considered, including conduction, convection and
radiation. The material, environmental parameters are calculated in each cell. After achieve the temperature
profile of wall/roof, the calculation of energy consumption is able to be accomplished.
67
Figure 3.33 temperature profiles (Celsius) in ‗Heat transfer calculation‘ worksheet
The control loop of HVAC system applies into this model. Each cell‘s temperature profile will be compared
with HVAC‘s setting temperature, and the program will decide whether launch or shut down the HVAC
system. Through this method, the total working hours of HVAC system will be calculated. All of the above
data will then be transferred into ‗Energy consumption output‘ section in the ‗Main‘ worksheet.
Figure 3.34 applying control loop in ‗Heat transfer calculation‘ worksheet
Time(s) -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
120 20 20 20 20 20 20 20 20 20 20 20
240 18.84 20 20 20 20 20 20 20 20 20 20.11
360 17.96 19.83 20 20 20 20 20 20 20 20.02 20.21
480 17.28 19.58 19.97 20 20 20 20 20 20 20.04 20.28
600 16.72 19.3 19.92 20 20 20 20 20 20.01 20.07 20.35
720 16.27 19.01 19.84 19.99 20 20 20 20 20.02 20.1 20.41
840 15.88 18.73 19.74 19.97 20 20 20 20 20.03 20.14 20.46
960 15.55 18.46 19.62 19.94 19.99 20 20 20.01 20.04 20.17 20.51
1080 15.26 18.2 19.5 19.9 19.99 20 20 20.01 20.05 20.2 20.55
1200 15 17.96 19.37 19.85 19.98 20 20 20.02 20.07 20.23 20.59
1320 14.77 17.73 19.23 19.8 19.96 19.99 20 20.02 20.08 20.26 20.63
1440 14.56 17.52 19.1 19.74 19.94 19.99 20 20.03 20.1 20.29 20.67
1560 14.38 17.32 18.96 19.68 19.92 19.99 20.01 20.04 20.12 20.32 20.7
1680 14.21 17.13 18.82 19.61 19.89 19.98 20.01 20.04 20.13 20.34 20.73
1800 14.05 16.95 18.69 19.53 19.86 19.97 20.01 20.05 20.15 20.37 20.76
1920 13.91 16.78 18.56 19.46 19.83 19.96 20.01 20.06 20.17 20.39 20.79
2040 13.77 16.62 18.43 19.38 19.8 19.95 20.01 20.07 20.19 20.42 20.81
2160 13.65 16.46 18.3 19.3 19.76 19.94 20.01 20.08 20.2 20.44 20.84
2280 13.53 16.32 18.18 19.22 19.72 19.92 20.01 20.09 20.22 20.47 20.86
2400 13.42 16.18 18.06 19.14 19.67 19.9 20.01 20.09 20.24 20.49 20.88
2520 13.32 16.05 17.94 19.06 19.63 19.88 20 20.1 20.25 20.51 20.9
2640 13.23 15.93 17.83 18.98 19.58 19.86 20 20.11 20.27 20.53 20.93
2760 13.14 15.81 17.72 18.9 19.54 19.84 20 20.12 20.28 20.55 20.95
HVAC off HVAC cool HVAC heat temp_Cooltemp_Heat
0 20.71282
120 21.47614
120 22.28065
21.06852308
120 21.9376
120 22.83302
21.70069744
20.58968205
120 21.54943
120 22.52711
21.47015385
20.42871795
120 21.45312
120 22.4912
21.49093333
68
3.4. Validation of annual cooling/heating load with DesignBuilder (EnergyPlus) and eQuest (DOE-2) in
different climate zones
The validation of annual cooling/heating load with Excel tool, DesignBuilder (EnergyPlus) and eQuest
(DOE-2) is to evaluate the level of differences of simulated results among these programs. DesignBuilder
uses EnergyPlus (Crawley et al, 2004) engine, is developed by DesignBuilder Software Ltd (2015). eQuest
uses DOE-2 (James J. Hirsch, 2015) engine, is developed by James J. Hirsch (2015). Instead of simulating
real building conditions, the Excel tool was designed to perform simulation for researches under theoretical
(lab) conditions, for example, simulating a sealed room with no windows, doors or any infiltrations. Also,
the Excel tool is not as comprehensive on several aspects as DesignBuilder and eQuest, such as
distribution/ductwork system, occupants schedule and activity level, solar angle etc. The validation does
not intend to value the software quality, but to give a brief evaluation of results among these three energy
simulation programs.
A base model setting is determined for three energy simulation programs (Table . 3.4). The test will use the
same base model setting in different climate zones. In this base model, existing features in Excel tool is
specified as input data for both DesignBuilder and eQuest, such as exterior wall material, HVAC system,
weather data etc. Some unique features that are not included in the Excel tool have been disabled in both
DesignBuilder and eQuest, such as thermal insulation, windows and doors. Some other unchangeable
unique features may cause results differences among three programs, such as solar angle, distribution
system, ductwork etc. The model is simulated in both eQuest (Fig.3.35) and DesignBuilder (Fig. 3.36).
69
DesignBuilder eQuest Excel tool
Heating system
Type Furnace
Power Natural gas
AFUE 0.8
Cooling system
Type Fan coil DX coil ductless split heat pump system
Power Electricity Electricity Electricity
EER 16.4 16.4 16.4
Exterior wall/roof/ground floor material
Type Concrete
Thickness 0.2 meter
HVAC setting
Internal temperature 25 Celsius 25 Celsius 25 Celsius
Temperature offset Not specified Not specified 3 Celsius
Thermal insulation around the building
None
Windows and doors
None
Occupancy schedule
On 24/7 On 24/7 Default is 24/7
Heater distribution system & ductwork
specified specified None
Geometry information
Conditioned area 50 square meter
Room height 2.5 meter
Solar angle
counted counted None
Weather data time step
1 hour 1 hour 120 seconds
Table 3.4 base case model settings
70
Figure 3.35 eQuest model
Figure 3.36 DesignBuilder model
The annual cooling and heating load for three programs are listed (Table 3.5 and 3.6). The results
differences can be clearly observed from the tables. The Excel tool has higher annual cooling load than both
DesignBuilder and eQuest. It has lower annual heating load than both DesignBuilder and eQuest. In spite of
the differences, for all three programs, the cooling load keeps dropping and the heating load keeps rising
from hot to cold climate. It can be predicted the existing of the differences because the different calculation
algorisms and custom user inputs. But generally, the Excel tool results are in the acceptable range.
DesignBuilder eQuest Excel tool
Miami 2750 2830 2971
Phoenix 2661 2860 3054
Los Angeles 861 360 1408
Seattle 447 80 705
Pittsburgh 788 460 1196
Minneapolis 861 470 1210
Fargo 842 390 1062
Table 3.5 annual cooling load (kWh) for three programs
71
DesignBuilder Equest Excel tool
Miami 1280 787 1760
Phoenix 6125 5848 6357
Los Angeles 7895 8493 8431
Seattle 23220 27609 20351
Pittsburgh 25875 30956 20900
Minneapolis 31657 40530 27405
Fargo 38965 47044 32072
Table 3.6 annual heating load (kWh) for three programs
3.5. Conclusion
A numeric heat transfer model based on forward finite element method and heat transfer theory has been
developed in Excel. The Excel tool is able to use weather data from different cities and calculate wall/roof
temperature profiles throughout a year. It shows the thermal time lag of selected construction material. It
also provides energy consumption monthly and annually. The model has various independent parameters
that can be adjusted to observe different results of energy consumption. The interface of the program is
designed user friendly. Without switching the program, users can obtain weather data from other
spreadsheets. The entire calculation processes are automated and control by Excel macros. Further research
can be accomplished using this simulation program.
72
Chapter 4: Results and Discussion
4.1. Scope of work
The Excel tool intends to be able to perform simple energy modeling with user customizations. It is similar
to EnergyPlus (Crawley et al, 2015) and DOE-2 (James J. Hirsch & Associates, 2012), but with different
research purposes. As the Excel tool ought to have the ability to study specific material and environment
parameter‘s effect on building energy performance. With the development of the heat transfer model,
various output data can be obtained from different input settings. The tests were conducted in the following
order. The resultsarel displayed in charts and tables for the comparison among different settings. This
section includes data description and is followed by discussions and conclusions.
Part 1: Material and environmental parameters‘ effects on exterior wall thermal time lag. The tested
parameters are listed (table 4.1).
Test 1 Material parameters include conductivity, density, specific heat, exterior wall
thickness
Test 2 Validate Excel tool thermal time lag results with other researches
Test 3 Boundary parameters include exterior/interior temperature, indoor/outdoor surface
convection factors and solar radiation
Table 4.1 test parameters in part 1
Part 2: Material and environment parameters‘ effect on building energy performance. The energy
performance calculation is separated with thermal time lag calculation. Hence the results in part 2
are irrelevant with that in part 1. The tested parameters are listed (Table 4.2)
Test 1 Material parameters include conductivity, density, specific heat, exterior wall
thickness, thermal time lag
Test 2 Test results in different climate zones in US
Test 3 HVAC settings include controller temperature offset and indoor temperature setting
Test 4 Environment parameters include exterior wall surface emissivity, surrounding radiant
temperature and exterior convection coefficient
Table 4.2 test parameters in part 2
Part 3: Economic evaluation with different input settings. This section tends to explore the potential
usage of the Excel tool to evaluate material and energy costs. The feature has not yet added into the
Excel tool, but can be calculated in a separated spreadsheet.
73
Test 1 Energy price varies with different heating system (different heater and fuel)
Test 2 Energy price and material prices varies with period of use with different material
types
Table 4.3 test parameters in part 3
4.2. Test of thermal time lag and various parameters
Thermal time lag remains a potential standard for building energy performance evaluation in respect of heat
transfer. It has competitive features with conventional measurement like R-value and U-value (Tony Atkins,
Marcel Escudier, 2013). But unlike R-value and U-value, thermal time lag have more independent factors,
including material and environmental properties. It is necessary to explore different factors‘ effect on
thermal time lag and energy performance.
The thermal time lag has a separate calculation process for energy performance. The thermal time lag input
setting has its own input section in the input section of the Excel tool. This section will explore material and
environment properties effect on thermal time lag. The results will display in charts and tables for the
comparison among different material types.
4.2.1. Material properties effects on thermal time lag
Material properties, including thickness, conductivity, density, specific heat, have different levels of effects
on thermal time lag. According to the heat transfer equation (equation 3.1 to 3.3), thermal time lag is
function of material parameters and environment factors. Realizing the conventional concept that thickness
increases thermal time lag, it also requires exploring the effectiveness of the material properties over
thermal time lag.
Tests will be conducted using Excel ‗thermal time lag calculation‘ section. In order to conduct the
experiment, five common material types are selected for the test, including cement layer, concrete block,
brick block, plastic board and sandstone block (table 4.2). The boundary condition is also set to a base
condition (table 4.1).
74
Excel tool
Thickness 0.2 meter
Indoor temp 25°C
Environment Max temp 30°C
Environment Min temp 20°C
Indoor convection factor 18.6
Outdoor convection factor 8.7
Solar radiation 20 Watt
Table 4.4 base case boundary condition
Conductivity Density Specific heat
W/(mK) kg/m3 J/(kgK)
Cement layer 0.36 700 1050
Concrete block 0.51 1400 1000
Brick block 0.62 1800 840
Plastic board 0.5 1050 837
Sandstone block 1.83 2200 712
Table 4.5 test material types
Thickness test
In the thickness test, ten different thicknesses are selected to be input in the Excel tool from 0.05 meter to
0.3 meter. The results show the thicker wall has higher thermal time lag, but the effectiveness is different
among five material types. Concrete block has the higher increasing rate compared with other material
types. Sandstone block has the lowest increasing of thermal time lag in respect of thickness. The sandstone
block also has a relatively high value of conductivity compared with the other four. For all the five material
types, the increasing rate of thermal time lag is faster in the high thickness range than the lower ones (Table
4.3).
Thickness
(Meter)
0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3
Cement layer 1.23 2.31 3.48 4.61 5.64 6.59 7.54 8.57 9.75 11.14 12.81
Concrete block 1.87 3.23 4.56 5.74 6.84 7.98 9.28 10.83 12.73 15.23 >21
Brick block 1.82 3.12 4.38 5.52 6.57 7.62 8.78 10.15 11.79 13.82 16.78
Plastic board 1.22 2.22 3.32 4.38 5.35 6.25 7.13 8.04 9.06 10.23 11.61
Sandstone block <1 2.11 2.92 3.7 4.43 5.11 5.74 6.36 6.98 7.63 8.32
Table 4.6 thickness (meter) affects thermal time lag (hours)
75
Conductivity test
In the conductivity test, ten different conductivity values are selected based on the actual (base case)
conductivity of that material. The range is set from -0.25 to +0.25. The results show material with higher
conductivity have lower thermal time lag. All material types show more significant change in the lower
range of conductivity than the higher range. Besides, each material responds differently with increasing
conductivity. Cement layer has the highest change rate in all conductivity range, while sandstone block has
the lowest change rate. The thermal time lag of sandstone block almost stays constant with changing of
conductivity. In comparison with material parameter, sandstone block also has the highest density while
cement layer has the lowest density.
Conductivity
(W/mK)
-0.25 -0.2 0.15 -0.1 -0.05 Original 0.05 0.1 0.15 0.2 0.25
Cement layer 21+ 12.45 10.19 8.94 8.12 7.54 7.09 6.72 6.42 6.16 5.92
Concrete block 15.16 12.92 11.54 10.57 9.84 9.28 8.82 8.44 8.13 7.86 7.62
Brick block 12.06 11.03 10.26 9.66 9.18 8.78 8.44 8.16 7.91 7.69 7.49
Plastic board 10.34 9.23 8.48 7.92 7.48 7.13 6.83 6.57 6.34 6.14 5.97
Sandstone block 6.04 5.98 5.92 5.86 5.79 5.74 5.69 5.64 5.59 5.54 5.49
Table 4.7 conductivity (W/mK) affects thermal time lag (hours)
Figure 4.1 thickness (meter) affects thermal time lag (hours)
76
Density test
In the density test, ten different density values are selected based on the actual density (base case) of that
material. The range is set from -1000 Kg/m3 to +1000 Kg/m3. The results show material with higher
density tends to have higher thermal time lag. Among five material types, cement layer and plastic board is
more sensitive to density change.
Density
Kg/m3
-1000 -800 -600 -400 -200 Original 200 400 600 800 1000
Cement layer 1.96 4.67 6.29 7.54 8.73 9.97 11.31 12.76 14.42
Concrete block 4.5 5.74 6.72 7.58 8.42 9.28 10.17 11.12 12.13 13.21 14.41
Brick block 5.59 6.32 6.97 7.58 8.18 8.78 9.41 10.04 10.72 11.41 12.14
Plastic board Limit 2.81 4.37 5.49 6.37 7.13 7.84 8.56 9.29 10.06 10.85
Sandstone block 4.02 4.44 4.82 5.16 5.46 5.74 6.01 6.26 6.49 6.73 6.96
Table 4.8 density (Kg/m3) affects thermal time lag (hours)
Figure 4.2 conductivity (W/mK) affects thermal time lag (hours)
Figure 4.3 density (Kg/m3) affects thermal time lag (hours)
77
Specific heat test
In the specific heat test, ten different specific heat values are selected based on the actual specific heat (base
case) of that material. The range is set from -500 J/kgK to +500 J/kgK. The results show material with
higher specific heat tends to has higher thermal time lag. The sensitivity of specific heat change is quite
small among all five material types.
Specific heat
(J/kgK)
-500 -400 -300 -200 -100 Original 100 200 300 400 500
Cement layer limit 3.05 4.67 5.81 6.72 7.54 8.33 9.13 9.97 10.85 11.78
Concrete block 3.49 5.53 6.89 8.08 9.28 10.54 11.92 13.44 15.22 >21
Brick block 0.88 4.26 6.13 7.49 8.78 10.14 11.62 13.26 15.19 >21
Plastic board limit 3.23 4.96 6.16 7.13 8.03 8.93 9.87 10.87 11.92
Sandstone block 1.42 3.44 4.78 5.74 6.52 7.22 7.92 8.63 9.37
Table 4.9 specific heat (J/kgK) affects thermal time lag (hours)
Based on the material parameter test, thickness, density, specific heat have a an increasing effect on thermal
time lag. Only conductivity has negative effects on thermal time lag. Instead of linear relationship, material
tends only to be more sensitive to a parameter on certain part of the range. It is hard to decide which
parameter contributes more to the thermal time lag change. Generally speaking, thermal time lag is affected
by all these material parameters in their own ways.
4.2.2. Validation of thermal time lag
According to the data validation with other researches, Asan (2005) and Xing Jin (2011), the value of
thermal time lag among various construction material types have some diversity comparing with the other
two researches, which uses Crank-Nicolson scheme to solve the differential equations. Both researches
solve the thermal time lag equation by using one-dimension heat transfer model in. However, their results
have slight difference with each other because of using different boundary conditions including
Figure 4.4 specific heat (J/kgK) affects thermal time lag (hours)
78
environment temperature and indoor temperature. This could also be one of the reasons that the Excel based
tool has different result with those two papers (chapter 4.2.2).
Crank-Nicolson scheme uses numerical solution to solve the heat transfer equation, while Finite element
method uses massive database (solar radiation and temperature data). The form of the weather data requires
the heat transfer calculation breaking down based on its time steps. Crank-Nicolson scheme is difficult to
perform such calculation. Forward finite element (FFE) has both advantages and disadvantages over
Crank-Nicolson scheme. FFE scheme was used in Excel tool to solve the heat transfer equations with
boundary conditions. Basing on one-dimension heat transfer concept, the FFE scheme has the advantage of
tracking temperature changes in every little block within the structure in a certain time period. This feature
can be observed in each cell in Excel. This feature is very important in later energy flow calculation. FFE
also has some disadvantages. The precision of the tool is very sensitive to the number of the cell a wall
breaks into. The more cells, the more precise the results can be. This means some scale of the wall/roof may
excess the range of the Excel tool.
.
Xing Jin Asan*= Excel tool
Indoor temp 26°C 0.5°C 26°C/0.5°C
Environment Max temp 35°C 1°C 35°C/1°C
Environment Min temp 25°C 0°C 25°C/0°C
Indoor convection factor 18.6
Unknown 18.6
Outdoor convection factor 8.7
Unknown 8.7
Solar radiation Not include Not include 0 Watt
Table 4.10 boundary conditions in researches and tool
Thermal time lag results between Xing Jin (2011) and Excel tool
The two researchers focused more on theoretical situation than actual architecture situation in reality. They
neither add solar radiation and other environment factors into the equation, nor use regular boundary
conditions as test setting. In Asan‘s test, the temperature is 0.5°C (indoor) and from 0°C to 1°C
(environment). It is more like setting a heat transfer model to study the thermal lag phenomenon. The
thermal time lag calculation in Excel tool has added solar radiation into the equations. The tool results are
fairly close to Xing Jin‘s with the general diversity around 10% with exception of a few. This is not the case
with Asan‘s paper, which has fairly large difference in both 0.2 and 0.3 meters. The difference of the results
does not necessarily mean the accuracy of the tool, since they use different settings and functions. The
purpose of this contradistinction is more on to validate the growing trend of time lag among different
material types.
79
Building materials Excel Tool
results
Xing jing
(2011)
Difference
Hours Hours
Cement layer 9.34 9 3.78%
Concrete block 12.21 10.5 16.29%
Brick block 11.31 10 13.10%
Gypsum plastering 10.63 9.5 11.89%
Granite (red) block 7.12 7.5 5.07%
Marble (white) block 7.84 7.75 1.16%
Sandstone block 6.73 7 3.86%
Clay layer 9.63 9.25 4.11%
Asphalt sheet Limit 12 Limit
Steel slab 5.28 5.75 8.17%
Aluminum slab Limit 5.5 Limit
Cork board Limit 15.5 Limit
Wood block Limit 19 Limit
Plastic board 8.69 8.75 0.69%
Rubber board Limit 19.5 Limit
P.V.C board Limit 17.25 Limit
Asbestos sheet Limit 23.5 Limit
Formaldehyde board 7.68 7.25 5.93%
Thermalite board 13.29 10.75 23.63%
Fiberglass Limit 12.5 Limit
Siporex board Limit 12.5 Limit
Polyurethane board 5.23 5 4.60%
Light plaster 15.04 11.5 30.78%
Dense plaster 11.61 10.25 13.27%
Table 4.11 validation with Xing Jin‘s (2011) results of thermal time lag
Note: Limit means the results exceed the calculation limit of the tool
Thermal time lag results between Asan (2005) and Excel tool
In Asan‘s results, the model uses material with thickness of 0.2 and 0.3 meter. There is one test on each
thickness. The deviation of results is more significant in this test than with Xing Jin‘s (2011) results. The
explanation of the deviation is that the calculation method is different between Asan (2005) and Excel tool.
The Excel tool uses forward finite element method (FFE) while Asan (2005) uses Crank-Nicolson scheme.
Besides, on the exterior wall surface the Excel tool applies solar radiation and long-wave radiation from
surrounding environment.
80
Building materials Excel Tool
results
Asan
(2005)
Difference
Hours Hours
cement layer 7.48 5.12 46.09%
concrete block 8.92 6.81 30.98%
brick block 8.53 6.65 28.27%
gypsum plastering 8.19 5.93 38.11%
granite (red) block 6.13 5.01 22.36%
Marble (white) block 6.62 5.31 24.67%
Sandstone block 5.78 4.47 29.31%
Clay layer 7.7 5.98 28.76%
Asphalt layer 10.66 8.82 20.86%
Steel slab Limit 4.41 Limit
Aluminum slab Limit 3.43 Limit
Cork board 14.41 10.02 43.81%
Wood board 19.26 13.31 44.70%
Plastic board 7.11 4.94 43.93%
Rubber board Limit 14.34 Limit
PVC board 16.49 11.92 38.34%
Asbestos layer Limit 17.41 Limit
Formaldehyde board 6.29 3.19 97.18%
Fiberglass Limit 5.7 Limit
Thermalite board 9.27 6.52 42.18%
Siporex board 10.91 7.81 39.69%
Polyurethane board 4.15 1.63 154.60%
Table 4.12 validation with Asan‘s(2011) results of thermal time lag (0.2meter)
Note: Limit means the results exceed the calculation limit of the tool
Building materials Tool results Asan
(2005)
Diversity
Hours Hours
cement layer 11.22 8.23 36.33%
concrete block 13.74 10.31 33.27%
brick block 12.96 9.86 31.44%
gypsum plastering 12.43 9.27 34.09%
granite (red) block 8.42 6.95 21.15%
Marble (white) block 9.32 7.56 23.28%
Sandstone block 8.16 6.45 26.51%
Clay layer 11.37 8.84 28.62%
Asphalt layer 16.98 12 41.50%
81
Steel slab 5.61 5.09 10.22%
Aluminum slab Limit 4.14 Limit
Cork board Limit 15.77 Limit
Wood board Limit 20.28 Limit
Plastic board 10.52 7.84 34.18%
Rubber board Limit 21.82 Limit
PVC board Limit 18.01 Limit
Asbestos layer Limit >24 Limit
Formaldehyde board 9.51 5.96 59.56%
Fiberglass Limit 9.92 Limit
Thermalite board 14.71 10.43 41.04%
Siporex board 18.46 12.31 49.96%
Polyurethane board 6.67 3.36 98.51%
Table 4.13 validation with Asan‘s(2011) results of thermal time lag (0.3 meter)
Note: Limit means the results exceed the calculation limit of the tool
4.2.3. Boundary conditions affect thermal time lag
The boundary condition has an effect on the material‘s thermal time lag. According to the heat transfer
equation (equation 3.1 to 3.3), thermal time lag is a function of material and environmental properties.
From the equations (equation 3.1 and 3.2), thermal time lag will be affected by both indoor and outdoor
temperature. It is also affected by other environmental factors such as solar radiation and radiation heat
from surrounding objects. A test is required to examine the relationship between boundary conditions
(environment factors) and thermal time lag. The test will include examination of material thickness,
environment temperature, indoor temperature and solar radiation. Five common construction material types
were selected for the test: cement layer, concrete block, plastic board, and sandstone block.
In the results comparison among Asan (2005), Xing Jin (2011) and Excel tool (table 4.11), it shows thermal
time lag has an unstable value changing with different environment factors. The tool‘s boundary condition
is closer to Xing Jin‘s test than Asan‘s test (table 4.11). The tool‘s thermal time lag value also appears to be
closer to Xing Jin‘s test. Other than errors caused by excessing the tool limits, the diversity of material
thermal time lag between Xing Jin and tool are considerably small, which is under 10% among nineteen
material types. In comparison with Asan‘s tests, nearly all of the results show large diversity with tool
results. This shows the value of thermal time lag varies with different boundary conditions.
82
Xing jin Asan Excel tool
Indoor temp 26°C 0.5°C 23°C
Environment Max temp 35°C 1°C 30°C
Environment Min temp 25°C 0°C 10°C
Indoor convection factor 18.6
Unknown 18.6
Outdoor convection factor 8.7
Unknown 8.7
Solar radiation Not include Not include 20 Watt
Table 4.14 boundary condition settings from different thermal time lag tests
Building materials Excel tool results Difference compared with with other tests
hours 0.24 meter (Xing jin) 0.2 meter (Asan) 0.3 meter (Asan)
Cement layer 8.99 0.11% 46.29% 41.31%
Concrete block 11.02 4.95% 32.31% 43.94%
Brick block 10.42 4.20% 29.17% 39.86%
Gypsum plastering 9.96 4.84% 38.79% 41.64%
Granite (red) block 7.03 6.27% 21.76% 22.45%
Marble (white) block 7.69 0.77% 24.29% 25.40%
Sandstone block 6.71 4.14% 28.41% 26.51%
Clay layer 9.2 0.54% 28.93% 33.71%
Asphalt sheet 13.84 15.33% 25.17% Limit
Steel slab 5.2 9.57% Limit 11.00%
Aluminum slab Limit Limit Limit Limit
Cork board Limit Limit 58.08% Limit
Wood block Limit Limit Limit Limit
Plastic board 8.47 3.20% 43.93% 37.76%
Rubber board 6.33 7.54% 63.67% 63.79%
P.V.C board Limit Limit Limit Limit
Asbestos sheet Limit Limit Limit Limit
Formaldehyde board 7.61 4.97% 97.49% 62.42%
Thermalite board 11.68 8.65% 44.33% 55.70%
Fiberglass Limit Limit Limit Limit
Siporex board 14.53 16.24% 44.30% Limit
Polyurethane board 5.24 4.80% 155.21% 99.11%
Light plaster 12.61 9.65%
Dense plaster 10.63 3.71%
Table 4.15 validation with different boundary condition
Note: Limit means the results exceed the calculation limit of the tool
83
The tests of boundary condition with thermal time lag have shown that additional tests need to be run in
order to study the relationships between the parameters.. Test of environment factors effect on thermal time
lag will display in the following order. The environment factors include solar radiation, indoor and outdoor
temperature settings. Five different construction material types are selected for the test (table 4.14). Before
conduct the tests, a based model is required (Table 4.13). The location is Los Angeles (climate zone 3). The
test will follow a control variable method.
Outdoor maximum temperature effect on thermal time lag
Outdoor minimum temperature effect on thermal time
Indoor temperature effect on thermal time
Different temperature range effect on thermal time
Temperature swing effect on thermal time
Solar radiation effect on thermal time
Excel tool
Thickness 0.2 meter
Indoor temp 25°C
Environment Max temp 30°C
Environment Min temp 20°C
Indoor convection factor 18.6
Outdoor convection factor 8.7
Solar radiation 20 Watt
Table 4.16 base case boundary condition
Conductivity Density Specific heat
W/(mK) kg/m3 J/(kgK)
Cement layer 0.36 700 1050
Concrete block 0.51 1400 1000
Brick block 0.62 1800 840
Plastic board 0.5 1050 837
Sandstone block 1.83 2200 712
Table 4.17 test material types
Outdoor maximum temperature test
To perform the outdoor maximum temperature test, ten different temperatures are selected from 30°C to
40°C. The thermal time lag shows a mild negative response to the increasing outdoor maximum
temperature. For all five material types, with increasing of 10°C the thermal time lag varies within 0.2°C.
Concrete block shows sensible to the temperature change.
84
Outdoor maximum temperature
(Celsius)
30 31 32 33 34 35 36 37 38 39 40
Cement layer 7.54 7.53 7.53 7.52 7.52 7.52 7.51 7.51 7.51 7.51 7.5
Concrete block 9.28 9.24 9.21 9.19 9.17 9.15 9.13 9.12 9.11 9.09 9.08
Brick block 8.78 8.76 8.74 8.72 8.71 8.69 8.68 8.67 8.66 8.65 8.64
Plastic board 7.13 7.12 7.12 7.12 7.11 7.11 7.11 7.11 7.11 7.11 7.11
Sandstone block 5.74 5.74 5.74 5.74 5.74 5.73 5.73 5.73 5.73 5.73 5.73
Table 4.18 outdoor maximum temperature (Celsius) affects thermal time lag (hours)
Outdoor minimum temperature test
In the outdoor minimum temperature test, ten different temperatures are selected from 10°C to 20°C. The
thermal time lag shows mild positive respond to the increasing outdoor minimum temperature. For all five
material types, with increasing of 10°C the thermal time lag varies within 0.2°C. Again, concrete block is
more sensible to the temperature change.
Outdoor minimum temperature
(Celsius)
10 11 12 13 14 15 16 17 18 19 20
Cement layer 7.49 7.49 7.49 7.5 7.5 7.51 7.51 7.52 7.52 7.53 7.54
Concrete block 9.01 9.02 9.03 9.06 9.07 9.09 9.12 9.15 9.18 9.23 9.28
Brick block 8.59 8.6 8.61 8.62 8.64 8.66 8.67 8.69 8.72 8.74 8.78
Plastic board 7.11 7.11 7.11 7.11 7.11 7.11 7.11 7.12 7.12 7.12 7.13
Sandstone block 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74
Table 4.19 outdoor minimum temperature (Celsius) affects thermal time lag (hours)
Figure 4.5 outdoor maximum temperature (Celsius) affects thermal time lag (hours)
85
Indoor temperature test
The indoor temperature test is performed in the same pattern from 20° C to 30° C. The results shows thermal
time lag stays constant with changing the indoor temperature setting.
Indoor temperature
(Celsius)
20 21 22 23 24 25 26 27 28 29 30
Cement layer 7.54 7.54 7.54 7.54 7.54 7.54 7.54 7.54 7.54 7.54 7.54
Concrete block 9.28 9.28 9.28 9.28 9.28 9.28 9.28 9.28 9.28 9.28 9.28
Brick block 8.78 8.78 8.78 8.78 8.78 8.78 8.78 8.78 8.78 8.78 8.78
Plastic board 7.13 7.13 7.13 7.13 7.13 7.13 7.13 7.13 7.13 7.13 7.13
Sandstone block 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74
Table 4.20 indoor temperature (Celsius) affects thermal time lag (hours)
Different temperature range test
In the different temperature range test, ten different ranges are selected from -30° C~-20° C to 70°C~80°C.
The purpose of this test is to examine the thermal time lag variation in different climates, which is displayed
for different temperature ranges. Results show more significant variation compared with the former tests
(outdoor max, min and indoor temperature test). Figure 4.7 shows increasing temperature range helps
increase thermal time lag. Generally, changing a wall‘s climate zone from a colder one to a hotter one will
increase its thermal time lag. Besides, concrete block again is the most sensitive material towards
temperature range. But even with relatively large variation comparing with the other tests, the variation is
still within 0.32 hour range.
Figure 4.6 outdoor minimum temperature (Celsius) affects thermal time lag (hours)
86
Colder weather Hotter weather
Outdoor max
(Celsius)
-20 -10 0 10 20 30 40 50 60 70 80
Outdoor min
(Celsius)
-30 -20 -10 0 10 20 30 40 50 60 70
Cement layer 7.39 7.43 7.46 7.48 7.51 7.54 7.57 7.59 7.62 7.64 7.67
Concrete block 8.38 8.58 8.76 8.94 9.11 9.28 9.44 9.6 9.76 9.91 10.06
Brick block 8.16 8.29 8.42 8.54 8.67 8.78 8.89 9.01 9.11 9.22 9.32
Plastic board 7.07 7.08 7.09 7.11 7.12 7.13 7.14 7.14 7.16 7.17 7.17
Sandstone block 5.8 5.79 5.78 5.77 5.76 5.74 5.73 5.71 5.7 5.68 5.67
Table 4.21 different temperature range (Celsius) affects thermal time lag (hours)
Temperature swing test
In the temperature swing test, ten different temperature swings are selected between outdoor maximum
temperature and outdoor minimum temperature from 2°C to 50°C. After examining the test in different
climate types, it is necessary to test climate with mild and large temperature swing. The purpose of this test
is to examine the thermal time lag variation in climates on same latitude, which has similar solar radiation
throughout a year but with different humidity level therefore with different temperature swing. The results
show big swing does not affect thermal time lag change. But with mild swing (within 10°C difference) the
thermal time lag increase rapidly. Among five material types, concrete block again is the most sensitive
material towards outdoor temperature swing.
Figure 4.7 different temperature range (Celsius) affects thermal time lag (hours)
87
Large swing Small swing
Outdoor max
(Celsius)
66 62 58 54 50 46 42 38 34 30 26
Outdoor min
(Celsius)
-16 -12 -8 -4 0 4 8 12 16 20 24
Cement layer 7.49 7.48 7.48 7.48 7.48 7.48 7.48 7.49 7.5 7.54 7.88
Concrete block 8.88 8.89 8.89 8.9 8.91 8.93 8.95 8.99 9.07 9.28 11.04
Brick block 8.51 8.51 8.51 8.52 8.52 8.53 8.55 8.58 8.63 8.78 10.06
Plastic board 7.11 7.11 7.1 7.1 7.1 7.1 7.1 7.1 7.11 7.13 7.33
Sandstone block 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.74 5.75 5.77
Table 4.22 different outdoor temperature swing (Celsius) affects thermal time lag (hours)
Solar radiation test
In the solar radiation test, ten different solar radiation values are selected from 0 Watt to 800 Watt. The
result shows the solar radiation level increases the thermal time lag. All five material temperature lines
show linear relationship in the Figure. Again concrete block is more sensitive than other material types.
Solar radiation
(Watt)
0 80 160 240 320 400 480 560 640 720 800
Cement layer 7.53 7.54 7.56 7.57 7.58 7.59 7.61 7.62 7.63 7.64 7.65
Concrete block 9.26 9.33 9.4 9.47 9.54 9.61 9.67 9.74 9.81 9.87 9.94
Brick block 8.77 8.82 8.87 8.92 8.96 9.01 9.06 9.11 9.15 9.19 9.24
Plastic board 7.13 7.13 7.13 7.14 7.14 7.14 7.15 7.16 7.16 7.16 7.17
Sandstone block 5.74 5.74 5.73 5.72 5.72 5.71 5.71 5.7 5.69 5.69 5.68
Table 4.23 solar radiation (Watt) affects thermal time lag (hours)
Figure 4.8 different outdoor temperature swing (Celsius) affects thermal time lag (hours)
88
4.2.4. Conclusion and discussion of material and environmental factors influence on thermal time lag
Material properties have significant effect on thermal time lag. For instance, by adding 50% of its original
specific heat, a 0.2 meter concrete block can raise its thermal time lag from 9.28 hour to over 21 hours. This
is over 100% of original value, which means the material selection plays an important role on thermal time
lag design. Also by observing the trend of the graphics, the thermal lag distribution of density seems more
disordered than other properties. This means the other properties have more significant effect on thermal
time lag than density. Therefore, it still affects the function even when changes large amount of density. On
the design stage, it is important to select proper material with fixed regulations like thickness, weight,
thermal resistance etc.
Boundary conditions (environmental factors) have less effect on thermal time lag comparing with material
properties. In some cases, it can be neglected. For instance, by raising the indoor temperature setting, the
thermal time lag stays constant. Also, by raising the outdoor minimum temperature, the thermal time lag of
all five material types only raises with 0.5 hours. So far, the biggest change of thermal time lag is the test of
different climate types and test of different outdoor temperature swings. By moving from a colder to a
hotter climate, concrete block is the most sensitive, and can reach as high as 1.68 hours. By changing the
outdoor temperature swing from 10°C to 2°C, concrete block raise1.76 hours (from 9.28 hours to 11.04
hours) of its thermal time lag. But again thermal time lag is only suggested to be used in climate type with
big temperature swing to save more energy. Hence in 2°C temperature swing scenario, thermal time lag can
hardly be a passive energy saving strategy.
Material properties and boundary conditions (environmental factor) both have effects on thermal time lag
of construction material. Even though material properties show much greater effects on thermal time lag,
several environmental factor can cause proper amount of thermal time lag variation in some cases. It can be
summarized as follows:
Figure 4.9 solar radiation (Watt) affects thermal time lag (hours)
89
For material properties,
Thermal time lag increases with higher thickness, density and specific heat.Thermal time lag
decreases with increasing conductivity
Material properties have more significant effects on thermal time lag than environmental factors,
therefore it is important to select a proper construction material and thickness.
For boundary conditions (environmental factors),
The thermal time lag increases under the following circumstance separately (when other properties
are fixed): Increasing the interior temperature down-limit, moving material from cold to hot
climate, increasing solar radiation level.
Increasing of the exterior up-limit temperature reduces the thermal time lag when other properties
are fixed
Changing indoor temperature setting has no or little effect on thermal time lag
Change of climate has notable effects on thermal time lag. For example, Moving a concrete block
from cold place (-30°C to -20°C) to a hotter place (40°C to 50°C), can raise thermal time lag as high
as 1.22 hours.
Change of exterior temperature daily swing has notable effects on thermal time lag. For instance,
by reducing the outdoor temperature swing from 10°C to 2° C, concrete block can raise time lag by
1.78 hours.
The overall effect of environmental factors are not as significant as material factors
From this specific test, concrete block is more sensitive in respect of thermal time lag than the other
four material types.
4.3. Material and environment parameters effect on heating and cooling system energy performance
The calculation for HVAC energy consumption is separated from thermal time lag calculation. Although
they both use forward finite element method, many more parameters are added in the energy calculation
spreadsheet. This includes weather data for the purpose of studying different climate types. The size of the
calculation spreadsheet is much bigger than thermal time lag. The purpose of adding various material and
environmental parameters is to set a simulation environmental close to an actual condition. Using weather
data is to study the energy performance in different area globally.
In this section, several simulations will be conducted to study the energy performance of the target wall
system. The energy performance will be showed as HVAC energy consumption (Figure 4.10). The energy
performance is affected by different factors with similar or unique effects. Different factors will be adjusted
and compared with each other using control variable method. The target properties include thermal time lag,
90
climate zones, HVAC settings and environmental factors. The results will show their effects on the energy
performance of wall system. The discussion will focus on the level of influence and the synergy among
them.
Figure 4.10 annual HVAC energy consumption
To examine the effect of different parameters on HVAC system energy consumption, the test will use a
control variable method. A base model setting will be selected. The base model contains weather data,
HVAC setting, room setting and environment setting. The following tests changes single or multiple
variables to explore their specific effects on energy consumption.
Los Angeles is selected as base model climate in climate zone 3. The city has relative large daily swing due
to its dry climate type. The significant daily temperature change should have effects on indoor environment.
In the environment setting (table 4.21), indoor and outdoor convection factors are selected to normal values.
Wall emissivity depends on color and surface condition is also selected. It is assumed that the model has no
surrounding radiant temperature. The solar absorption is set to 0.2.
Symbol Unit Value
Convection indoor hin W/(m2•K) 8.7
Convection outdoor hout W/(m2•K) 18.6
Wall Emissivity Epsilon N/A 80%
Surrounding Radiant temperature Tradout Celsius 0
Solar Absorption As N/A 0.2
Table 4.24 base model environment setting
The model‘s cooling and heating system uses a ductless split heat pump, which is commonly used in a
small-size room. Both heating and cooling in this base model use electricity and are performed by this air
conditioner. The air conditioner has a regular value of COP of xxx. Due to the Excel tool features (Chapter
5.3.2), instead of using the manufacturer‘s value, the cooling and heating capacity is calculated based on
Cool Heat total Cool Heat Cool Heat
Jan -434.3 69.2 503.5 53.8 223.6 80.7 447.2
Feb -526.2 59.0 585.2 83.1 179.3 124.6 358.5
Mar -752.3 59.9 812.2 166.0 161.9 249.1 323.8
Apr -947.0 46.7 993.6 277.4 96.9 416.2 193.8
May -1146.9 40.6 1187.5 375.4 59.8 563.1 119.5
Jun -1217.5 34.7 1252.2 419.5 38.1 629.2 76.1
Jul -1290.8 34.7 1325.5 449.0 36.5 673.5 73.0
Aug -1475.2 25.9 1501.2 516.3 14.6 774.5 29.1
Sep -1313.9 24.4 1338.3 407.1 23.6 610.7 47.1
Oct -1007.5 34.6 1042.1 230.2 78.5 345.3 157.1
Nov -578.9 53.5 632.4 86.8 158.9 130.2 317.8
Dec -230.4 93.0 323.4 18.5 264.3 27.8 528.7
Grand -10920.8 576.2 11497.02 3083.1 1335.9 4624.7 2671.8
Theoretical Energy consume (kWh/m2) HVAC load (kWh)
527.9
483.1
572.9
610.0
682.6
705.3
746.5
803.6
657.8
502.4
448.0
556.5
Grand HVAC load
(kWh)
7296.5
HVAC (hour)
91
calculation requirements. In order keep accuracy of the heat transfer calculation, the heating and cooling
capacity is auto-calculated based on weather data and HVAC inputs. This feature requires to be improved in
the future. Furthermore, the temperature offset of the control system is set by the tester, which is 3 Celsius.
http://www.ajmadison.com/cgi-bin/ajmadison/LS090HYV.html
Module name LG Art Cool Premier LS090HYV
Type ductless split heat pump system
EER (cooling) 16.4 (COP is 4.8)
HSPF (heating) 12 (COP is 3.5)
Table 4.25 base model cooling and heating system
Symbol Unit Value
Cooling capacity Cool Watt Calculated by Excel
Heating capacity Heat Watt Calculated by Excel
Temperature offset DeltaT Celsius 3
COP-cooling η1 N/A 4.8
COP-heating η2 N/A 3.5
Table 4.26 base model HVAC setting
The room, which is the size of the model, has area of 50 square meters with wall height of 2.5 meters (Table
4.24). Except for the floor, the roof and four wall pieces will be calculated in the model.
Symbol Unit Value
Conditioned area Area m2 50
Roon height H m 2.5
Room volume Vr m3 125
Roof/wall area Aroof m2 120.71
Table 4.27 base model room setting
4.3.1. Thermal time lag and material properties effects on energy performance
Thermal time lag and material properties both have effects on building energy performance. In reality,
thermal time lag usually applied with other passive energy strategies like nature ventilation. For example,
during night time night flush uses cool air instead of air conditioner to cool down the room temperature.
This is quite energy efficient working with thermal mass material. In this test, however, the model is
completely sealed without any natural ventilation. This helps with studying the effect of thermal time lag
and material properties on model energy performance without disturbance from other factors. It should be
indicated that although thermal time lag is not an independent parameter of material, it represents the
92
synergy between material and environmental properties. Thus the result shows the effect of both material
and environmental properties on building energy performance.
4.3.1.1. Thermal time lag effect on energy performance
Firstly, annual cooling and heating system load is tested under different thermal time lag values. The test
uses 13 types of common construction material under different thermal time lag. The value of time lag is set
from 2 hours to 14 hours (Table 4.26). Different thermal time lag is achieved by adjusting the thickness of
the material (Table 4.26). The test settings are from the base model.
Thermal conductivity Density Specific heat
[W/(mK)] (kg/m3) [J/(kgK)]
Cement layer 0.36 700 1050
Concrete block 0.51 1400 1000
Brick block 0.62 1800 840
Gypsum plastering 0.42 1200 837
Granite (red) block 2.9 2650 900
Marble (white) block 2 2500 880
Sandstone block 1.83 2200 712
Clay layer 0.85 1900 837
Plastic board 0.5 1050 837
Formaldehyde board 0.03 30 1674
Thermalite board 0.19 753 837
Light plaster 0.16 600 1000
Dense plaster 0.5 1300 1000
Table 4.28 tested material properties
93
6 hours 8 hours 10 hours 12 hours 14 hours 16 hours
Cement layer 0.16 0.21 0.255 0.288 0.315 0.335
Concrete block 0.13 0.175 0.213 0.241 0.264 0.281
Brick block 0.136 0.184 0.223 0.253 0.277 0.295
Gypsum plastering 0.144 0.192 0.232 0.263 0.288 0.306
Granite (red) block 0.195 0.273 0.334 0.382 0.42 0.446
Marble (white) block 0.178 0.246 0.3 0.343 0.377 0.401
Sandstone block 0.21 0.29 0.352 0.401 0.44 0.47
Clay layer 0.15 0.205 0.25 0.284 0.311 0.331
Plastic board 0.168 0.225 0.271 0.306 0.334 0.356
Formaldehyde board 0.191 0.25 0.298 0.335 0.364 0.386
Thermalite board 0.129 0.17 0.204 0.23 0.251 0.267
Light plaster 0.12 0.16 0.193 0.217 0.237 0.252
Dense plaster 0.135 0.181 0.219 0.248 0.272 0.289
Table 4.29 material thickness in different thermal time lag
The first set of results show the annual cooling load under different thermal time lags (Table 4.27). The
line chart (figure 4.11) displays the general trend of cooling load by adding up thermal time lag. For all
material types, the cooling load starts dropping with higher thermal time lag. The lines show similar
patterns among these material types. The drop becomes less significant after a 10 hour lag. The only
exception Formaldehyde board (lowest conductivity) shows the lowest annual cooling load.
6 hours 8 hours 10 hours 12 hours 14 hours 16 hours
Cement layer 1888 1270 909 728 622 560
Concrete block 2609 1736 1272 1043 907 829
Brick block 2800 1859 1385 1141 1000 919
Gypsum plastering 2221 1475 1076 866 744 676
Granite (red) block 4271 2792 2251 2004 1861 1781
Marble (white) block 3984 2584 2060 1795 1644 1560
Sandstone block 3681 2380 1869 1602 1449 1358
Clay layer 3124 2051 1538 1282 1136 1051
Plastic board 2243 1480 1085 881 761 688
Formaldehyde board Error Error 14 63 53 46
Thermalite board 1403 925 664 528 446 399
Light plaster 1313 851 605 481 406 362
Dense plaster 2525 1683 1241 1013 877 803
Table 4.30 Annual cooling capacity (kWh) in different thermal time lag
94
Conductivity plays an important role in the test cooling load results. In comparison among different
material types, granite (red) block has the highest cooling load. The next are marble (white) block,
sandstone block, and clay layer. The formaldehyde board has the lowest annual cooling load. Form the
material chart (table 4.25), granite (red) block has the highest value of conductivity, and formaldehyde
board has the lowest value of conductivity. Despite these facts, the cooling load can still be affected by
combination of other material properties.
The annual heating load has very similar trend with cooling load except for the value. The annual heating
load is about 1000 kWh higher than the cooling load comparing with both results (table 4.30 an 4.31). The
annual heating load decreases with increasing thermal time lag. The heating system results also depend on
the heating capacity and system COP. If the system uses natural gas heaters instead of heat pump, which
uses electricity as power sources, the results will be different due to different COP value.
Figure 4.11 Annual cooling capacity (kWh) in different thermal time lag
95
6 hours 8 hours 10 hours 12 hours 14 hours 16 hours
Cement layer 2599 1750 1253 1005 860 775
Concrete block 3572 2376 1740 1428 1242 1135
Brick block 3810 2527 1882 1550 1359 1248
Gypsum plastering 3036 2018 1472 1186 1020 927
Granite (red) block 5714 3704 2974 2642 2451 2346
Marble (white) block 5352 3447 2740 2384 2181 2068
Sandstone block 4963 3194 2502 2142 1936 1814
Clay layer 4239 2778 2081 1733 1535 1421
Plastic board 3067 2024 1485 1206 1043 944
Formaldehyde board Error Error 1273 88 74 65
Thermalite board 1928 1273 915 729 618 553
Light plaster 1806 1172 836 666 562 502
Dense plaster 3444 2295 1692 1382 1197 1095
Table 4.31 Annual heating capacity (kWh) in different thermal time lag
The annual heating load also seems greatly affected by conductivity just like the trend in cooling load test
(Figure 4.12). Material with higher conductivity has bigger drops and more annual load than material with
lower conductivity. The formaldehyde board also has the lowest heating load among all the material types.
The total annual load (Table 4.29) results is close to cooling and heating load, since both cooling and
heating load results share same pattern. The annual total load drops with increasing thermal time lag. The
line chart (Figure 4.13) also shows that conductivity has influence on annual load.
6 hours 8 hours 10 hours 12 hours 14 hours 16 hours
Figure 4.12 Annual heating capacity (kWh) in different thermal time lag
96
Cement layer 4486 3020 2162 1733 1482 1336
Concrete block 6181 4112 3012 2471 2149 1964
Brick block 6610 4386 3267 2691 2359 2167
Gypsum plastering 5257 3493 2548 2051 1763 1603
Granite (red) block 9985 6496 5226 4646 4312 4127
Marble (white) block 9336 6031 4801 4179 3825 3628
Sandstone block 8644 5574 4372 3745 3385 3172
Clay layer 7363 4829 3619 3015 2671 2472
Plastic board 5310 3503 2570 2086 1804 1632
Formaldehyde board Error Error 1287 150 127 112
Thermalite board 3331 2198 1579 1258 1064 953
Light plaster 3119 2022 1441 1147 968 864
Dense plaster 5969 3978 2933 2395 2074 1898
Table 4.32 Annual total capacity (kWh) in different thermal time lag
4.3.1.2. Material properties effect on energy performance
Material properties are the primary independent factors of thermal time lag. They should also have notable
effects on cooling and heating load. From the thermal time lag test, conductivity already shows significant
effects on annual heating and cooling load. This section is going to test thickness, conductivity, density and
specific heat on annual cooling and heating load. The test material is selected as concrete block since it is a
common construction material with high thermal mass. The test will use the base model setting. Each
material property will be tested individually.
Figure 4.13 Annual total capacity (kWh) in different thermal time lag
97
Thickness test
In the thickness test, eight different thicknesses are selected from 0.16 meters to 0.3 meters (Table 4.30).
The line chart (figure 4.14) shows both the heating and cooling load drops with increasing thickness. The
drop of energy load is more significant at low thickness than at high thickness. The curve is smooth. The
pattern is close to the results of ‗thermal lag vs. energy load‘ test. This is because in the thermal lag test, the
thermal lag is directly adjusted by adding the thickness of the material.
0.16 m 0.18 m 0.2 m 0.22 m 0.24 m 0.26 m 0.28 m 0.3 m
Cooling capacity 1982 1662 1408 1206 1050 927 833 760
Heating capacity 2700 2265 1918 1643 1430 1264 1135 1036
total 4682 3927 3326 2849 2480 2191 1968 1796
Table 4.33 Annual capacity (kWh) with different thickness (Meter)
Conductivity test
In conductivity test, eight different values of conductivity are selected from 0.1 W/(mK) to 0.8 W/(mK)
(table 4.31). The results (figure 4.15) show significant positive effect on annual cooling and heating load.
The annual load increases with higher conductivity. The total energy load increases from 572 kWh to 5093
kWh with increasing 0.7 W/mK conductivity. The increasing rate is 790%. The result is close to linear
relationship between conductivity and annual load. The results are as expected because conductivity
already shows significant positive effect in the thermal lag test in chapter 7.2.1.1.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
W/(mK) W/(mK) W/(mK) W/(mK) W/(mK) W/(mK) W/(mK) W/(mK)
Cooling capacity 239 491 781 1084 1380 1658 1919 2161
Heating capacity 333 676 1070 1480 1880 2255 2607 2932
total 572 1167 1851 2563 3259 3913 4525 5093
Table 4.34 Annual capacity (kWh) with different conductivity (W/(mK))
Figure 4.14 Annual capacity (kWh) with different thickness (Meter)
98
Density test
In the density test, eight different values of density are selected from 600 kg/m3 to 2000 kg/m3 (Table 4.32).
The results show negative effect on energy load. The energy load reduces with increasing density. From the
line chart (figure 4.16), the dropping rate is moderate and close to a linear relationship between density and
energy load.
600 800 1000 1200 1400 1600 1800 2000
kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kg/m3
Cooling capacity 2103 1885 1694 1536 1408 1306 1225 1163
Heating capacity 2879 2578 2314 2095 1918 1776 1665 1577
total 4982 4462 4008 3631 3327 3082 2890 2740
Table 4.35Annual capacity (kWh) with different density (kg/m3)
Figure 4.15 Annual capacity (kWh) with different conductivity (W/(mK))
Figure 4.16 Annual capacity (kWh) with different density (kg/m3)
99
Specific heat test
In the specific heat test, eight different values of specific heat are selected from 700 kg/m3 to 1400 kg/m3
(Table 4.33). The results show very similar pattern as density. It has negative effect on energy load. From
the line chart (figure 4.17), the dropping rate is also moderate and close to a linear relationship between
specific heat and energy load.
700 800 900 1000 1100 1200 1300 1400
J/(kgK) J/(kgK) J/(kgK) J/(kgK) J/(kgK) J/(kgK) J/(kgK) J/(kgK)
Cooling capacity 1712 1596 1495 1408 1334 1271 1218 1174
Heating capacity 2339 2178 2039 1918 1815 1728 1655 1593
total 4051 3773 3534 3327 3149 2998 2873 2766
Table 4.36 Annual capacity (kWh) with different specific heat (J/(kgK))
4.3.2. Climate effects on energy performance
Climate always has a significant effect on the building‘s energy performance for skin dominated buildings.
(Laarger, internal load dominated buildings are less sensitive.) This is especially true on annual average
temperature and solar radiation level. For example, annual heating hours are much more in Fargo (Climate
zone 7) than in Miami (Climate zone 1). On contrast, annual cooling hours are more in Phoenix (Climate
zone 2) than in Minneapolis (Climate zone 6). Besides these obvious facts, the efficiency of wall with
different thickness is required to be tested in different climates. And it also brings the question ‗is the
thicker wall a better wall in respect of energy saving?‘ This section is going to explore how effective by
using thermal mass material and what value of thermal time lag is more efficient in cold, mild and hot
climate. It is going to test different material types in different climates with different thermal time lags.
Figure 4.17 Annual capacity (kWh) with different specific heat (J/(kgK))
100
The following tests are going to use the base model settings. A representative US city in each climate zone
is selected (Table 4.34). From climate zone 1 to 7, selected cities are Miami, Phoenix, Los Angeles, Seattle,
Pittsburgh, Minneapolis and Fargo. The annual weather data including information of temperature and solar
radiation is gathered from weather station. The weather data gathered from weather station is in hourly
scale, and has been transferred into 2 minutes scale into Excel spreadsheet.
Climate zone 1 2 3 4 5 6 7
City Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Table 4.37 representative city in each climate zone
13 types of common construction material will be used in this test (table 4.35). The test will also use
material with an 8 hour thermal time lag in each climate zone. The thickness of the material is also listed in
the table.
Building materials Thermal conductivity Density Specific heat 8 hour lag thickness
W/(mK) kg/m3 J/(kgK) Meter
Cement layer 0.36 700 1050 0.21
Concrete block 0.51 1400 1000 0.175
Brick block 0.62 1800 840 0.184
Gypsum plastering 0.42 1200 837 0.192
Granite (red) block 2.9 2650 900 0.273
Marble (white) block 2 2500 880 0.246
Sandstone block 1.83 2200 712 0.29
Clay layer 0.85 1900 837 0.205
Plastic board 0.5 1050 837 0.225
Thermalite board 0.19 753 837 0.17
Light plaster 0.16 600 1000 0.16
Dense plaster 0.5 1300 1000 0.181
Table 4.38 test material properties
4.3.2.1. Material with 8 hours lag in different climate zones
The first test is to explore the energy performance of different material with 8 hours lag in different climate
zones. The purpose of this test is to explore the energy efficiency of constant thermal time lag in hot, mild
and cold climate and the difference among different material types. The test uses base model settings and
weather data from climate zone 1 to climate zone 7.
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Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Cement layer 2343 2386 1270 669 1031 988 858
Concrete block 3379 3455 1736 897 1455 1532 1375
Brick block 3693 3788 1859 953 1641 1719 1542
Gypsum plastering 2789 2846 1475 769 1207 1165 1034
Granite (red) block 6536 6877 2792 1665 2972 3115 2807
Marble (white) block 5889 6184 2584 1471 2704 2802 2508
Sandstone block 5204 5497 2380 1289 2414 2482 2215
Clay layer 4170 4344 2051 1043 1929 1975 1777
Plastic board 2814 2872 1480 771 1214 1175 1044
Thermalite board 1668 1695 925 490 745 710 619
Light plaster 1523 1547 851 452 684 651 569
Dense plaster 3262 3335 1683 871 1397 1451 1301
Table 4.39 cooling load of different material types (8 hours lag) in seven climate zones
The cooling hours in Seattle is close to it in Fargo (Fargo is slightly higher). The reason can be observed
from the annual temperature data. From the weather profile of Seattle (Figure 4.19) and Fargo (Figure 4.20),
Seattle has less the temperature zone above the indoor setting temperature than Fargo. Even though the
annual average temperature of Fargo is much lower and it has colder winter, the cooling hour depending on
the indoor setting temperature still stays similar. This also explains the curve from Seattle to Pittsburgh and
to Minneapolis. In comparison, the temperature zone above the indoor setting temperature of Phoenix
(Figure 4.21) is much more than that in Seattle. This causes the significant drop from Phoenix to Seattle.
Figure 4.18 Annual capacity (kWh) with different specific heat (J/(kgK))
102
Figure 4.19 annual temperature data of Seattle (climate zone 4)
Figure 4.20 annual temperature data of Fargo (climate zone 7)
Figure 4.21 annual temperature data of Phoenix (climate zone 2)
103
The heating load test result (table 4.37) in different climate zones keeps increasing from Miami to Fargo.
The most significant increasing of heating load occurs between Los Angeles and Seattle. This means the
amount of heating load increases significantly from Los Angeles to Seattle. This can be also explained from
annual temperature data of both cities (figure 4.19 and figure 4.22). The temperature zone below indoor
setting temperature is much more in Seattle, and the winter temperature in Seattle is much lower.
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Cement layer 497 1249 1742 3644 3738 4764 5527
Concrete block 597 1725 2365 5250 5414 7124 8297
Brick block 609 1868 2527 5733 6011 7885 9172
Gypsum plastering 545 1458 2018 4337 4450 5700 6652
Granite (red) block 828 3317 3704 10190 10761 14132 16460
Marble (white) block 796 3017 3447 9127 9727 12713 14779
Sandstone block 690 2707 3194 8094 8670 11299 13126
Clay layer 632 2154 2778 6465 6919 8993 10464
Plastic board 540 1464 2024 4377 4491 5761 6726
Thermalite board 380 906 1273 2596 2663 3380 3919
Light plaster 356 833 1172 2371 2431 3082 3572
Dense plaster 586 1672 2295 5071 5213 6832 7965
Table 4.40 heating load (kWh) of different material types in seven climate zones
Figure 4.22 annual temperature data of Los Angeles (climate zone 3)
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The annual total load test result (table 4.38) in different climate zones keeps increasing from Miami to
Fargo with the exception of Los Angeles. In fact, except for Los Angeles, the increasing value of the other
6 climate zones is close to a linear relationship. From the results of cooling load (Table 4.36) and heating
load (Table 4.37), Los Angeles has low values of energy consumption comparing with other cities. This
means the annual average temperature of Los Angeles is close to the indoor setting temperature (25 Celsius).
Therefore less air conditioning is required in Los Angeles.
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Cement layer 2841 3635 3012 4312 4769 5751 6386
Concrete block 3976 5181 4101 6147 6869 8656 9671
Brick block 4302 5656 4386 6686 7651 9604 10714
Gypsum plastering 3333 4304 3493 5106 5657 6865 7686
Granite (red) block 7364 10194 6496 11855 13733 17247 19267
Marble (white) block 6685 9202 6031 10598 12431 15515 17287
Sandstone block 5894 8204 5574 9382 11084 13782 15341
Clay layer 4802 6498 4829 7508 8849 10967 12242
Plastic board 3353 4336 3503 5148 5705 6936 7770
Thermalite board 2049 2601 2198 3087 3408 4090 4538
Light plaster 1879 2379 2022 2823 3115 3732 4141
Dense plaster 3848 5007 3978 5942 6610 8283 9266
Table 4.41 total load (kWh) of different material types in seven climate zones
Figure 4.23 heating load (kWh) of different material types in seven climate zones
105
4.3.2.2. Different thermal time lag in different climate zones
The former test of an 8 hour lag in different climate zones, explains the energy performance of different
material with same time lag from Miami to Fargo. Based on the results in each climate zones, different
thermal time lags also require to be explored to study their energy performance in each climate zone. This
section is will focus on testing a selected material (concrete block) with thermal time lag from 6 hours to 16
hours in all 7 different climate zones. The reason concrete block was selected is that it is a common heavy
weight construction material with high thermal mass.
Six different values of thermal time lag are selected from 6 hours to 16 hours. The cooling load test (Table
4.39) shows the annual cooling load drops with increasing thermal time lag. The line chart (Figure 4.25)
shows the pattern is same as it is in the thermal lag test in Chapter 7.2.1.1. It also shows the most significant
drop occurs between 6 hours and 10 hour lag time. The line then starts to flatten from 10 hours to 16 hours.
Based on the annual temperature, Miami and Phoenix have the highest cooling load since they have the
warmest climate type among all the climate zones.
6 8 10 12 14 16
Miami 4538 3379 2798 2492 2290 2164
Phoenix 4713 3455 2883 2577 2373 2245
Los Angeles 2609 1736 1272 1043 907 829
Seattle 1420 897 626 494 414 369
Pittsburgh 2268 1455 1096 925 821 760
Minneapolis 2325 1532 1096 930 835 778
Fargo 2132 1375 940 764 673 621
Figure 4.24, total load (kWh) of different material types in seven climate zones
106
Table 4.42 thermal lag (hours) in different climates effect on annual cooling load (kWh)
The heating load test (table 4.40) has very similar pattern as the cooling load test. The line chart (Figure
4.26) shows the heating load drops with increasing thermal time lag. The most significant drop also occurs
between 6 hours and 10 hours. The heating load of Miami is much lower compared with other cities. This is
caused by its low demand on annual heating. The average temperature in Miami is higher than the indoor
setting temperature (25 Celsius).
6 8 10 12 14 16
Miami 1317 597 328 217 155 124
Phoenix 2800 1725 1334 1144 1026 956
Los Angeles 3556 2365 1732 1421 1236 1130
Seattle 6826 5250 4360 3873 3551 3349
Pittsburgh 7257 5414 4481 3987 3664 3460
Minneapolis 9281 7124 5877 5268 4872 4618
Fargo 10701 8297 6873 6145 5680 5384
Table 4.43 thermal lag (hours) in different climates effect on annual heating load (kWh)
Figure 4.25 thermal lag (hours) in different climates effect on annual cooling load (kWh)
107
The annual total load (table 4.40) also shows the similar pattern. From the line chart (figure 4.27), the total
load drops with increasing thermal time lag value. The drop is more significant from 6 to 10 hours lag. The
line then smoothly flattens after a 10 hour thermal lag. Miami and Los Angeles have the lowest annual
energy load among these cities. This is because the annual average temperature of both cities is close to the
indoor setting temperature. Less air conditioning is required in both cities.
6 8 10 12 14 16
Miami 5855 3976 3127 2709 2445 2288
Phoenix 7513 5181 4217 3720 3400 3202
Los Angeles 6165 4101 3004 2464 2143 1959
Seattle 8246 6147 4986 4367 3966 3718
Pittsburgh 9525 6869 5577 4912 4485 4220
Minneapolis 11607 8656 6974 6197 5707 5396
Fargo 12833 9671 7813 6908 6353 6006
Table 4.44 thermal lag (hours) in different climates effect on annual total load (kWh)
Figure 4.26 thermal lag (hours) in different climates effect on annual heating load (kWh)
Figure 4.27 thermal lag (hours) in different climates effect on annual total load (kWh)
108
4.3.3. HVAC setting temperature effects on energy performance
Heating and cooling system setting is the most import factor for HVAC system energy performance. This is
simply because it direct controls the energy output and efficiency of the system. Except for the known fact
that a system with higher efficiency saves more energy, the indoor setting temperature and controller
temperature offset are also important factors that can affect total energy load. By adjusting small values of
indoor setting temperature or temperature offset can cause significant changes in the annual energy load in
different climates. For example, switching in the indoor setting temperature from 25 Celsius to 26 Celsius,
bring the cooling or heating one degree higher. This means the working condition for heating and cooling
system has changed throughout a year. This is crucial change for the HVAC energy output.
Instead of testing cooling and heating system capacity and COP on energy performance, this test will use
indoor setting temperature and controller temperature offset. This is because the test of capacity and COP
will exceed the calculation limits of the Excel tool, and it will make the results inaccurate. Based on the
model and Excel spreadsheet calculation method (FFE), the sufficient value of heating/cooling capacity and
COP has very narrow range. Changing heating and cooling capacity has reached the range of the model. For
example, once cooling load is not sufficient to balance the heat energy from outside, the room will keep
increasing its own temperature and became extremely hot. The same condition occurs in the cooling system.
This means although the air conditioner is on 24/7 it cannot control the temperature of the room because the
energy flow from outside environment is too much for the air conditioner to handle. The study becomes
pointless in this situation.
4.3.3.1. Indoor setting temperature effect on energy performance in different climates
By using the base model setting, the indoor setting temperature cooling load test uses 10 different value of
indoor setting temperature from 15 Celsius to 25 Celsius in each climate zone (Table 4.42). The test
material is concrete block due to its common use in construction and its high thermal mass. The line chart
(Figure 4.28) shows linear relationship between indoor setting temperature and cooling load. With
increasing indoor setting temperature, the annual cooling load drops in all climate zones. The drop rate is
similar in each climate zone, which is about 300 kWh every 1 degree indoor setting temperature increasing.
The drop of cooling load is significant. For example, Miami, a city require lots of cooling, raises its indoor
setting temperature from 15 Celsius to 25 Celsius. The annual cooling load drops from 6699 kWh to 2971
kWh, which is 3728 kWh. The drop rate is 56%. Seattle has even higher drop rate of 69%.
109
15 16 17 18 19 20 21 22 23 24 25 Rate
Miami 6699 6301 5904 5509 5118 4731 4352 3984 3630 3292 2971 56%
Phoenix 6144 5789 5442 5106 4780 4464 4159 3865 3583 3312 3054 50%
Los Angeles 4123 3776 3443 3123 2819 2534 2270 2025 1800 1595 1408 66%
Seattle 2311 2087 1877 1682 1503 1339 1189 1051 925 810 706 69%
Pittsburgh 3114 2874 2645 2425 2215 2017 1829 1654 1489 1337 1196 62%
Minneapolis 2950 2734 2524 2323 2131 1948 1778 1621 1473 1336 1210 59%
Fargo 2573 2376 2187 2012 1847 1692 1550 1418 1293 1174 1062 59%
Table 4.45 cooling load (kWh) in different cities by change indoor temperature setting (Celsius)
The heating load test (Table 4.43) also shows linear relationship between indoor setting temperature and
annual heating load. The increasing of heating load is more significant than the cooling load. The line chart
(Figure 4.29) shows the heating rises with increasing indoor setting temperature. The line slope of Seattle,
Pittsburgh, Minneapolis and Fargo are very similar. The curves from Miami, Phoenix and Los Angeles are
more bended because the heating load is extreme low in these cities.
15 16 17 18 19 20 21 22 23 24 25 Rate
Miami 8 13 19 28 42 62 93 139 204 290 400 4643%
Phoenix 185 247 322 412 514 631 762 908 1072 1250 1446 684%
Los Angeles 148 223 315 426 559 717 904 1117 1357 1626 1918 1192%
Seattle 1351 1592 1853 2133 2436 2759 3102 3461 3836 4226 4631 243%
Pittsburgh 1902 2122 2357 2603 2864 3140 3431 3738 4061 4401 4756 150%
Minneapolis 3142 3394 3654 3927 4211 4508 4823 5156 5501 5861 6236 98%
Fargo 3893 4170 4459 4767 5089 5424 5777 6143 6520 6903 7298 87%
Table 4.46 heating load (kWh) in different cities by change indoor temperature setting (Celsius)
Figure 4.28 cooling load (kWh) in different cities by change indoor temperature setting (Celsius)
110
The annual total load (Table 4.44) is more complex. With increasing indoor setting temperature, both
increasing and decreasing of annual total load occur in all 7 climate zones. Annual total load of Miami,
Phoenix decreases with increasing of indoor setting temperature. Annual total load of Seattle, Pittsburgh,
Minneapolis and Fargo increases with increasing of indoor setting temperature. The annual load of Los
Angeles is the lowest and it bended with increasing indoor setting temperature. This can be explained with
heating or cooling demand in these climate zones. In Miami and Phoenix, due to their high annual average
temperature, cooling is more dominant than heating throughout a year. Therefore, increasing the indoor
setting temperature reduces the pressure on cooling. Vice versa, in Seattle, Pittsburgh, Minneapolis and
Fargo, heating is more dominant in a year. Decreasing the indoor setting temperature helps bring down the
annual heating load. In Los Angeles, the temperature is closer to the indoor setting temperature. The
demand of air conditioning is less.
The condition in real life is different from the test results. For example, in reality few people use heating in
winter in Miami. Sometimes, the heating load can be neglected in Miami. Same in Fargo there are very few
days in a year in Fargo need cooling. The actual cooling load in Fargo will be much less than the calculated
results.
Figure 4.29 heating load (kWh) in different cities by change indoor temperature setting (Celsius)
111
15 16 17 18 19 20 21 22 23 24 25
Miami 6708 6314 5923 5537 5159 4793 4445 4123 3834 3582 3372
Phoenix 6329 6036 5764 5518 5295 5095 4921 4773 4656 4562 4501
Los Angeles 4271 3999 3759 3550 3378 3250 3174 3141 3157 3221 3327
Seattle 3661 3679 3730 3815 3940 4098 4290 4512 4761 5036 5336
Pittsburgh 5015 4996 5002 5029 5079 5156 5260 5392 5550 5738 5952
Minneapolis 6092 6129 6179 6250 6342 6456 6601 6777 6973 7197 7446
Fargo 6467 6546 6646 6779 6936 7115 7327 7561 7813 8077 8360
Table 4.47 total load (kWh) in different cities by change indoor temperature setting (Celsius)
4.3.3.2. Controller temperature offset effect on energy performance in different climates
The other important factor in heating and cooling system setting is the ‗controller temperature offset‘.
According to the HVAC system control loop (Chapter 4.3.2), the controller temperature offset determines
what temperature to start heating or cooling. The purpose of this test is to explore the optimum temperature
offset in certain climates with setting conditions. The tests will examine the controller temperature offset
energy performance in particular and in all climate zones. It will follow the base model setting. In the tests,
the test material is concrete block. The thickness is 0.2 meters, and the thermal time lag of the concrete
block is 9.26 hours.
The first test will use 10 different values of controller temperature offset in Los Angeles (Climate zone 3).
The controller temperature offset test results (Table 4.45) shows with increasing offset temperature, the
annual cooling, heating and total load all drops. The line chart (Figure 4.31) shows the most significant drop
occurs between 1 Celsius and 1.5 Celsius. Then the energy load starts to flatten after 2 Celsius. This applies
Figure 4.30 total load (kWh) in different cities by change indoor temperature setting (Celsius)
112
to all annual cooling, heating and total load. This means under base model circumstance, for a 0.2 meter
concrete block in Los Angeles, temperature offset bigger than 2 Celsius is the most energy efficient value
for such model and air conditioner combination. The most efficient temperature offset value can be varied
depends on settings.
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Cooling 1806 1489 1414 1411 1408 1405 1402 1399 1396 1393
heating 2461 2028 1927 1923 1918 1914 1910 1905 1902 1897
total 4266 3517 3341 3334 3327 3319 3312 3304 3298 3290
Table 4.48 annual load (kWh) by changing air conditioner offset temperature (Celsius) in Los Angles
The following tests uses 10 different values of controller temperature offset in all 7 climate zones. A city is
selected in each climate zone. The purpose of the tests is to explore the controller temperature offset effect
on energy load in different climate zones.
In the annual cooling test (Table 4.46), the result from all climate zones shows very similar patterns as it is
in Los Angeles. The most significant drop occurs between 1 Celsius and 2 Celsius. The line chart (Figure
4.32) shows the annual cooling load reduces with increasing controller temperature offset temperature. The
only slight disturbance of the pattern occurs between 1.5 Celsius and 3 Celsius in Minneapolis, Pittsburgh
and Fargo.
Figure 4.31 annual load (kWh) by changing air conditioner offset temperature (Celsius) in Los Angles
113
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
1 3497 3584 1806 1085 1749 1830 1689
1.5 3134 3307 1489 845 1516 1551 1414
2 2976 3146 1414 728 1378 1408 1261
2.5 2973 3056 1411 707 1254 1324 1180
3 2971 3054 1408 706 1196 1210 1062
3.5 2969 3053 1405 704 1194 1169 992
4 2966 3052 1402 702 1192 1166 988
4.5 2964 3049 1399 700 1190 1165 986
5 2962 3048 1396 698 1189 1164 985
5.5 2960 3046 1393 696 1187 1163 983
Table 4.49 annual cooling load (kWh) in different climate zones
In the annual heating load test (Table 4.47), the results also shows similar pattern in all climate zones. The
line chart (Figure 4.33) shows the annual heating load reduces with increasing controller temperature offset.
Like the cooling load test, the most significant drop occurs between 1 Celsius and 2 Celsius.
Figure 4.32 annual cooling load (kWh) in different climate zones
114
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
1 1119 2170 2461 5148 5510 7082 8153
1.5 623 1791 2028 4820 5193 6701 7779
2 407 1572 1927 4661 5003 6506 7570
2.5 403 1449 1923 4633 4834 6392 7458
3 400 1446 1918 4631 4756 6236 7298
3.5 397 1444 1914 4628 4753 6179 7202
4 394 1443 1910 4625 4750 6176 7196
4.5 391 1440 1905 4622 4747 6175 7194
5 388 1437 1902 4620 4745 6173 7192
5.5 385 1435 1897 4617 4743 6171 7190
Table 4.50 annual heating load (kWh) in different climate zones
In the annual total load test (Table 4.48), the results also shows similar pattern overall with annual cooling
and heating loads. In warmer cities, including Miami, Phoenix and Los Angele, the optimum temperature
offset is about 3.5 Celsius, while in colder cities the optimum temperature offset is about 2 Celsius. These
facts demonstrate the influence of controller temperature offset is very similar in different climate zones.
The influence is slightly more effective in warmer climates than in colder climates.
Figure 4.33 annual heating load (kWh) in different climate zones
115
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
1 4616 5754 4266 6233 7258 8911 9842
1.5 3757 5098 3517 5665 6709 8251 9193
2 3383 4718 3341 5389 6381 7914 8831
2.5 3376 4505 3334 5340 6088 7716 8638
3 3372 4501 3327 5336 5952 7446 8360
3.5 3366 4497 3319 5332 5948 7348 8194
4 3361 4494 3312 5327 5942 7342 8184
4.5 3356 4489 3304 5322 5938 7340 8180
5 3350 4485 3298 5318 5934 7337 8177
5.5 3344 4480 3290 5313 5930 7334 8173
Table 4.51 annual total load (kWh) in different climate zones
4.3.4. Environmental factors effects on energy performance
There are numbers of environmental factors that have influence on thermal performance of a wall system.
In this section, the tests will focus on the environmental factors used in the Excel tool. This includes
emissivity, environment radiant temperature and convection factors. According to the parameters
introduction (chapter 5.2.1), emissivity is the material ability to emissive radiant energy, which depends on
the surface condition. Environment radiant temperature is the radiant temperature from surrounding objects.
The convection factor is the material‘s ability to transfer heat through conduction, which depends on wind
speed.
The test will use the base model settings. It uses Los Angeles weather data. The selected material is concrete
block with 0.2 meter width.
Figure 4.34 annual total load (kWh) in different climate zones
116
In the emissivity test, 10 different values of emissivity are selected from 0% to 100% (table 4.49). The
higher value of emissivity means the wall system emissive more radiant energy into the surrounding
environment. Therefore, it reduces building heat gain and the annual cooling load. The result follows this
pattern and it shows linear relationship between emissivity and energy load. In the line chart (Figure 4.35),
the annual heating load increases, and the annual cooling load decreases with emissivity level. The total
energy load slightly decreases with increasing emissivity.
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Cooling 2997 2726 2479 2255 2052 1868 1700 1548 1408 1281 1164
heating 933 1042 1156 1274 1397 1523 1653 1785 1918 2053 2188
total 3930 3768 3634 3529 3449 3391 3353 3332 3327 3334 3352
Table 4.52 energy load (kWh) by changing emissivity
The environment radiant temperature is the radiant temperature from the surrounding objects. According to
the radiation heat transfer equation (equation 4.1), the environment radiant temperature can either be the
higher temperature (TH) or the lower temperature (TL). This depends on the wall surface temperature. The
environment radiant temperature directly affects model‘s emissive energy to the surrounding environment.
Equation 4.1
The environment radiant temperature has significant effect on annual energy load. In the test, the higher
value of environment radiant temperature means the wall is more possible to absorb radiant heat from the
surrounding environment. 10 different values are selected from 0 Celsius to 100 Celsius (Table 4.50). The
line chart (Figure 4.36) shows the cooling load increasing significantly with increasing environment radiant
temperature. The annual cooling load increases about 9000 kWh with increasing 100 Celsius environment
radiant temperature. The annual heating load drops dramatically and reaches zero around 80 Celsius
Figure 4.35 energy load (kWh) by changing emissivity
117
environment radiant temperature. Also, the annual total load increases because of the large amount of
cooling load.
0 10 20 30 40 50 60 70 80 90 100
Cooling 1408 1725 2139 2676 3359 4192 5194 6345 7608 8978 10455
heating 1918 1443 1000 621 331 129 32 10 5 5 4
total 3327 3168 3140 3297 3690 4321 5226 6354 7613 8984 10459
Table 4.53 energy load (kWh) by changing environment radiant temperature (Celsius)
The convection factor affects the convection heat transfer between outside air and wall surface. Convection
heat transfer is the only heat exchange process between wall and outside air (Chapter 5.2.3). The value of
convection factor directly affects model heat gain or loss. The convection factor for building heating
transfer depends on the wind speed. According to the air convection factor equation (equation 4.2,
simplified equation), the wind speed and the convection factor can be observed from the figure (Figure
4.37). From wind speed 1 m/s to 10 m/s, the convection factor increases from around 20 W/(m2•K) to 30
W/(m2•K).
Equation4.2
http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html
Figure 4.36 energy load (kWh) by changing environment radiant temperature (Celsius)
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In the convection factor test (Table 4.51), 10 different values of convection factor are selected from 20
W/(m2•K) to 30 W/(m2•K). The corresponding wind speed is from approximately 1m/s to 10m/s. The
higher value of convection factor the more heat loss takes place in the wall through convection heat transfer.
The line chart (Figure 4.38) shows the cooling load reduces and the heating load increases with growing of
convection factors. However, the slope shows the variation of both cooling and heating load is small, and
the total energy load almost stays constant. This shows the energy load has low sensitivity level at wind
speed up to 10 m/s.
20 21 22 23 24 25 26 27 28 29 30
Cooling 1297 1226 1161 1100 1044 993 946 902 861 824 788
heating 1992 2041 2089 2134 2179 2222 2263 2303 2342 2380 2416
total 3289 3268 3250 3234 3224 3215 3210 3206 3203 3203 3204
Table 4.54 energy load (kWh) by changing outside convection factor h (W/(m2•K))
Figure 4.37 air convection factor (W/(m2•K)) in different wind speed m/s
Figure 4.38 energy load (kWh) by changing outside convection factor h (W/(m2•K))
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4.3.5. Energy performance conclusion and discussion
It is important to point out that all the test condition is based on specific ‗base model setting‘ from Excel
tool, which in this case is a sealed model without any natural ventilation. The air conditioner in this base
model is running 24/7 throughout the entire year. The setting can actually be varied by the tester for
different research purposes. The tests already done are for research of the various parameters influence on
HVAC system energy load. There is a big gap between test condition and real life conditions. In reality, the
air conditioner may only run half time of a year for domestic use. The different types of heating system can
also lead to vary different annual heating load. For example, by using cheap natural gas powered heating
system, the COP can be lower than electric heating system. If a geothermal heat pump is applied into the
model, the heating load will be using geothermal power, which reduces the energy usage. It is important to
see these results from both testing and real condition.
The change of test settings will have tremendous effect on the results. For example, in this test conductivity
shows greater effect on energy load than density and specific heat. But once uses night flush in a climate
type with big daily temperature swing, the cooler air during night will cool down the wall. The heavier
material such as concrete block will have the ability to store more energy on the next day. In this case, wall
built with high conductivity means its temperature curve is closer to the outside curve and it is less useful
using nature ventilation as its passive strategy.
Material property test
In the material property test, conductivity, density and specific heat all show notable effect on annual
energy load. But conductivity shows more significant effect in the thermal time lag test despite of other
independent material properties. This means the annual energy load is slightly more sensitive to material
conductivity.
Thermal time lag test
In the ‗8 hours lag in different climate zones‘ test,
In the different thermal lag in different climate zone test, annual cooling, heating and total load shows
similar pattern, this is close to the result in thermal time lag test in chapter 7.2.1.1. The energy load drops
with increasing thermal time lag in all climate zones. The most significant drop occurs between 6 to 10
hours lag. Considering the material cost for a thicker wall, energy wise this could mean the most efficient
thermal time lag is between 6 to 10 hours lag for concrete block in those climate zones.
120
HVAC setting test
The indoor setting temperature test shows linear relationship between annual heating/cooling load and
indoor setting temperature. The indoor setting temperature has dramatic influence on both annual heating
and cooling load. For example, in Seattle the cooling load reduces from 6699 kWh to 2971 kWh with
increasing 10 Celsius indoor setting temperature. The decreasing rate is 56%. The effect is also different in
different climate zones. For example, when increasing 1 Celsius of indoor temperature in a hot climate,
increasing of heating load is more significant than reduction of cooling load. In cold climate, where
heating system is more dominant, the annual heating load is more sensitive to the change of indoor setting
temperature.
The controller temperature offset test shows the energy load variation is similar in all 7 climate zones
with increasing values of controller temperature offset. The effect is slightly more effective in warmer
than in colder climate zones. The most significant drop occurs between 1 and 2 Celsius in cold cities and
between 1 and 4 Celsius in cold cities. This indicates the optimum temperature offset is between 2 Celsius
to 4 Celsius depends on the climate types.
Environmental factors test
The environmental factors test uses three different the environmental factors that have been added into the
Excel tool. This includes emissivity, environment radiant temperature and convection factor. The
emissivity test shows increasing heating load and decreasing cooling load, because the model has higher
radiant heat loss with increasing emissivity. However, the total energy load does not has significant change.
The environment radiant temperature test shows significant increasing of cooling load and decreasing of
heating load with increasing value of environment radiant temperature. The heating load is about 0 kWh
with 100 Celsius environment radiant temperature. The higher value of environment radiant temperature
means more radiant heat gain from surrounding environment. The results are close to expectation.
In the convection factor test, although convection heat transfer is the only heat transfer process occurs
between outside air and wall surface, the results shows mild influence of convection factors. The results
show decreasing cooling load and increasing heating load with increasing values of convection factors.
However, with different settings, such as model size and HVAC system, it may have different results.
121
4.4. Economic evaluation
Economic evaluation is helpful to assess the worth of installing a certain type of wall or air conditioning
system. In reality, there are plenty of costs that are related to wall or energy systems. Material wise, there
are material purchases, transportation, labor, maintenances cost etc. Energy system wise, there are energy
costs, distribution system, model purchases, installation, maintenances cost etc. There are also plenty of
other related costs have not been mentioned. All these factors affect the financial expenditure for a house
holder. A professional financing economic evaluation will examine all these factors with certain standards
and equations. The results help with the selection of optimum HVAC system and envelope system in
respect of their initial and lifespan costs.
The design objective of the Excel tool is not only to explore the energy performance of a wall system, but
also to find its economic value. With various factors input, the tool is able to simulate the model with
different settings. The energy bills vary with different energy performance. For example, moving a wall
system from Miami (Climate zone 1) to Fargo (Climate zone 7), the annual cooling load drops while the
annual heating load increases dramatically. The energy cost depends on the performance of the heating and
cooling system and the energy source. Even with large amount of heating load, the total cost can still be low
if the heating system uses an efficient and cheap energy source like natural gas (for a furnace). The selection
of material also has crucial effects on material cost. A well-insulated wood block, which is usually
expensive depending on types, can be a great choice of exterior wall material based on its high thermal mass,
low conductivity and natural appearance. The great energy performance lowers the energy bill, but the high
material price raises the initial cost. In comparison, concrete block also has great thermal mass features, but
with lower material cost. These are two reasons that concrete block is such a popular construction material
in general (Amanda Partridge, 2012).
The economic evaluation in this section will focus on the simulation on material cost and energy cost. The
cost of labor, transportation, maintenance and other factors that are not related with model energy
performance will not be included in the tests. Based on the energy performance study (Chapter 7.2), the
Excel tool shows potential to assess the cost of material usage and energy source by adjusting different
material and environmental parameters. The tests done (Chapter 7.2) indicates the annual cooling and
heating load changes significantly with different HVAC, climates and environmental settings. The different
thicknesses and selections of material consume different usage of construction material. The cost efficiency
of different settings is able to be evaluated based on different energy sources and material prices. The
relationship between energy performance and total cost is also worth to be explored in this section.
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4.4.1. Economic value varies with different types of heating system
The selection of cooling and heating system is important for both energy performance and cost. This
includes fuel types, heating and cooling system capacity, COP (or efficiency) and various temperature
settings. For example, in the test of energy performance with different HVAC settings (chapter 7.2.3),
different indoor setting temperature and controller temperature offset have significant effects on both
heating and cooling load in different climate zones. The tests show the HVAC setting has notable influence
on energy output. The tool is unable to test the influence of heating and cooling capacity, because the
current version of Excel tool (Chapter 5.3.2) auto-calculates the cooling and heating capacity by the annual
temperature profile from weather data. In this section, tests will be conducted with different types of heating
system and COP value in order to explore their relationship with the energy cost.
The test will only focus on different types of heating system using electricity or natural gas, rather than
switching the whole HVAC system. This is because most HVAC air conditioning (or cooling system) uses
refrigeration cycle, which only consumes electricity. Heating system category has more diversity
depending on types and energy sources. There is notable price difference between natural gas and
electricity. According to the energy price in Los Angeles area (http://www.bls.gov/, 2015), in October 2015
the average electricity price is 21.3 cents per kilowatt hour (kWh), while the natural gas price is $1.253 per
therm. The tests will use this as energy source cost (table 4.52).
Original price (USD) Converted into kWh (USD)
Natural gas $0.213/kWh $0.213/kWh
Electricity $1.253/therm $0.043/kWh
Table 4.55 cost of electricity and natural gas (USD) in Los Angeles area in October 2015
Ref: http://www.bls.gov/regions/west/news-release/averageenergyprices_losangeles.htm
There are two types of heating system, direct heating and central heating. Central heating system includes
furnace, boiler and heat pump system, while direct heating is small sized space heater using electricity or
heating fuel for small size room (Tony Atkins, Marcel Escudier, 2013). It usually has poor efficiency and
requires natural ventilation. Furnace and boiler can both be electric powered or natural gas powered.
Although gas powered heater costs less on energy bill, it required ventilation facility to drive off the
byproduct from insufficient combustion. Heat pump is a reversed air conditioner which uses electricity. The
COP of heat pump is higher than furnace and boiler, because it can deliver more heat than consumed
electricity. The ground source heat pump (GSHP) is considered a sustainable system because most of the
heat comes from the ground (Tony Atkins, Marcel Escudier, 2013). It is usually used in cold climates where
it requires large amount of annual heating. However heat pump has a finite temperature range. Once the
exterior temperature drops too low, a pre-heat must be added, which requires extra energy.
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4 different types of heater are selected for the test (Table 4.53), including 2 types of electricity powered
heater and 2 types of natural gas powered heater. The operating performance information is from the
manufacture specifications. The first heater is electricity powered space heater (direct heating). The second
heater is air-source heat pump uses electricity (central heating). The third and fourth heaters are natural gas
powered furnace and boiler (central heating). The efficiency of these heaters has been transferred into
equivalent COP for the calculation convenience in Excel tool. The cooling system setting is same in all four
types of heater.
Type Power source Module Efficiency Equivalent COP
1 Electric space heater Electricity
Duraflame
SKU#DFL1025
68% 0.68
2 Air source heat pump Electricity
LG Art Cool Premier
LS090HYV
GSHP:
12
3.5
3 Natural gas furnace Natural gas
Goodman
GDS80403AX
AFUE:
80%
0.8
4 Natural gas boiler Natural gas
Rinnai E50CN
Condensing Boiler
AFUE:
95.6%
0.956
Table 4.56 specifications of different heaters (Appendix C)
The test results include the annual energy source cost and annual heating load. Before conducting the tests,
the other input settings are determined as base model setting (Table 4.54). This includes environmental,
HVAC, climate zone and room settings. The simulated located is set in Los Angeles (Climate zone 3). Two
types of construction material with same thickness (0.2 meter) will be tested, which is concrete block and
wood block (Table 4.55)
Environment setting
Symbol Unit Value
Convection indoor hin W/(m2•K) 8.7
Convection outdoor hout W/(m2•K) 18.6
Wall Emissivity Epsilon N/A 80%
Surrounding Radiant temperature Tradout Celsius 0
Solar Absorption As N/A 0.2
HVAC setting
Cooling COP η1 N/A 4.8
Indoor temperature Tin Celsius 25
Controller temperature offset DeltaT Celsius 3
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Room setting
Conditioned area Area m2 50
Roon height H m 2.5
Room volume Vr m3 125
Roof/wall area Aroof m2 120.71
Table 4.57 base model setting
Thermal conductivity Density Specific heat thickness
Concrete block 0.51 W/(mK) 1400 kg/m3 1000 J/(kgK) 0.2 meter
Wood block 0.16 W/(mK) 1050 kg/m3 837 J/(kgK) 0.2 meter
Table 4.58 test material properties
Test 1: Concrete block annual energy cost
The first test material is concrete block. The annual heating load (table 4.56) increases with colder climate
zones. The annual heating load is transferred into annual heating cost (table 4.57). The line chart (figure
4.39) shows the annual heating cost increases in colder climates. By adding the cooling load (table 4.40),
which is same for different heaters, the annual total load (table 4.58) increases with climate zones. The
annual total load is transferred into annual total energy cost (table 4.59). The line chart (figure 4.40) shows
the annual heating cost also increases with climate zones (from hot to cold), except for Los Angeles. This
has the same reason as the climate zone test (chapter 4.2.2). The annual average temperature of Los Angeles
is close to the indoor setting temperature, which is 25 Celsius.
Among 4 types of heaters, the electric space heater has much higher annual heating cost than the other types.
This is because the electric space heater is designed for small space heating. It has much lower efficiency
compared with other heaters. It is not energy efficient for large space like the model (50 square meter). The
air source heat pump, although has the least annual energy consumption, has higher energy cost than natural
gas heaters. This is because the electricity price is much higher than the natural gas price. The natural gas
boiler has higher efficiency than natural gas furnace. Therefore, the annual energy cost is less than natural
gas furnace.
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 2071 7479 9919 23943 24589 32242 37733
Air source heat pump 400 1446 1918 4631 4756 6236 7298
Natural gas furnace 1760 6357 8431 20351 20901 27405 32073
Natural gas boiler 1473 5320 7056 17030 17490 22933 26839
Table 4.59 annual heating load (kWh) for different heating systems
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Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 441 1593 2113 5100 5238 6867 8037
Air source heat pump 85 308 409 986 1013 1328 1554
Natural gas furnace 76 273 363 875 899 1178 1379
Natural gas boiler 63 229 303 732 752 986 1154
Table 4.60 annual heating energy cost (USD) for different heating systems
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Cooling load (kWh) 2971 3054 1408 706 1196 1210 1062
Cooling cost (USD) 633 651 300 150 255 258 226
Table 4.61 annual cooling load (kWh) and cost (USD)
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 5042 10534 11328 24649 25785 33451 38795
Air source heat pump 3372 4501 3327 5336 5952 7446 8360
Natural gas furnace 4731 9412 9840 21057 22097 28615 33135
Natural gas boiler 4444 8374 8464 17736 18686 24143 27901
Table 4.62 annual total load (kWh) for different heating systems
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 1074 2244 2413 5250 5493 7125 8263
Air source heat pump 718 959 709 1136 1268 1586 1780
Natural gas furnace 709 924 663 1025 1154 1436 1605
Natural gas boiler 696 880 603 882 1007 1244 1380
Table 4.63 annual total energy cost (USD) for different heating systems
Figure 4.39 annual heating energy cost (USD) for different heating systems
126
Test 2: Wood block annual energy cost
The second test material is wood block, which is exactly the same as the test for concrete block. The annual
heating load (table 4.61) increases with colder climate zones. The annual heating load is transferred into
annual heating cost (table 4.62). The line chart (figure 4.41) shows the annual heating cost increases with
climate zones (from hot to cold). By adding the annual cooling load (table 4.63), the annual total load (table
4.64) is transferred into annual total energy cost (table 4.65). The line chart (figure 4.42) shows the annual
energy cost is much higher in Miami and Phoenix than in the concrete block test. The energy cost drops at
Los Angeles, and then increase with climate zones.
The increase of energy cost in Miami and Phoenix is caused by reduction of annual heating load. The wood
block consumes much less heating load than concrete block. The difference between concrete block and
wood block test can be explained by their material properties (Table 4.55). The density and specific heat of
wood block is much less than concrete block. However, the conductivity of wood block is much lower than
concrete block. The huge reduction on heating demand is caused by low conductivity of wood block.
According to the material property test (chapter 4.2.1), the conductivity has significant effect on energy
performance under base model setting.
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 184 2376 2685 8480 8830 11864 13837
Air source heat pump 36 462 522 1648 1715 2305 2688
Natural gas furnace 156 2019 2282 7208 7505 10085 11762
Natural gas boiler 131 1690 1910 6032 6280 8439 9843
Table 4.64 annual heating load (kWh) for different heating systems
Figure 4.40 annual total energy cost (USD) for different heating systems
127
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 39 506 572 1806 1881 2527 2947
Air source heat pump 8 98 111 351 365 491 573
Natural gas furnace 7 87 98 310 323 434 506
Natural gas boiler 6 73 82 259 270 363 423
Table 4.65 annual heating cost (USD) for different heating systems
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Cooling load 1061 1107 1408 149 352 366 283
Cooling cost 226 236 300 32 75 78 60
Table 4.66 annual cooling load (kWh) and cost (USD)
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 1245 3483 3060 8629 9182 12230 14121
Air source heat pump 1097 1569 897 1796 2068 2671 2972
Natural gas furnace 1217 3127 2658 7357 7857 10450 12045
Natural gas boiler 1192 2797 2285 6181 6633 8805 10126
Table 4.67 annual total load (kWh) for different heating systems
Miami Phoenix Los Angeles Seattle Pittsburgh Minneapolis Fargo
Electric space heater 672 1157 872 1956 2136 2785 3173
Air source heat pump 641 749 411 501 620 749 799
Natural gas furnace 640 738 398 460 578 692 732
Natural gas boiler 639 724 382 409 525 621 649
Table 4.68 annual total energy cost (USD) for different heating systems
Figure 4.41 annual heating cost (USD) for different heating systems
128
4.4.2. Economic value varies with different material cost
The change of wall material or its thickness not only varies the energy performance of the model, but also
the cost of material itself. For example, assuming the wall and roof area is 120 square meter. With
increasing 0.1 meter wall thickness, the increasing amount of material is 12 cubic meters. This could be
considerably big expenses if the construction material has high price. Meanwhile, the increasing of wall
thickness also has better energy performance. This has been tested in Chapter 4.2.12. It decreases the annual
heating and cooling load, as well as the energy cost. The total cost varies with both material selection and
energy settings.
Five most common types of construction material are selected for the test (table 4.66). The cost of material
by its weight and volume are listed (Table 4.66). The material manufacture information is from the internet,
selected from the most common price (Appendix D). Among these material types, concrete block is the
cheapest one. Wooden material has the most variable price range depending on different types of timber.
There are very few exterior walls are constructed with pure wood. The laminated veneer lumber (LVL) is a
construction multiple layer wood piece that usually used as beams based on its high strength. The price of
laminated veneer lumber is in reasonable range. The select of plastic wall material is only for the purpose of
research. There is no plastic exterior wall. The selected plastic material is recycled plastic.
Figure 4.42 annual total energy cost (USD) for different heating systems
129
Building materials Thermal conductivity Density Specific heat Cost by Weight Cost by Volume
W/(mK) kg/m3 J/(kgK) Ton Cubic meter
Cement layer 0.36 700 1050 N/A $185/m3
Concrete block 0.51 1400 1000 $75/ton N/A
Brick block 0.62 1800 840 N/A $574/m3
Wood block 0.16 800 2093 N/A $1103/m3
Plastic board 0.5 1050 837 $850/ton N/A
Table 4.69 test material properties
The test will first calculate the material cost in different thicknesses. It will then calculate the energy cost in
different thickness. The test location is Los Angeles (climate zone 3). The test conducts under base model
setting (table 4.67). The cooling and heating system is selected as ductless split heat pump system. The
environment, HVAC and room settings are same as the based model in the energy source cost test.
Environment setting
Symbol Unit Value
Convection indoor hin W/(m2•K) 8.7
Convection outdoor hout W/(m2•K) 18.6
Wall Emissivity Epsilon N/A 80%
Surrounding Radiant temperature Tradout Celsius 0
Solar Absorption As N/A 0.2
HVAC setting
Module name LG Art Cool Premier LS090HYV
Type ductless split heat pump system
Cooling COP η1 N/A 4.8
Heating COP η2 N/A 3.512
Indoor temperature Tin Celsius 25
Controller temperature offset DeltaT Celsius 3
Room setting
Conditioned area Area m2 50
Roon height H m 2.5
Room volume Vr m3 125
Roof/wall area Aroof m2 120.71
Table 4.70 base model setting
11 different thicknesses of the wall are selected from 0.15 meter to 0.4 meter. The weight (table 4.68) and
volume (table 4.69) of the material are calculated based on material properties. The cost of material can also
be calculated using material price by weight or volume (table 4.70). The line chart (Figure 4.43) shows the
130
increasing rate of material cost varies with different material types. The wood material is the most
expensive while the concrete block is the lowest on cost.
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 12.7 14.8 16.9 19.0 21.1 23.2 25.3 27.5 29.6 31.7 33.8
Concrete block 25.3 29.6 33.8 38.0 42.2 46.5 50.7 54.9 59.1 63.4 67.6
Brick block 32.6 38.0 43.5 48.9 54.3 59.8 65.2 70.6 76.0 81.5 86.9
Wood block 14.5 16.9 19.3 21.7 24.1 26.6 29.0 31.4 33.8 36.2 38.6
Plastic board 19.0 22.2 25.3 28.5 31.7 34.9 38.0 41.2 44.4 47.5 50.7
Table 4.71 material weight (Ton) in different thickness (meter)
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
All Material 18.1 21.1 24.1 27.2 30.2 33.2 36.2 39.2 42.2 45.3 48.3
Table 4.72 material volume (m3) in different thickness (meter)
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 3350 3908 4466 5025 5583 6141 6699 7258 7816 8374 8933
Concrete block 1901 2218 2535 2852 3169 3486 3802 4119 4436 4753 5070
Brick block 10393 12125 13858 15590 17322 19054 20786 22519 24251 25983 27715
Wood block 19972 23300 26629 29957 33286 36615 39943 43272 46600 49929 53258
Plastic board 16160 18853 21547 24240 26934 29627 32320 35014 37707 40400 43094
Table 4.73 material cost in different thickness (meter)
The energy performance of different material and thickness can be calculated using base model settings. By
using the Los Angeles weather data, the annual cooling load (table 4.71), heating load (table 4.72) and total
load (table 4.73) can be calculated for test material. The line chart (figure 4.44) shows, the annual energy
load drops with increasing thickness. The energy cost (electricity) can also be calculated with electricity
Figure 4.43 material cost in different thickness (meter)
131
price (table 4.74), since the heating and cooling system both uses electricity as its power. The line chart
(figure 4.45) shows the energy price drops with increasing thickness. The pattern is same as the energy load
results (Figure 4.44). The wood block has the least annual energy load and cost, while the plastic board has
the most annual load and cost. It shows the wood block has significant energy performance advantage upon
the test material types on same thickness.
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 2045 1674 1374 1132 941 792 676 590 522 471 433
Concrete block 2170 1736 1408 1163 985 855 760 691 637 593 557
Brick block 2471 2001 1640 1365 1162 1011 899 816 753 702 658
Wood block 551 440 376 332 299 273 251 232 216 202 190
Plastic board 2564 2129 1771 1480 1246 1058 911 796 706 638 584
Table 4.74 annual cooling load (kWh) in different thickness (meter)
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 2805 2297 1886 1555 1294 1089 931 813 720 651 598
Concrete block 2960 2368 1921 1587 1344 1167 1037 944 871 811 762
Brick block 3365 2722 2230 1857 1580 1374 1223 1110 1024 955 896
Wood block 760 608 520 460 415 379 350 324 303 284 268
Plastic board 3509 2914 2424 2026 1706 1450 1249 1092 969 876 803
Table 4.75 annual heating load (kWh) in different thickness (meter)
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 4850 3972 3260 2687 2235 1881 1607 1403 1242 1122 1031
Concrete block 5130 4104 3329 2750 2329 2021 1797 1636 1508 1405 1319
Brick block 5837 4723 3870 3222 2741 2385 2122 1926 1777 1657 1555
Wood block 1311 1048 895 791 714 652 601 557 519 486 458
Plastic board 6073 5044 4195 3506 2951 2508 2160 1888 1676 1515 1387
Table 4.76 annual total load (kWh) in different thickness (meter)
132
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 1033 846 694 572 476 401 342 299 265 239 220
Concrete block 1093 874 709 586 496 431 383 348 321 299 281
Brick block 1243 1006 824 686 584 508 452 410 378 353 331
Wood block 279 223 191 169 152 139 128 119 111 104 97
Plastic board 1294 1074 894 747 629 534 460 402 357 323 295
Table 4.77 annual energy source cost (USD) in different thickness (meter)
The first year total cost (table 4.75) can be calculated by adding material cost (table 4.70) and energy cost
(table 4.74). The total cost for five years and ten years span can also be calculated (table 4.70 and table 4.74)
by adding up annual energy cost.
The total cost difference among 1, 5 and 10 years span can be observed. For first year (figure 4.46), the
material cost is more dominant than the energy cost. The lines are straight, close to linear relationship. The
Figure 4.44 annual total load (kWh) in different thickness (meter)
Figure 4.45 annual energy source cost (USD) in different thickness (meter)
133
pattern is close to the material cost chart (figure 4.43). Wood material even thought with good energy
performance, cost more than other material because the material cost is much higher. Concrete block
remains the lowest on total cost.
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 4383 4754 5161 5597 6059 6542 7042 7557 8081 8613 9152
Concrete block 2994 3092 3244 3438 3665 3916 4185 4468 4757 5052 5351
Brick block 11636 13131 14682 16276 17906 19562 21238 22929 24629 26336 28046
Wood block 20251 23524 26819 30126 33438 36753 40071 43390 46711 50033 53355
Plastic board 17454 19928 22440 24987 27562 30161 32780 35416 38064 40723 43389
Table 4.78 annual total cost (USD), including material and energy cost
For fifth year (Figure 4.47), the lines begin to bend because of increasing influence by annual energy cost.
The difference can be observed on wood material. Between thickness of 0.15 meter and 0.175 meter, the
cost of plastic board surpasses wood. The energy cost (figure 4.47) shows plastic board has the highest
annual energy cost among the test material types. The curve of concrete block starts to bend by effect of
energy cost. The total cost is higher in low thickness range.
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 8515 8138 7938 7886 7963 8144 8411 8752 9139 9569 10031
Concrete block 7364 6588 6080 5781 5649 5638 5716 5861 6043 6249 6474
Brick block 16609 17155 17979 19022 20241 21594 23046 24570 26143 27748 29371
Wood block 21368 24417 27582 30800 34047 37309 40583 43865 47153 50447 53745
Plastic board 22628 24225 26015 27974 30077 32298 34621 37024 39492 42014 44571
Table 4.79 total cost for five years (USD), including material and energy cost
Figure 4.46 annual total cost (USD), including material and energy cost
134
For tenth year (figure 4.48), the influence of energy cost becomes more significant comparing with first
year (figure 4.46) This has obvious effect on wood material. At thickness of 0.15 meter, the cost of wood
block is same as brick block. Between the thickness of 0.15 meter and 0.225 meter, the cost of plastic board
is more than wood block. Besides, the bending of concrete block and cement layer becomes more
significant. The energy cost is much higher in the lower thickness range.
0.15 0.175 0.2 0.225 0.25 0.275 0.3 0.325 0.35 0.375 0.4
Cement layer 13680 12368 11410 10747 10344 10148 10122 10246 10462 10764 11128
Concrete block 12827 10959 9625 8710 8130 7791 7630 7603 7649 7745 7879
Brick block 22825 22185 22100 22453 23161 24134 25305 26622 28035 29513 31027
Wood block 22763 25533 28536 31643 34807 38003 41222 44458 47706 50965 54232
Plastic board 29096 29596 30483 31707 33220 34970 36921 39035 41276 43627 46049
Table 4.80 total cost for ten years (USD), including material and energy cost
Figure 4.47 total cost for five years (USD), including material and energy cost
Figure 4.48 total cost for ten years (USD), including material and energy cost
135
The relationship between cost and energy is always an issue of concern. It is necessary to explore whether
there is a perfect thickness which can save energy while spend least money. As a matter of fact, the results
of total cost over years and energy performance can be synergized into one chart with secondary axis. In
this way, the relationship can be observed in one chart with different thickness. Based on the first and tenth
year total cost and annual energy load results, dual-axis line charts are built for test material (Figure 4.49 to
figure 4.53). In the chart, the red line is the annual energy load, the green line is the first year cost and the
blue line is the tenth year cost of that material.
From the charts, the difference of life span cost among test material is obvious. For same material, the first
year cost is close to the material cost, while the tenth year is more affected by the annual energy cost. There
is a notable difference between first and tenth year‘s cost at small thickness. The red line shows energy
performance increasing with thickness of material. When material thickness is small, the energy cost
increasing with years. This causes the raise of cost at small thickness.
Thickness is more important for long term cost efficiency. The influence of energy cost increases with life
span of material. For example, using concrete block (figure 4.50) at tenth year, the most cost-efficient
thickness is around 0.275 meter. The most cost-efficient thickness for cement layer (figure 4.49) is around
0.25 meter. Following this trend, the most cost-efficient thickness will be higher if the life span is longer.
The only difference is wood block (figure 4.52), which has similar first and tenth year cost. This is cause by
its high material cost and good energy performance overall.
The purpose of the cost-energy chart is to provide a method to examine energy and cost efficiency in
multiple ways. The point of intersection between cost and annual load does not have special significance.
The cost-energy chart also provides a way to select material thickness under certain standard. For example,
the model uses brick block (figure 4.51). The energy code regulates a mandatory annual load bottom line,
which is 3000 kWh. The cost range will be selected after thickness of 0.225 meters.
136
Figure 4.49 cement annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter)
Figure 4.50 concrete block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter)
Figure 4.51 brick block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter)
137
4.4.3. Economic evaluation discussion
Energy source cost test
The results of energy cost among different heaters are close to expectation. The energy cost difference is
significant using different energy sources. Generally, electricity heaters have more heating cost than natural
gas heaters, because electricity cost more than natural gas. The electric space heater is neither energy or cost
efficient compared with other types of heater based on its design purpose for small-size room. The heat
pump although has higher COP and less energy consumption, the annual energy cost is still higher than gas
heaters. The two natural gas heaters have similar annual energy cost. The difference is caused by their
efficiency.
The selection of heater is also based on its utility. The test only examines the heaters from energy
performance point of view. In reality, there are also other factors like distribution system cost, model
purchases, installation, maintenances cost etc. The selection of heaters is more complicated this way. The
climate zones also have influence on heating system selection. For example, in warm states like Florida and
Arizona, electric heater and small-size direct heater are more popular. This is because the annual heating
Figure 4.52 wood block annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter)
Figure 4.53 plastic board annual load (kWh, primary axis) and annual total cost (USD, Secondary axis) in
different thickness (meter)
138
demand is low in both states, while the electric heater occupies less room than natural gas heater. The
installation of electric heater is also simpler. In cold state like Alaska, natural gas heater is more popular
because of large amount of annual heating demand (Craig Muccio, 2013).
Material and total cost test
The test of material and total cost shows the selection of material and its thickness has significant influence
on total cost and energy performance. (The results of material and thickness influence on model‘s energy
performance are explained in chapter 4.2.1) The material cost has more dominant effect on total cost in
short terms (first few years) (Figure 4.46), while the energy performance has more effect on total cost in
long terms (10+ years) (figure 4.48). The cost-energy charts show the relationship between total cost and
energy performance of test material. The chart helps with selection of cost-efficient material and thickness
under certain energy performance standards.
The test results provide the way to compare energy performance and cost of certain types of material. It is
also worth to explore the results using different setting and different material types. The results vary with
different cooling/heating system and different settings. For example, the energy cost of annual heating is
different if switching the heat pump to natural gas boilers. The annual load also varies with climate types,
environmental factors and room settings. These require future work on the different settings and material
types.
139
Chapter 5: Conclusions and future work
A simplified building energy simulation tool was designed by the author, using Excel Visual Basic for
Applications (VBA). It has the ability to calculate building heating and cooling system energy load with
customized user inputs. The tool can use local weather data (temperature and solar radiation) to simulate the
model in different locations. The idea of tool design is inspired from the latest energy simulation engines
EnergyPlus (Crawley et al, 2015) and DOE-2 (James J. Hirsch & Associates, 2012). In comparison with
these two programs, the Excel tool has its advantages and simplifications (Table 5.1). Instead of modeling
real conditions (like EnergyPlus and DOE-2), the current version of Excel tool simulates in theoretical (lab)
conditions. For example, the HVAC system operates throughout the entire year with no breaks while the
sealed model has no windows, doors, or any other infiltrations. In order to improve the Excel tool with more
comprehensive functions, much more features require to be developed in the future. In other words, the
current version of Excel tool is only legit for theoretical researches. The validation among Excel tool,
EnergyPlus and DOE-2 using base model settings shows that result differences do exist among these
programs (Chapter 3.4). Based on the specific objective of this research on thermal mass materials, the
Excel tool is more focused on exterior wall heat transfer mechanisms typical of smaller skin dominated
buildings. The time step is lower than EnergyPlus and DOE-2 because of the necessity to investigate the
detailed temperature changes within the exterior wall. The Excel tool also has the ability to investigate the
building energy load with different thermal time lag and other material properties, which EnergyPlus and
DOE-2 do not have. The Excel tool does make several simplifications to the model design and heat transfer
solution algorithms. This includes the simplification of solar radiation, model customization, simplified
convection coefficient etc. The Excel tool also has limits including ability to calculate only 1 layer of wall
in the current tool version. These aspects require further investigation in the future.
140
Features DOE-2 EnergyPlus Excel tool
Inputs Text, BDL Text, IDF/IDD
Extensive
Material and environment
properties
Outputs Summary & hourly
reports
Extensive summary &
detailed reports with user
specified time steps
Exterior wall thermal time
lag & annual HVAC load
Algorithms Surface heat balance:
Response Factor, CTF;
Zone Weighting Factors
Surface heat balance; Zone
air heat balance
2-D heat transfer model
using forward finite element
method (FFE)
ime Step 1 hour, fixed 1 to 60 minutes Hourly 120 seconds or lower
Weather Data 1 hour, fixed 1 to 60 minutes Hourly 120 seconds or lower
User
customization
User functions Energy Management
System, External Interface,
Functional Mockup
Interface
User can design a simple
cubic room with customized
settings in different locations
Language Fortran Fortran Excel VBA
Table 5.1 comparison between EnergyPlus DOE-2 and Excel tool
The current version of the tool is able to calculate exterior wall thermal time lag with customized material
and environment parameters. The test results show that material properties have different levels of effect on
thermal time lag, including conductivity, density and specific heat. Because of using forward finite element
method, the results of thermal time lag from Excel tool have some deviations with previous researches
(Asan, 2005 & Jing Xin, 2011) which use Crank-Nicolson scheme. The differences in results indicate the
effect of boundary conditions on material thermal time lag. The effect of material properties is more
significant than effect of boundary conditions (Table 5.2).
141
Material
properties
Thickness
Thermal time lag increases significantly with thickness among all
material types
Density
Thermal time lag increases with density, the effect varies with
different material types
Conductivity
Thermal time lag decreases with conductivity, the effect varies
with different material types
Specific heat
Thermal time lag increases significantly with specific heat among
all material types
Boundary
condition
Exterior maximum
temperature
Thermal time lag decreases slightly with exterior maximum
temperature
Exterior minimum
temperature
Thermal time lag increases slightly with exterior minimum
temperature
Interior temperature Has no effect on thermal time lag
Exterior temperature
Range
Thermal time lag is higher in warmer climates, the effect varies
with different material types
Exterior temperature
swing
Thermal time lag increases with lower temperature swing,
especially when the swing is extreme low (e.g. from 24 Celsius to
26 Celsius)
Solar radiation Thermal time lag increases slightly with solar radiation
Table 5.2 material and boundary parameters effects on thermal time lag
The key feature of the Excel tool is to calculate the annual heating and cooling system load of HVAC
system with customized settings, but limited temperature ranges. The calculation of energy load is
separated from calculation of thermal time lag because the necessity of increasing the accuracy of the
model by lowering the time step. In order to test in different climate zones, the heat transfer calculation is
assisted by Excel VBA macros to inject weather data. Several tests are conducted to investigate the
effects of material and environment parameters on HVAC loads. This includes thermal time lag, climate
zones, HVAC settings and environmental factors. Some base model settings have been determined. The
test result shows the HVAC load is affected by synergies of material and environmental parameters in
different levels. The results vary with thickness, density, conductivity, specific heat, climate zones, indoor
setting temperature, controller offset temperature, emissivity, wind speed and solar radiation (Table 5.3).
142
Material
properties
Thermal time lag
Annual load reduces with increasing thermal time
lag, more efficient at low thermal time lag than at
high thermal time lag
Density Annual load reduces with increasing density
Conductivity
Annual load increases significantly with increasing
conductivity, the effect varies with different
material types
Specific heat Annual load reduces with specific heat
Climate zones
Material with 8 hours thermal
time lag in different climate
zones
Both cooling and heating load varies with climate
zones, the annual total load is higher in colder
climate zones
Different thermal time lag in
different climate zones
Annual load reduces with increasing thermal time
lag
HVAC settings
Indoor setting temperature in
different climate zones
Cooling load decreases while heating load increases
with increasing indoor temperature. The annual
total load varies in different climate zones
Controller temperature offset
effect on energy performance in
difference climate zones
Annual load decreases with increasing temperature
offset. The biggest drop of annual load occurs from
1 Celsius to 2 Celsius, then the annual load stays
constant
Environmental
factors
Exterior wall emissivity
Annual load reduces slightly with increasing
emissivity
Long-wave radiation
Annual load increases with increasing long-wave
radiation
Exterior wall convection
coefficient
Annual load reduces slightly with increasing
exterior convection coefficient
Table 5.3 material and environmental parameters effects on heating and cooling system load
The Excel tool also provides simplified evaluations of the economic value of the simulation model. A
balance of material cost, energy load and cost can be further investigated using this feature of the Excel
tool. The economic value includes the material cost and energy cost. The costs of labor, transportation,
maintenance are not included in the tests. The evaluation can be accomplished with sufficient information
of the local energy price and heating/cooling system performance data. This feature has not been added
into the program itself, but can be conducted in a separate worksheet. Once the behavior of the base
model is determined, the test result shows the annual heating costs vary significantly with different
143
heating systems (electric driven heat pump and natural gas heater), and climate zones. Because of the
higher efficiency of natural gas heater and cheaper energy price, it costs much less than the electrical heat
pump. The total costs also vary with different construction material in consideration of the material cost
and its energy performance. The material cost has significant initial impact on the total cost, while energy
cost becomes more dominant in the life span of the material. The test also shows the relationship between
energy performance and total costs in graphics.
Several functions in the Excel tool require further development in the future. In comparison with powerful
energy simulation engine, EnergyPlus (Crawley et al, 2015), the tool focuses more on theoretical (lab)
researches instead of real building cases. Although the current version is sufficient for this project, a lot
more features can be added for other research objectives to make the model closer to real conditions.
Besides the potential of the tool, some functions of the current version require to be fixed or developed in
the next step. This includes the simplifications of solar radiation, model customization, simplified
convection coefficient, thermal time lag limitation, the number of the exterior wall layers and the cooling
and heating capacity inputs. For solar radiation and exterior wall convection coefficients, extra
information must be gathered depending on the location of the model. The actual solar radiation requires
local latitude and solar angles data of the model. Exterior wall convection coefficient requires local wind
speed data transferred into 120 seconds‘ scale due to the model time step. Thermal time lag limitations
can be solved with smaller time steps in the thermal time lag calculation section. In order to add more
layers of the exterior wall, the program has to be modified with different codes, meaning lots of changes
on the existing tool. Instead of auto-calculation, the heating and cooling capacity can be improved to be
an input for users. Besides, the current model limits on an ideal cubic room without window and
infiltration, which also limits the customization for users. Further research is required on the development
of model customizations.
144
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146
Appendix A
Excel Macros
Macro to get weather data and transfer into 120 second scale
147
Macro to Calculate the heat transfer mechanisms in 120 seconds scale
148
Thermal time lag results comparison with Xing Jin (2011) and Asan (2005)
Thermal time lag validation with different boundary conditions
Building materials Tool results Xing jing (2011) Diversity
Hours Hours
Cement layer 8.99 9 0.11%
Concrete block 11.02 10.5 4.95%
Brick block 10.42 10 4.20%
Gypsum plastering 9.96 9.5 4.84%
Granite (red) block 7.03 7.5 6.27%
Marble (white) block 7.69 7.75 0.77%
Sandstone block 6.71 7 4.14%
Clay layer 9.2 9.25 0.54%
Asphalt sheet 13.84 12 15.33%
Steel slab 5.2 5.75 9.57%
Aluminum slab Limit 5.5 Limit
Cork board Limit 15.5 Limit
Wood block Limit 19 Limit
Plastic board 8.47 8.75 3.20%
Rubber board 6.33 19.5 7.54%
P.V.C board Limit 17.25 Limit
Asbestos sheet Limit 23.5 Limit
Formaldehyde board 7.61 7.25 4.97%
Thermalite board 11.68 10.75 8.65%
Fiberglass Limit 12.5 Limit
Siporex board 14.53 12.5 16.24%
Polyurethane board 5.24 5 4.80%
Light plaster 12.61 11.5 9.65%
Dense plaster 10.63 10.25 3.71%
Table 0.1 validation with Xing jin‘s (2011) results of thermal time lag (0.24 meter)
149
Building materials Tool results Asan (2005) Diversity
Hours Hours
cement layer 7.49 0.69 46.29%
concrete block 9.01 1.14 32.31%
brick block 8.59 1.15 29.17%
gypsum plastering 8.23 0.89 38.79%
granite (red) block 6.1 1.28 21.76%
Marble (white) block 6.6 1.25 24.29%
Sandstone block 5.74 0.92 28.41%
Clay layer 7.71 1.1 28.93%
Asphalt layer 11.04 2.31 25.17%
Steel slab Limit 1.79 Limit
Aluminum slab Limit 1.13 Limit
Cork board 15.84 1.1 58.08%
Wood board Limit 2.27 Limit
Plastic board 7.11 0.73 43.93%
Rubber board 5.21 3.01 63.67%
PVC board Limit 1.9 Limit
Asbestos layer Limit 3.39 Limit
Formaldehyde board 6.3 0.23 97.49%
Fiberglass Limit 0.52 Limit
Thermalite board 9.41 0.81 44.33%
Siporex board 11.27 0.92 44.30%
Polyurethane board 4.16 0.12 155.21%
Table 0.2 validation with Asan‘s(2011) results of thermal time lag (0.2meter)
150
Building materials Tool results Asan (2005) Diversity
Hours Hours
cement layer 11.63 8.23 41.31%
concrete block 14.84 10.31 43.94%
brick block 13.79 9.86 39.86%
gypsum plastering 13.13 9.27 41.64%
granite (red) block 8.51 6.95 22.45%
Marble (white) block 9.48 7.56 25.40%
Sandstone block 8.16 6.45 26.51%
Clay layer 11.82 8.84 33.71%
Asphalt layer Limit 12 Limit
Steel slab 5.65 5.09 11.00%
Aluminum slab Limit 4.14 Limit
Cork board Limit 15.77 Limit
Wood board Limit 20.28 Limit
Plastic board 10.8 7.84 37.76%
Rubber board 7.9 21.82 63.79%
PVC board Limit 18.01 Limit
Asbestos layer Limit >24 Limit
Formaldehyde board 9.68 5.96 62.42%
Fiberglass Limit 9.92 Limit
Thermalite board 16.24 10.43 55.70%
Siporex board Limit 12.31 Limit
Polyurethane board 6.69 3.36 99.11%
Table 0.3 validation with Asan‘s(2011) results of thermal time lag (0.3 meter)
151
Appendix B
Weather data
The following data are from National Climatic Data Center (2015). The data type is .csv file.
Figure 0.1 weather data of Miami
Figure 0.2 weather data of Phoenix
Figure 0.3 weather data of Los Angeles
152
Figure 0.4 weather data of Seattle
Figure 0.5 weather data of Pittsburgh
Figure 0.6 weather data of Minneapolis
153
Figure 0.7 weather data of Fargo
154
Appendix C
Heater model used in the test in chapter 4.4.1.
Electric space heat
Duraflame PowerHeat Infrared Quartz Heater — 5200 BTU, Oak Finish, Model# 9HM9126-O142
http://www.wayfair.com/Duraflame-Quartz-Space-Heater-9HM9126-O142-DFL1025.html
155
Heat pump
LG Art Cool Premier LS090HYV
http://www.ajmadison.com/cgi-bin/ajmadison/LS090HYV.html
156
Natural gas furnace
Goodman 80% AFUE 40,000 BTU Downflow 1 Stage Gas Furnace Heater
https://www.acwholesalers.com/Goodman-Air-Conditioner/GDS80403AX-80-AFUE-40000-BTU-Down
flow-1-Stage-Gas-Furnace-Heater/14751.ac?catId=cat1002&mainCat=&subCat=
157
Natural gas boiler (condensing)
Rinnai E50CN Condensing Boiler Max Btu 50,000 Combi, Natural Gas
http://www.kbauthority.com/Rinnai-E50CN-Condensing-Boiler-Max-Btu-50-000-Combi-Natural-Gas.ht
ml?utm_source=PLA&utm_medium=CPC&utm_campaign=ProductsUp&pup_e=1&pup_ptid=11494497
3854&pup_kw=&pup_c=pla&pup_id=IDRinnaiE50CN&gclid=COSi2pPIwckCFc5gfgodANEPGw
158
Appendix D
Material specifications and prices
Concrete
Available at
http://www.concretenetwork.com/concrete-prices.html
Cement layer
Available at:
https://www.google.com/search?q=cement+price&oq=cement+price&aqs=chrome..69i57.6619j0j7&sour
ceid=chrome&es_sm=93&ie=UTF-8
Brick block
Available at:
http://www.homedepot.com/p/Old-Mill-Brick-Dixie-Clay-Colonial-Collection-Thin-Brick-Flats-TB-2700
4CS/205050375?cm_mmc=SEM%7cTHD%7cG%7c0%7cG-Pro-PLA-D22-MaterialsSupply%7c&gclid=
CJLC1L-nzMkCFU5afgodwUoPoA&gclsrc=aw.ds
Wood block
Laminated veneer lumber (LVL)
Available at:
http://www.homedepot.com/p/Boise-Cascade-2-in-x-6-in-x-8-ft-Versa-Stud-LVL-SP-2650-1-7-2-Piece-p
er-Box-2112005/206565341?cm_mmc=shopping-_-googleads-_-pla-_-206565341&ci_sku=206565341&
ci_gpa=pla&ci_src=17588969&gclid=CJLSgdbozskCFYVrfgod-PMMEQ&gclsrc=aw.ds
Plastic board
Scrap plastic $850/ton
Available at:
http://www.alibaba.com/showroom/scrap-plastic-price-per-ton.html
Abstract (if available)
Abstract
Construction material choice and environmental parameters have shown significant influence on building energy performance. The current building energy simulator, EnergyPlus (Crawley et al, 2015) and DOE-2 (James J. Hirsch & Associates, 2012), focus on calculations of HVAC system energy load with user customization. Although the heat transfer calculation algorithms of both engines are comprehensive for the energy simulation purpose, it is difficult to make experimental tests on specific parameters such as thermal time lag and climate zone effects. A tool is required to be developed to study specific material and environmental parameters‘ influence on building energy performance. The tool ought to have the ability of simple building information modeling with user customization and showing building energy performance results according to target material or environment parameter. In order to study the material energy performance, the tool also needs to improve the features upon EnergyPlus and DOE-2 such as input data configuration, exterior wall boundary conditions, weather data (time steps), HVAC operation loop etc. ❧ A prototype tool has been developed. The current version of the tool has several simplifications and differences compared with EnergyPlus and DOE-2. It has the ability to perform monthly/annual energy simulation for a cubic room with user customization. The tool is based on Excel visual basic applications (VBA), which codes the exterior wall heat transfer mechanism and environment properties. The Excel tool calculates two dimensional heat transfer using forward finite element (FFE) method. The time step is 120 seconds, which is smaller and more accurate than EnergyPlus (1-60 minutes) and DOE-2 (1 hour fixed-). Various tests have been conducted to study different material and environment parameters effects on building energy performance and to explore the potential usage and further development of this tool.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Qian, Chenchuan
(author)
Core Title
A simplified building energy simulation tool: material and environmental properties effects on HVAC performance
School
School of Architecture
Degree
Master of Science
Degree Program
Building Science
Publication Date
07/21/2016
Defense Date
06/08/2016
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
building information modeling,building material,energy cost,energy modeling,energy modeling tool design,energy simulation,Excel,Excel VBA,forward finite element method (FFE),heat transfer,HVAC,OAI-PMH Harvest,thermal lag,thermal mass,thermal time lag,time steps,weather data
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Kensek, Karen (
committee chair
), Noble, Douglas (
committee member
), Schiler, Marc (
committee member
)
Creator Email
chenchuq@usc.edu,qiancc228@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c40-271263
Unique identifier
UC11280723
Identifier
etd-QianChench-4567.pdf (filename),usctheses-c40-271263 (legacy record id)
Legacy Identifier
etd-QianChench-4567.pdf
Dmrecord
271263
Document Type
Thesis
Format
application/pdf (imt)
Rights
Qian, Chenchuan
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
building information modeling
building material
energy cost
energy modeling
energy modeling tool design
energy simulation
Excel
Excel VBA
forward finite element method (FFE)
heat transfer
HVAC
thermal lag
thermal mass
thermal time lag
time steps
weather data