COMBINED HEAT AND MOISTURE TRANSPORT MODELING FOR RESIDENTIAL BUILDINGS
Sponsored by
U.S. National Institute of Standards and Technology
HL 2008-3 Project Award No: 60NANB4D1091
Submitted by: Zhipeng Zhong, Graduate Research Assistant James E. Braun, Principal Investigator
Approved by: Patricia Davies, Director Ray W. Herrick Laboratories
AUGUST 2008
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TABLE OF CONTENTS
Page
LIST OF TABLES..........................................................................................................................vi LIST OF FIGURES .......................................................................................................................vii NOMENCLATURE ........................................................................................................................ x ABSTRACT..................................................................................................................................xiv CHAPTER 1. INTRODUCTION .................................................................................................... 1
1.1. Building Structure Problems Caused by Moisture ................................................................ 1 1.2. Comfort and Health Problems Related to Moisture .............................................................. 5 1.3. Introduction of Moisture Transfer......................................................................................... 8 1.4. Objectives of this Research ................................................................................................. 12 1.5. Organization of this Thesis ................................................................................................. 14
CHAPTER 2. MODELING OF HEAT AND MOISTURE TRANSFER IN EXTERIOR WALLS.............................................................................................................................. 17
2.1. Modeling of The Heat and Moisture Transfer in Building Envelope.................................. 17 2.1.1. Major Assumptions of the Heat and Moisture Transfer Model.................................... 17 2.1.2. Mathematical Description of the Heat and Moisture Transfer Model.......................... 18 2.1.3. Comparison of Moisture Transfer Modeling Tools...................................................... 24 2.1.4. Properties of Building Material .................................................................................... 27 2.1.5. Boundary Conditions .................................................................................................... 29
2.2. Numerical Scheme and Flow Chart of the Program............................................................ 31 2.3. Example of Moisture Build up Caused by Solar Heating after Rain................................... 38 2.4. Summary ............................................................................................................................. 42
CHAPTER 3. EXPERIMENTAL VALIDATION OF EXTERIOR WALL MODEL ................. 43 3.1. Methodology for the Experimental Validation ................................................................... 44 3.2. Equipment and Calibrations ................................................................................................ 45 3.3. Experimental Procedure ...................................................................................................... 56 3.4. Uncertainty Analysis ........................................................................................................... 62 3.5. Model Validation................................................................................................................. 65 3.6. Summary ............................................................................................................................. 73
CHAPTER 4. A SIMPLIFIED MODEL FOR GROUND-COUPLED HEAT TRANSFER IN FLOOR SLABS................................................................................................................... 75
4.1. Introduction ......................................................................................................................... 75 4.2. Methodology ....................................................................................................................... 78
4.2.1. Case Study Descriptions ............................................................................................... 78 4.2.2. Finite-Element Model................................................................................................... 81 4.2.3. Simplified Ground-Coupled Floor Modeling ............................................................... 82 4.2.4. Process for Correlating Perimeter Heat Loss Factor and Soil Depth............................ 84
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4.3. Results and Discussion........................................................................................................ 86 4.3.1. Floor Configuration A: 4heavy-weight concrete on soil............................................ 86 4.3.2. Floor Configuration B: 10 cm (4 Inches) HWC Slab with 4 inches of Gravel............. 90 4.3.3. Numerical Validation ................................................................................................... 91
4.4. Summary ............................................................................................................................. 92 CHAPTER 5. WHOLE BUILDING HEAT AND MOISTURE MODELING............................. 93
5.1. Description of the Whole Building Heat-Moisture Balance Model .................................... 93 5.1.1. Infiltration, Inter-zonal, and Ventilation Air Flows......................................................96 5.1.2. Internal Moisture and Heat Generation ........................................................................ 96 5.1.3. Wall, Ceiling, and Floor Heat and Moisture Fluxes ..................................................... 99 5.1.4. Windows..................................................................................................................... 100 5.1.5. Moisture Buffer .......................................................................................................... 101 5.1.6. HVAC Equipment and Thermostat ............................................................................ 102 5.1.7. Weather Processing and Boundary Conditions ..........................................................103 5.1.8. Model Implementation and Numerical Solution ........................................................104 5.1.9. Comparisons with Other Models ................................................................................ 108
5.2. Case Study Results ............................................................................................................ 109 5.2.1. Case Study Description .............................................................................................. 109 5.2.2. Results for Indoor/Attic Conditions and Equipment .................................................. 111 5.2.3. Results for Envelope Moisture ................................................................................... 116 5.2.4. Importance of Whole-building Analysis for Wall Moisture Performance ................. 119
5.3. Summary ........................................................................................................................... 122 CHAPTER 6. CASE STUDIES FOR BUILDING HEAT AND MOISTURE
PERFORMANCE.............................................................................................................. 124 6.1. Heating Climate-Minneapolis, MN................................................................................... 124 6.2. Mixed Climate-Nashville, TN........................................................................................... 131 6.3. Hot and Dry Cooling Climate- Phoenix, AZ..................................................................... 137 6.4. Hot and Humid Cooling Climate- Houston, TX ............................................................... 141 6.5. Summary ........................................................................................................................... 146
CHAPTER 7. CONCLUSIONS AND FUTURE WORK ........................................................... 147 7.1. Conclusions ....................................................................................................................... 147 7.2. Challenges for Future Studies ........................................................................................... 150
LIST OF REFERENCES............................................................................................................. 154 APPENDIX . INTRODUCTION OF CONTAMW .................................................................... 164
A.1. Background on the Multi-zone Model CONTAM ........................................................ 165 A.2. Building Representation in CONTAM............................................................................. 166 A.3. Solution Methods ............................................................................................................. 168 A.4. Boundary Conditions........................................................................................................ 172 A.5. Simplified Model Applied in Whole Building Model...................................................... 173
VITA............................................................................................................................................ 175
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LIST OF TABLES
Table Page 1.1 Survey of moisture problems in residential buildings. .............................................................. 3 3.1 Comparison of the measurement technologies for moisture content. ...................................... 47 3.2 Material properties and geometry of the test specimen: Sugar-pine........................................48 3.3 The position of the moisture pin-pairs for the 1-layer specimen. ............................................ 50 3.4 Radiation Measurements at Different Locations on the Wood Specimen (W/m2). ................. 52 3.5 Calibration for the relative humidity sensor and transmitter. .................................................. 54 3.6 Calibration for the thermal couples.......................................................................................... 54 3.7 Air velocity, Temperature and Re number for computing hr/hc............................................... 58 3.8 Uncertainties of directly measured values/material properties. ............................................... 62 3.9 Uncertainty analysis for hmix_cold............................................................................................... 64 3.10 Uncertainty analysis for convective heat transfer coefficient. ............................................... 64 3.11 Uncertainty analysis for wood specimen surface absorptance............................................... 64 3.12 Uncertainty analysis for specimen surface vapor flux. .......................................................... 65 3.13 Experimental condition summary. ......................................................................................... 65 3.14 Validation model condition summary.................................................................................... 67 4.1 Base case thermal properties of floor and ground materials. ................................................... 80 5.1 U-factor and SHGC for windows. ......................................................................................... 101 5.2 Adsorption isotherm constants for curtain and bedding. ....................................................... 102 5.3 Parameters for building structure........................................................................................... 110 5.4 Sizing results for the HVAC equipment. ............................................................................... 111 6.1 Locations for the parametric studies. ..................................................................................... 124 6.2 Parameters for building structure in Minneapolis.................................................................. 127 6.3 Sizing result for the HVAC equipment in Minneapolis......................................................... 127 6.4 Parameters for building structure for Nashville_sandwich type. ........................................... 134 6.5 Sizing results for the HVAC equipment in Nashville............................................................ 134 6.6 Parameters for external wall structure for Nashville_conventional wall structure ................ 136 6.7 Parameters for building structure in Phoenix......................................................................... 138 6.8 Sizing result for the HVAC equipment in Phoenix................................................................ 138 6.9 Sizing result for the HVAC equipment in Houston. .............................................................. 142
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LIST OF FIGURES
Figure Page 1.1 Examples of problems caused by moisture................................................................................ 2 1.2 Microscope and macro scope view of mold............................................................................... 4 2.1 The schematic for the moisture balance................................................................................... 19 2.2 The schematic for the energy balance...................................................................................... 21 2.3 The schematic for sorption isotherm........................................................................................ 29 2.4 Depiction of wall nodes for numerical solution....................................................................... 31 2.5 Depiction of wall nodes for the exterior boundary. ................................................................. 33 2.6 Flow diagram for envelope heat and moisture transfer model................................................. 36 2.7 Comparison for the node temperature with result from FEHT. ............................................... 37 2.8 Comparison for the inner surface temperature with result from Laplace Transform............... 38 2.9 Comparison of wall temperatures after rain shower with/without solar heating. .................... 41 2.10 Comparison of wall moisture contents after rain shower with/without solar heating............ 42 3.1 Experimental set up.................................................................................................................. 45 3.2 Delmhorst moisture content pin pairs and Kil-Mo-Trol Plus system. ................................... 48 3.3 Plan for the location of moisture pin pairs. .............................................................................. 49 3.4 Illustration of the effect of shrinkage and grain orientation on shape...................................... 50 3.5 Heating lamps, reflective shields and pyranometer. ................................................................ 52 3.6 Blower (driven by Variable Frequency Drive) and honey-comb-core outlet. ......................... 53 3.7 Relative humidity sensor and the ambient air temperature thermocouples. ............................ 54 3.8 Calibration for the moisture content pin pairs. ........................................................................ 56 3.9 Schematic of setup and measurements for estimating hc, hr and ........................................... 57 3.10 Specify the overall and the radiant heat transfer coefficient for the unheated side. .............. 58 3.11 Comparison of hc from tests and hc from a textbook correlation.......................................... 59 3.12 Preconditioning to soak the specimen. ............................................................................... 61 3.13 Room air dry bulb temperature during the experiment. ......................................................... 66 3.14 Room air relative humidity during the experiment. ............................................................... 66 3.15 Measured and prediction surface temperatures for the wood specimen. ............................... 68 3.16 Moisture content at inch beneath surface B of the specimen............................................. 69 3.17 Moisture content at the center line of the specimen............................................................... 70 3.18 Moisture content at inch beneath surface A of the specimen............................................. 71 3.19 The specimen weight change for the drying process. ............................................................ 72 3.20 The specimen weight change for the drying process (with edge vapor leakage included in the
model)..................................................................................................................................... 73 4.1 Schematic of the slab-on-ground geometry. ............................................................................ 79 4.2 Example variations in ambient sol-air and zone temperatures................................................. 80
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Figure Page 4.3 Schematic of the two-dimensional finite-element modeling mesh. ......................................... 82 4.4 Simplified 3-node models for a one-dimensional ground-coupled floor. ................................ 83 4.5 Example optimization of soil depth for centerline heat flux.................................................... 86 4.6 Comparison of centerline heat flux for finite-element and simplified models (Configuration A,
base case)................................................................................................................................ 86 4.7 Curve fit for optimized soil depth for centerline heat flux (Configuration A)......................... 87 4.8 Comparison of average floor surface heat flow flux for finite-element and simplified models
(Configuration A, base case). ................................................................................................. 88 4.9 Effect of soil conductivity and half-floor length on optimized perimeter heat loss factor
(Configuration A, no edge insulation). ................................................................................... 88 4.10 Curve-fit results for edge heat loss factor (Configuration A). ............................................... 89 4.11 Curve fit for optimized soil depth for centerline heat flux (Configuration B). ...................... 90 4.12 Curve-fit results for edge heat loss factor (Configuration B). ............................................... 91 4.13 Example simplified model accuracy for New York in summer (Configuration A)............... 92 4.14 Example simplified model accuracy for Chicago in winter (Configuration B). ....................92 5.1 Schematic of moisture room paths and driving forces............................................................. 95 5.2 Example for typical daily indoor heat and moisture generation for a family of four............... 98 5.3 Schematic for attic and attic ventilation................................................................................. 100 5.4 The modular elements that form the whole building simulation. .......................................... 105 5.5 Flow diagram for the explicit solution scheme. ..................................................................... 107 5.6 Comparison of zone air temperatures with results from TRNSYS........................................ 109 5.7 Ambient air temperature and relative humidity for Indianapolis........................................... 111 5.8 The yearly attic air temperature and relative humidity. ......................................................... 112 5.9 Whole building simulation result for winter case. ................................................................. 114 5.10 Whole building simulation result for summer case.............................................................. 115 5.11 Cooling load condition for the equipment. .......................................................................... 117 5.12 Whole building simulation result for summer case.............................................................. 118 5.13 Isothermal absorption curve for selected building materials. .............................................. 119 5.14 Comparison of interior/exterior layer equilibrium RH for whole-building and stand-alone
wall modeling (vapor barrier on inside of insulation). ......................................................... 121 5.15 Comparison of interior/exterior layer equilibrium RH for whole-building and stand-alone
wall modeling (vapor barrier on outside of insulation). ....................................................... 122 6.1 Ambient air temperature and relative humidity for Minneapolis........................................... 126 6.2 Roof and ceiling equilibrium RH in Minneapolis..................................................................128 6.3 Wall structures internal equilibrium RH and temperature in Minneapolis (north)............... 129 6.4 Solar driven rain moisture build up for building structure..................................................... 130 6.5 Effect of vapor retarder location for cold climate condition.................................................. 131 6.6 Ambient air temperature and relative humidity for Nashville. .............................................. 132 6.7 Internal equilibrium RH and temperature for cold climate wall structure in Nashville......... 133 6.8 Sandwich wall structure internal equilibrium RH and temperature for Nashville. ................ 135 6.9 Conventional wall structures equilibrium RH for Nashville (no vapor retarder). ................ 136 6.10 Ambient air temperature and relative humidity in Phoenix. ................................................ 137 6.11 Roof and ceiling equilibrium RH for Phoenix. .................................................................... 139
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Figure Page 6.12 Wall structure internal equilibrium RH and temperature for Phoenix. ................................ 140 6.13 Wall structure equilibrium RH and temperature for Phoenix (no vapor retarder). .............. 141 6.14 Ambient air temperature and relative humidity in Houston................................................. 142 6.15 Roof and ceiling equilibrium RH for Houston..................................................................... 143 6.16 Moisture performance for the original wall structure (facing north) in Houston................. 144 6.17 Modified building structure moisture performance for Houston. ........................................ 145 Appendix Figure
A.1 Illustration of building idealization in CONTAM. ...............................................................166 A.2 Default wind pressure profile in MOIST whole building model (S&C_2_Long). ............... 174
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NOMENCLATURE
a absorptance for solar radiation, dimensionless
A building envelope orifice opening area, m2
A1,A2,A3 coefficient of sorption isothermal equilibrium, A1,A2 and A3 dimensionless
Af total floor surface area, m2
As amplitude of the ground surface temperature wave, C
B1,B2,B3 coefficient of water vapor permeability function, B1 and B2 in kg/m-s-Pa or Perminch, B3 dimensionless
cp specific thermal capacity, J/kg-C or BTU/lbm-F
C node thermal capacitance, J/C
C1,C2 coefficient for liquid diffusivity function, C1 in m2/s or ft2/hr, C2 dimensionless
Cd discharge coefficient, dimensionless
Cf mass flow coefficient, dimensionless
Cq volume flow coefficient, dimensionless
CT, C temperature and moister modification factor for k, W/m-C2 or BTU/hr-ft-F2
DAB diffusion coefficient, m2/s or ft2/hr
D liquid diffusivity, m2/s or ft2/hr
D* ratio of the soil depth to the soil depth associated with the baseline (45 cm)
e transfer function coefficient for previous outputs, W/m2
E0,E1,E2,E3 amplitude for temperature wave at 0,1,2,and 3 order for sin function, C
EH node enthalpy flow term, J/m3-C-s or BTU/ft3-F-hr
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F air mass flow rate, kg/s
Fp perimeter heat loss factor, W/m-K
h enthalpy, J/kg or BTU/lbm
hfg heat of vaporization, J/kg or BTU/lbm
hc convective heat transfer coefficient, W/m2-C or BTU/hr-ft2-F
hm mass transfer coefficient, kg/m2-Pa-s or lbm/hr-ft2-inHg
hr linearized radiation coefficient, W/m2-C or BTU/hr-ft2-F
H height, m or ft;
Heqp evenly distributed equipment long-wave radiation, W/m2 or BTU/ft2-hr
Hin solar radiation intensity on the envelope inner surface, W/m2 or BTU/ft2-hr
Hsol solar radiation intensity on envelope exterior surface, W/m2 or BTU/ft2-hr
I specified moisture generation source, kg/m3-s or lb/ft3-h
g acceleration of gravity (9.81 m/s2)
wallg moisture flux from building envelope, kg/m2-s or lbm/ft2-hr
genG& indoor moisture generation rate, kg/s or lbm/hr
k thermal conductivity, W/m-C or BTU/hr-ft-F
k* ratio of the thermal conductivity to the baseline k of 1.73 W/m-K
kv vegetation shade factor
K hydraulic conductivity for liquid, kg/m-s-Pa or lbm/ft-hr-inHg
L length of the internal zone, m
Le Lewis number (Le = 0.927 for air)
m mass, kg or lbm
m vapor flux, kg/m2-s or lb/ft2-hr
Me effective mass transfer coefficient, kg/m2-s-Pa or lbm/ft2-hr-inHg
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Mf air film moisture transfer conductance, kg/m2-s-Pa or lbm/ft2-hr-inHg
Mp surface moisture transfer conductance, kg/m2-s-Pa or lbm/ft2-hr-inHg
n mass flux, mol/ m2-s or mol/ft2-hr
P pressure, Pa or inHg
Pj, Pk total pressure at zones j and k, Pa
Pm length of the internal zone, m
Ps pressure difference due to density and elevation differences, Pa
Pw pressure difference due to wind, Pa
q heat flux, W/m2
q f heat flux from floor, W/m2
Q volumetric flow rate, m3/s;
Q& total heat transfer rate or heat generation rate, W
R node thermal resistance, K/W
s transfer function coefficient for previous temperatures, W/m2-K
S mass generation source, kg/m3-s or lb/ft3-hr
SHGC Solar heat gain coefficient
t time, s or hr
T temperature, C or F
Tsol-air sol-air temperature, C
Tg far depth soil temperature, C
Tm annual ambient air average temperature, C
u concentration in dimensions of amount of substance, mol/m3
U U-factor for windows heat conduction, W/m2-C
V air velocities, m/s
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VH approach wind speed at the upwind wall height, m/s;
y length, m or ft
z entry and exit elevations, m
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ABSTRACT
Zhong, Zhipeng. Ph. D., Purdue University, August, 2008. Combined Heat and Moisture Transport Modeling for Residential Buildings. Major Professor: Dr. James Braun, School of Mechanical Engineering.
Residential buildings are meant to provide a safe, healthy, and comfortable indoor
environment for occupants. However, many residential buildings suffer from a variety of
moisture problems. Unfavorable indoor relative humidity can make occupants uncomfortable.
Whats more, high humidity within building envelopes can lead to deterioration of material, and
cause some serious health problems due to the growth of mold and mildew.
This research addresses modeling of building envelope transient heat and moisture transfer
for structures used in residential buildings. The wall model development is based on a previously
developed one-dimensional model called MOIST 3.0, which incorporates water vapor diffusion
and water liquid capillary transfer. An important aspect of the current effort has been the
development of a wetted surface model that allows consideration of the moisture transfer caused
by wind-driven rain, where capillary liquid water transfer is an important mechanism.
In order to validate the MOIST model for heat/vapor/capillary transfer, an experiment was
devised and carried for drying of a sugar-pine panel. The panel was initially soaked until
saturation and then exposed to typically ambient conditions and surface radiant heating with
controlled air flow. The experiment was designed to simulate the effects of solar-driven moisture
transfer that would follow rain. An automated weighing system was used to trace the overall
wood moisture content and moisture pin-pairs measured the local moisture content within the test
specimen. During the transient drying test, radiant heating was projected on one surface then
switched to the other so as to develop a better understanding of the nature and significance of
solar-driven inward vapor diffusion. There was relatively good agreement between moisture
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content predictions and measurements from the moisture pin-pair sensors and very good
agreement of the overall moisture content from the weighing system.
Another contribution of this research is a simplified model for predicting transient heat
transfer in ground-coupled floor slabs. The model simplifies the traditional two-dimensional
approach by employing two parallel one-dimensional transient heat transfer paths. The model
incorporates correlations for the effects of ground soil properties and edge insulation that were
developed for two common floor configurations. Hourly heat flux predictions compared very
well with predictions from a two-dimensional finite-element program for these two geometries.
The method can be integrated within hourly simulation programs so that fast estimation of
transient heat transfer for the indoor air to the slab-on-ground can be realized.
A major contribution of the research is the coupling of the detailed envelope model with a
whole building model that allows investigation of the impacts of envelope design on occupant
comfort, energy use, and wall material conditions that can lead to mold growth, insulation
degradation, etc. In addition to the external wall model, the whole building model incorporates
several individual models that were developed, including: 1) weather data treatment including
wind driven rain and solar radiation, 2) air infiltration and inter-zonal air flow, 3) indoor heat and
moisture generation, 4) heat transfer through slab-on-ground floors, 5) indoor moisture storage
within furnishings and other soft materials, and 6) HVAC equipment. The model allows a
detailed analysis of indoor/attic air conditions and moisture information for building materials.
The original MOIST model only considered individual walls and assumed constant indoor
air conditions. In order to evaluate the importance of coupling the wall analysis to indoor
conditions, results of the whole building analysis were compared with a single wall analysis
performed with constant indoor conditions. The two approaches gave significantly different
predictions for moisture levels within materials located near the indoor space but gave essentially
the same results for layers located away from the interior space. The stand-alone wall analysis
resulted in relatively stable moisture for the interior gypsum layer because of the constant indoor
boundary condition, whereas the interior surface for the whole building analyses varied over a
relatively large range. Although the moisture levels would not cause mold or material damage
problems for the case study considered, the stand-alone wall analysis would not identify potential
problems that could occur due to more significant indoor moisture gains that could potentially
xvi
occur, such as moisture gains within a bathroom not having an exhaust fan. The whole building
model has the potential for evaluating moisture problems caused by indoor conditions and also
can consider the impacts of design choices on indoor air moisture levels. On the other hand, the
standalone model enjoys much lower computational cost and may be adequate for evaluating
many moisture problems caused by ambient effects.
The whole building analysis tool was used to perform some case studies. Moisture
performance of building envelopes was analyzed in some featured climates (heating climate,
mixed climate, and dry or humid cooling climate) with representative building constructions. It
was shown that for heating climates, a vapor retarder should be placed close to the room side so
as to prevent vapor excursion from the relatively warm and moist indoor air. For humid cooling
dominated climates, a vapor retarder should be positioned close to the ambient side to stop vapor
incursions. On the other hand, for hot and dry climates it is not necessary to use a vapor retarder.
For mixed climates, a conventional wall structure without a vapor retarder can work adequately.
However, a sandwiched structure with vapor retarders on both sides of a low-permeability
insulation is another option because it can handle either vapor incursion from the ambient during
summer or vapor excursion from the indoor air during winter.
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CHAPTER 1. INTRODUCTION
Building envelopes separate indoor from outdoor environments and play the most important
role in sustaining necessary indoor comfort conditions for occupants. According to Rengin et al.
(2004), an optimum building envelope should provide visual, thermal and acoustical comfort in
accordance with the function of the room. In addition, Rousseau (2003) notes that successful
building design requires an understanding of moisture movement in building materials and
techniques for managing moisture that come from controlling heat, air and moisture transport
through the careful choice of materials properties.
1.1. Building Structure Problems Caused by Moisture
HVAC designers must consider and deal with moisture in almost all of their work. Moisture,
from whatever sources, is commonly regarded as the single greatest threat to the durability and
long-term performance of the housing stock (Newport Partners Report, 2004). Figure 1.1 shows
some examples of damage to building materials caused by moisture. Failure to properly manage
the transport of heat, air and moisture across the wall assembly can cause the following problems:
1. Electrochemical corrosion of metal components such as HVAC equipment, ducts,
structural framing, reinforcement bars, masonry anchors, etc.;
2. The chemical deterioration and dissolution of materials such as gypsum sheathing,
ceiling tiles, especially wood products on the exterior walls (Roussau, 2004);
3. Discoloration of building finishes;
4. Volume changes (swelling, warping and shrinkage) that can cause degradation of
appearance, structural failure, cracking, etc.;
5. Freeze-thaw deterioration of concrete, stone, and masonry, especially for buildings in
cold areas if the building materials contain moisture (e.g., if the concrete holds more
than 44% moisture by pore volume, freeze-thaw damage to the concrete block may
happen if the temperature drops below the freezing point (Fagerlund, 1977);
2
6. The increase of material thermal conductivity due to the moisture within the material;
7. The growth of biological forms, including molds, mildews, mites, etc.
a.) corrosion of metal b.) deterioration of ceiling
c.) discoloration of finish d.) structure cracking
e.) freeze-thaw deterioration of concrete
Figure 1.1 Examples of problems caused by moisture.
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A survey and overview of the findings from cases studies of moisture problems in residential
crawl spaces, basements, roofs, and inside surfaces of exterior walls was presented by Tsongas
(2000). Most of the emphasis was on relevant U.S. and Canadian studies. It was found that most
residential buildings suffer from a variety of moisture problems. For instance, based on a survey
of 334 Iowa households, 98% of the residents reported at least one type of moisture problem.
The most common types of moisture problems were: condensation on windows (62%), exterior
paint peeling (41%), staining of interior windows frames and sills (31%), mildew on
walls/ceilings or closets (23%), decay/rotting of interior window frames/sills (20%),
moisture/mildew problems in summer (18%), frost/condensation on walls/ceilings (13%), and
interior paint peeling (10%).
Results from a survey made in the early 1980s in Canada (Jacques Rousseau, 1982) for case
studies related to the occurrence and significance of bulk moisture problems is summarized in
Table 1.1.
Table 1.1 Survey of moisture problems in residential buildings.
Location Sampling Units
*Serious Moisture-Related problem
Mold and
Mildew
Window Condensation
Attic Condensation
Siding Damage
Newfoundland 10,400 27% 3.0% 1.2% 2.2% 24% Maritimes 32,800 1.4% 0.6% 0.3% 0.2% 0.8%
Quebec 164,00 0.7% 0.3% 0.2% 0.6% 0% Ontario 276,000 0.7% 0.4% 0.2% 0.4% 0.004% Prairies 135,000 1.4% 0.1% 1.3% 0.7% 0.04%
B. Columbia 71,300 3.0% 1.3% 0.2% 2.7% 0%
*Serious moisture-related problems were regarded as:
Serious Condensation in Attic wood moisture content exceeding 22% or mold and mildew growth covers more than 50% of the attic sheathing and roof joists. Serious Wall Cavity Moisture wood moisture content exceeding 22% Serious Exterior Siding Moisture buckling or warping of more than 50% of the wall area, or paint damage affecting more than 0.3 square meters
Some other surveys can be found for a variety of climates from different countries such as
Finland (Lappalainen et al., 2001), Mauritius (Bholah and Subratty, 2003) and Portugal
(Loureno et al., 2006). There are many common problems identified in these studies, such as
4
growth of mold and mildew. Molds are forms of fungi, which are distinctly different from plants
and animals. Over 1,000 types of molds have been found in houses in North America. Mildew is
a term that is often used interchangeably with mold, generally referring to mold growing on
fabrics and bathroom tiles. Mold can appear cottony, velvety, grainy, or leathery, and it can be
any color, including white, pink, yellow, green, brown, gray, or black. Since the application of
biocides to kill fungi is always accompanied by additional health risks especially when used
indoors, the biocides are used selectively based on knowledge of the mechanism of mold growth.
Molds can produce and send out spores, which can be seen through a microscope, as shown in
Figure 1.2a, and which act like seeds. The following conditions are necessary and sufficient for
mold growth to occur on surfaces (Lstiburek etc. 1991):
1. Mold spores must be present;
2. A nutrient base must be available (most surfaces contain nutrients);
3. Temperature range between 4~38C (40~100F);
4. Relative humidity near the surface is above 70%.
Of these conditions, relative humidity near surfaces is the most practical to control. Figure
1.2b gives an example for the mold on books. Molds and mildews are one of the major causes of
the deterioration and decay of building materials. In addition, moisture-related biological growth
has taken on new significance due to the fact that the growth can have a major effect on indoor air
quality (IAQ) and occupant health, which will be discussed later.
a.) Micro view of molds b.) Macro view of molds
Figure 1.2 Microscope and macro scope view of mold.
5
A 70% relative humidity criteria for mold growth has been adopted by the Moisture Control
Handbook (Lstiburek and Carmody, 1991). In Europe, the lowest boundary line for possible
fungus activity is called LIM (Lowest Isopleth for Mold). DIN (German Institute for
Standardization) 4108 and DIN EN ISO 13788 mention 80% surface relative humidity as the
critical growth limit for mold, and DIN 68800-2 gives a material humidity criteria (e.g. 20 MC%)
for building products made of wood or wood materials. In addition, HUD (the Department of
Housing and Urban Development of the U.S) uses 80% average relative humidity on a surface
over a certain period of time during summer as the critical condition for mold growth, and
requires manufactured houses to have interior vapor retarders to avoid moisture problems (U.S.
Department of Housing and Urban Development, 1994).
Detailed discussion of the germination of molds is presented by Sedlbauer (2000). A
biohygrothermal method was developed so as to predict mold fungus formation based on all
mentioned biological growth conditions (temperature, humidity and substrate) for mold fungi at
transient boundary conditions.
Mold can grow on lots of materials found in homes, such as stucco (Kuenzel, 2001), organic
coatings (Van der Wel, 1999), wood (TenWolde, 1994), insulation materials (Andreas etc., 1999),
and everyday dust and dirt. Mold can grow on both internal and external surfaces of building
envelopes. Building components, such as windows, closets, attics, crawl spaces and basements,
are all places that mold is frequently found.
1.2. Comfort and Health Problems Related to Moisture
It is well known that temperature and humidity of indoor air are key factors that influence
directly the thermal sensation of the human body (Fanger, 1972). Furthermore, it has been found
that skin humidity is a major reason for discomfort at high air humidity (Toftum et al., 19981).
For humans, the respiratory track acts as an air-conditioning system that regulates the humidity
content and temperature of inhaled air on its way to the lungs. It has been verified that insufficient
respiratory cooling is a cause of local thermal discomfort, and the respiratory system has more
stringent requirements for air humidity than the skin (Toftum et al., 19982).
6
Whats more, Fang et al. (2000) conducted human body exposure experiments and
discovered that:
1. Air temperature and humidity have a significant impact on both the immediate and the
adapted perception of IAQ;
2. Decreasing the air temperature and humidity may ameliorate the perceived IAQ
significantly, and the acceptability of air can be increased linearly with decreasing
enthalpy of air;
3. Ventilation required for comfort may be significantly reduced when decreasing indoor
air enthalpy. The ventilation rate can be decreased from 10 L/s/person (21.2 cfm/person,
prescribed in existing ASHRAE standard 62-1999 for office buildings) to 3.5
L/s/person (7.4 cfm/person) when the indoor air enthalpy decreases from 45 kJ/kg (19
Btu/lb) at 23C/50% RH to 35 kJ/kg (15 Btu/lb) at 20C/40% RH without sacrificing
the perceived air quality.
Although high humidity levels are not good for occupant comfort, very low humidities can
lead to increased infections for the respiration system. In addition, a low humidity level is also
responsible for electro-static shocks of clothing, carpets, etc.
In addition to thermal comfort, it is a generally-known fact that fungi (e.g., mold) caused by
moisture can harm occupant health, and this type of IAQ problem has received increasing
attention recently.
Fungi can cause health hazards to human beings through inhalation or contact for allergic
reactions, eye and respiratory irritation, infection and toxicity. For people that are sensitive to
molds, symptoms such as nasal and sinus irritation or congestion, dry hacking cough, wheezing,
skin rashes or burning, watery or reddened eyes may occur. People with severe allergies to molds
may have more serious reactions, such as hay-fever-like symptoms or shortness of breath. People
with chronic illnesses or people with immune system problems may be more likely to get
infections from certain molds, viruses and bacteria. Molds can also trigger asthma attacks in
persons with asthma. Headaches, memory problems, mood swings, nosebleeds and body aches
and pains are sometimes reported in mold complaints (www.cdc.gov).
7
The health problems that come from exposure to molds can be summarized as:
1. Respiratory problems, such as wheezing, and difficulty in breathing;
2. Nasal and sinus congestion;
3. Burning and watering eyes;
4. Dry, hacking cough;
5. Sore throat;
6. Nose and throat irritation;
7. Shortness of breath;
8. Skin irritation;
9. Mood problems.
Sick Building Syndrome (SBS) is mentioned more and more frequently in the context of
mold. Occupants inside sick buildings can suffer several nonspecific symptoms (e.g. mucosal
irritations, smarting eyes, repeated common colds, fatigue and weakness of concentration)
without there being a definitive cause. Occurrence of SBC has been attributed to a variety of
causes, including viruses, pollen, mites, pesticides, tobacco smoke, carbon dioxide, carbon
monoxide, nitrogen oxides, ozone, radon, volatile organic compounds (VOC) emissions from
building and facility materials, and, of course, fungus spores. A recent paper addressed the
general hypothesis that Sick Building Syndrome (SBS) is associated with exposure to water-
damaged buildings (Shoemaker et al., 2004).
In addition to fungi, some other organisms that spawn in moisture damaged materials, such
as amoebae, are found to favor co-occurrence with bacteria and fungi and may also cause IAQ
problems (Terhi et al., 2004). Based on a careful investigation in Finland within 124 building
material samples from moisture-damaged buildings, it was found that amoebae were detected in
22% of the samples.
It is reasonable to assume that phenomena leading to harmful exposures and health effects
may include chemical deterioration of moistened building materials, and microbial growth on
moistened materials, with chemical and particle emissions of biological origin. Therefore, a
moisture damage index model was built by Haverinen et al. (2003). Using this model, it was seen
that the predicted risk for respiratory symptoms increases with increasing severity of damage.
Also, a linear relationship between residential moisture damage and occupant reported health
8
symptoms, which was developed as a compromise between the knowledge-based and statistical
models, is preferred because of its simplicity.
1.3. Introduction of Moisture Transfer
Moisture moves under different mechanisms in each of it phases. The primary transport
processes, beginning with the least powerful to the most, are:
1. Vapor diffusion within some porous materials;
2. Vapor convection (i.e., air movement);
3. Liquid water capillarity (i.e., wicking) through porous materials;
4. Liquid gravity flow (including hydrostatic pressure) through cracks, openings;
Vapor diffusion moves water vapor from regions of high vapor pressure to low pressure.
Water vapor pressure is a function of both temperature and relative humidity. High temperature
and relative humidity will result in high water vapor pressure the vapor diffusion driving force.
Diffusion acts to move vapor through air, or through the air within the porous materials. Water
vapor does not diffuse through non-porous materials like steel, glass, some plastics, etc.
Water vapor diffusion plays an important role in transporting water vapor into porous
building enclosures where it can sometimes condense when moisture builds up. To control this
flow, vapor barriers are often specified. However, vapor diffusion alone is not usually the cause
of moisture damage in walls. Vapor diffusion can be important in roofs and walls with absorptive
claddings. Rainwater is absorbed into the cladding and subsequently heated by the sun. Even in
cold climates, very high vapor pressure gradients can form in this situation and move damaging
quantities of moisture inward.
Capillary suction moves liquid moisture slowly and steadily through porous materials from
regions of high liquid concentration to regions of low concentration. The smaller the pores, the
more powerful the capillary suction but the slower the flow. Although the rate of moisture
transport by this mechanism is relatively slow, it can act for years. Capillary transfer is important
in constructions contacting soil, and rain-wetted surfaces. Capillary flow can be controlled or
9
eliminated by installing a barrier to capillary flow. A small air gap or a capillary inactive material
is often sufficient.
Gravity flow can be the most powerful means of moisture transport. Very large quantities of
liquid water, often measured in liter per second, can flow downward through openings, cracks,
pipes, or air spaces when driven by gravity. Gravity flow requires relatively large openings,
which require the dimension to be larger than 1 mm or larger, since capillary suction forces tend
to overwhelm gravity forces in small pores. Hence, water will not flow out of a saturated brick,
but can flow through a screw hole in a plastic windowsill.
Small flows of air can move much greater quantities of water vapor than diffusion can.
Convection through openings in the building enclosure is a major cause of interstitial
condensation, sometimes ten to hundreds of times more significant than diffusion. Therefore,
durable, stiff and strong air barrier systems must be provided in all building enclosures to control
or eliminate convective moisture transport.
Transport processes rarely act alone to move moisture within and through buildings. In
reality, a number of transport processes act in parallel and series. For example, liquid water from
the groundwater may wick upward to below the surface of a crawlspace floor, where it evaporates
and moves by diffusion through the soil into the crawlspace. Small air pressures then act to
transport the water vapor into the main space of the building, raising the interior humidity and
resulting in condensation on a cold water pipe within a suspended ceiling. The condensation
accumulates at this point until it begins dripping onto the drywall ceiling below. Here mold
accumulates and the ceiling is damaged.
Moisture gets into homes from both the outside and the inside. Typical sources of dampness
from the outside are:
1. Floods, ground water;
2. Roof leaks;
3. Inadequate or poor flashing;
4. Missing downspouts and gutters;
5. Window or door leaks;
6. Damaged building materials, etc.
10
Typical sources of dampness from the inside are:
1. Moisture in floors;
2. Unventilated bathrooms and kitchens;
3. Leaky plumbing;
4. Condensation in walls and windows;
5. Unventilated dryers;
6. People, pets, plants, etc.
Ground soil can be a significant source of moisture near basements, crawl spaces
foundations and the first floors of buildings. Soil is a large source of moisture in both liquid and
vapor forms. Liquid water draining directly from the surface or from the water table tends to
penetrate through cracks, holes and other unintentional openings. The liquid water stored within
the soil matrix will wick through the soil and porous building materials like concrete, stone,
wood, etc. Stored liquid water deep below the surface and bound to the soil also provides a
practically inexhaustible supply of water vapor. Since diffusion is a less powerful mechanism,
soil water vapor is less significant than liquid water, but it is still a large moisture source. Water
vapor from soil enters buildings primarily by diffusion, although convection (air leakage) may
occur through soil in some cases. Soil in a wet basement or an uncovered crawlspace has been
found to evaporate at a rate of 100 to 500 g/m2 per day (Straube, 2002). Gravels or crushed stones
act as a capillary break between moist soil and the building enclosure, while the air gap between
stones allows vapor diffusion to act relatively unhindered. Hence, sheet or paint-applied vapor
barriers are often widely used near the exterior of below grad assemblies.
Pipe leaks and rain penetration are sources of water that must be avoided. Rain deposition on
roofs is usually of the order of several hundred to one thousand kg/m2 (200 lb/ft2) in most
climates. Walls typically receive about 25% to 50% of this load (Straube et al., 2000). Even little
leakage can cause serious problems, since liquid water from these sources can quickly reach
catastrophic proportions. Rain leaks or plumbing pipe failures can result in hundreds of gallons of
water being discharged into a building.
Moisture built-in to building materials can be important, but is specific to the type of
building construction and only plays a role for the first few years of a buildings life. Wood
framing typically loses close to 10% of its weight in moisture. A normal concrete mix contains
11
about 200 kg (440 lb) of water per cubic meter, of which about half is later released as vapor.
Hence, a typical house basement system containing 20 to 30 m3 (700 to 1050 ft3) of concrete will
release thousand liters of water over the first year or two. Similarly, a 200 mm (8 in.) thick
reinforced concrete floor slab in an office building can be expected to release 20 liters of water
per m2 during the first two years (Straube, 2002).
Water vapor can be almost as problematic as direct liquid water sources, although the
magnitude of the moisture involved is typically much less. Water vapor condensation may happen
on cold surfaces like water pipes, walls and window surfaces. Water vapor from the exterior
enters the building both through intentional ventilation and unintentional air infiltration through
the building enclosure and ducts.
In many types of buildings, a significant amount of moisture can be released or generated by
occupants, their activities and process. Also pets and plants raised inside the building can also
contribute to moisture generation.
For moisture-damage problems to occur, it is necessary for at least the following conditions
to be satisfied:
1. A moisture source must be available;
2. There must be a route or means for this moisture to travel;
3. There must be some driving force to cause moisture movement, and
4. The materials involved must be susceptible to moisture damage.
It is possible to avoid a moisture problem by eliminating any one of the four conditions. In
reality, it is practically impossible to remove all moisture sources, to create buildings with no
imperfections, or to remove all forces driving the moisture movement. It is also uneconomical to
use only materials that are not susceptible to moisture damage. Hence, in practice, it is often
advantageous to address two or more of these prerequisites so as to reduce the probability of
having a problem.
In practice, for new constructions, building envelope assemblies with a high tolerance for
moisture are, of course, highly recommended. While, for existing buildings with moisture
problems, a change in building operation is often the practical option to control moisture. This
12
usually involves manipulating indoor temperature and humidity. However, moisture
accumulation in the building envelope also can be minimized by controlling the dominant
direction of airflow. Whats more, ventilation can be an effective way for removing moisture in
many cold winter climates: ventilation is intended to not only provide acceptable indoor air
quality, but also control humidity (TenWolde et al., 1994).
1.4. Objectives of this Research
This project was motivated by a desire to improve an existing model developed by NIST
called MOIST 3.0 (Burch et al., 1997). MOIST 3.0 is a public software that models transient
one-dimensional hygrothermal performance of external building envelope structures subject to
limited boundary conditions. The primary deficiencies in the MOIST model include:
1. Wetting of exterior surfaces by rain is not considered;
2. Very simple model for coupling of external walls and ambient to internal space:
a) does not couple the determination of the indoor air humidity to the moisture
transport through exterior structures,
b) fully-mixed internal zone state with lumped storage for energy and moisture within
internal structures and furnishings (transport of moisture by air movement is
neglected),
c) neglects the effects of solar transmitted through windows and internal radiative
gains,
d) doesnt include the effects of wind and ambient temperature on infiltration,
e) doesnt consider ground coupling;
3. Doesnt consider water pooling around foundation due to groundwater or snow melt;
4. Snow insulating effects for horizontal surfaces are neglected;
5. Transport of heat by liquid movement in walls is neglected;
6. Only considers one-dimensional heat and mass transfer;
The last three assumptions are relatively common and reasonable for most applications.
This thesis will address the first two deficiencies. Although the third deficiency can be very
important, it is difficult to address and beyond the scope of the current effort.
13
The first objective of this thesis is to develop a wetted surface model for exterior walls that
considers the effects of wind-driven-rain where water capillary transfer dominates. A number of
different codes have been developed for moisture transport in walls that consider capillary
transfer model and include a wetted surface condition (see Chapter 2). However, very little work
has been performed for validation of the water capillary transfer. Therefore, a key contribution of
the current work is a detailed validation of the water capillary wall model.
The second objective is to develop a detailed whole-building model for residences that more
appropriately models coupling of the envelope and ambient to the internal space, while
considering both energy and moisture transport. This will allow evaluations of the impacts of
envelope design on occupant comfort, energy use, and wall material conditions that can lead to
mold growth, insulation degradation, etc. In addition to the transient heat and mass transfer
model for exterior walls, the whole-building model incorporates models for air/moisture
infiltration and air/moisture movement within the space, moisture and heat generation, windows,
transient heat transfer within a floor slab and ground, energy and moisture storage within internal
structures and furnishings, and equipment.
One of primary considerations in the model development is computational speed. The
transport mechanisms for moisture within structural materials and heat within the ground are
relatively slow and require long simulation periods (e.g., multiple years) to erase the effects of
initial conditions and to identify worst case conditions. In addition, the simulation time step
needs to be significantly less than an hour in order to accommodate faster dynamics associated
with the zone air and internal furnishings that respond to driving conditions (internal gains, solar
radiation, etc.) that may vary significantly on an hourly basis.
The primary reason for incorporating internal air movement is to accommodate large
differences in moisture conditions that can occur within a house on different floors and within
confined spaces having high moisture generation (e.g., bathrooms). For instance, moisture
migration caused by air flow from a lower level to a higher level because of the stack effect can
cause severe condensation on the top floors for multi-floor buildings (Clarkin and Brennan,
1998). It is not necessary to determine detailed spatial variations in air conditions in order to
consider these effects. As a result, a simplified airflow network modeling approach incorporated
within CONTAMW 2.0 (Dols and Walton, 2002) will be used to solve air flow and vapor
14
migration for multiple zones. A simplified version of this model has been developed to provide
computationally efficient estimates of air flow rates from ambient to the building and from one
zone to another zone inside a multi-zone building. The coupling of the air flow and vapor
migration model to the hygrothermal wall model and whole building model will be a unique
contribution of this thesis.
Existing modeling approaches are also being used for other elements of the whole building
model. However, a key contribution of the research will be to identify modeling simplifications
and coupling approaches that lead to computational improvements. For instance, a simplified
model has been developed for transient ground heat transfer with slab-on-grade floors. In
addition, different approaches are considered for solving the system of equations that characterize
energy and moisture transport in buildings.
The third objective of this thesis is to utilize the whole-building moisture model to
investigate the impact of design choices and external driving factors on moisture buildup in
materials and internal moisture levels. The results of this analysis will be used to identify
guidelines for appropriate design practices so as to prevent and correct specific moisture
problems.
1.5. Organization of this Thesis
This thesis presents an enhanced heat and moisture transfer model for building materials,
which includes heat diffusion, water vapor diffusion and water liquid capillary transfer. The wall
model is driven by different boundary conditions, including dry bulb temperature, water vapor
pressure, solar radiation, and wind-driven-rain (which may bring the building material to a wet
regime where capillary transfer dominates). In order to validate the liquid capillary transfer, an
experiment which employed moisture pin-pairs and automated weighing system, was performed
for the drying process of the soaked wood specimen. Then, the validated single wall model was
incorporated into a whole building heat and moisture balance model that includes building
structure heat and moisture transfer, heat loss from a slab-on-ground floor, indoor heat and
moisture generation, inter-zonal and infiltration air flow, soft furnishing (bedding and curtain,
etc) moisture buffering, and HVAC equipment heat and moisture removal. This whole building
15
simulation toolkit was applied to evaluate building envelope heat and moisture performance for a
number of case studies and some general guidelines were developed.
There are seven chapters in this thesis as follows:
Chapter 1, Introduction. This chapter provided basic background on problems caused by
moisture, such as building material damage, thermal comfort problems, and
occupant health problems due to mold and mildew growth. The purpose was to
provide a motivation for the objectives, which were also presented in this chapter.
Chapter 2, Modeling of heat and moisture transfer in building exterior walls. The one-
dimensional mathematical heat and moisture transfer model that is incorporated in
MOIST 3.0 is developed. The assumptions and limitations of this model are
discussed and compared with other existing models from the literature. The model
from MOIST 3.0 is then enhanced to consider wetted surfaces caused by wind-
driven rain and is used to demonstrate the effects of solar driven moisture build up
within building materials.
Chapter 3, Experimental validation of exterior wall model. A laboratory test was
performed for the drying process of a sugar-pine panel from a soaked initial
condition. The surfaces were exposed to radiant heating and controlled air flow
boundary conditions and the data was used to validate the MOIST model for
heat/vapor/capillary transfer. An automated weighing system was used to trace the
overall wood moisture content and moisture pin-pairs measured the local moisture
content within the test specimen. During the transient drying test, radiant heating
was projected on one surface then switched to the other so as to develop a better
understanding of the nature and significance of solar-driven inward vapor
diffusion.
Chapter 4, Ground-coupled slab floor heat transfer model. A simplified model is developed
for predicting transient heat transfer in ground-coupled floor slabs that can be
integrated within hourly simulation programs. Since residential buildings usually
have only one or two floors, heat transfer to or from the slab can be a significant
16
component in the overall energy analysis. Results from the simplified model are
compared with results from a finite-element model.
Chapter 5, Whole building heat and moisture balance modeling. The whole-building model
couples the exterior wall and floor models to other models necessary to determine
moisture and mass balances within the space. These models include:
1. Weather data treatment: wind driven rain, sky temperature and solar radiation,
2. Indoor heat and moisture generation models,
3. Simplified multi-zone air flow model for air flow from ambient to the zone and
between zones,
4. Ground floor heat transfer model,
5. Indoor moisture buffering model associated with soft furnishing,
6. HVAC equipment (moisture removal by coils and energy consumption by
compressor).
With these detailed modules, the whole building simulation toolkit can realize heat
and moisture analysis for room/attic air temperature and relative humidity, and
moisture performance of building structures. In addition to presenting the whole
building analysis model, this chapter presents comparisons of results from the
whole building analysis with results for a single wall analysis performed with
constant indoor conditions.
Chapter 6, Case studies. Case studies for building heat and moisture performance are presented
to investigate the impact of design choices and external driving factors on moisture
buildup in materials and internal moisture levels. The results of this analysis are
used to identify guidelines for appropriate design practices so as to prevent and
correct specific moisture problems.
Chapter 7, Conclusions and future work. This chapter presents the overall conclusions,
remaining challenges and recommendations for future work.
17
CHAPTER 2. MODELING OF HEAT AND MOISTURE TRANSFER IN EXTERIOR WALLS
Building envelope hygrothermal analysis is complex, because heat and moisture transfer are
transient, and highly coupled with each other. Even though experimental studies are the most
direct approach for studying the moisture performance of building envelopes, testing is very
costly and time consuming. In particular, very long experimental durations would be necessary
due to very low speed of moisture migration. Therefore, it would be very difficult to
experimentally investigate varieties of building assemblies under different kinds of indoor and
outdoor conditions. On the other hand, numerical simulation techniques can provide relatively
fast estimates of the heat and moisture performance of the building materials with acceptable
accuracy.
This chapter presents the basic assumptions and modeling approach that will be applied for
heat and moisture within external wall assemblies. This approach is compared with other existing
models and improvements are developed to handle wetted surface effects. Some demonstration
results are then given for the effects of solar driven vapor diffusion after wind-driven rain.
2.1. Modeling of The Heat and Moisture Transfer in Building Envelope
2.1.1. Major Assumptions of the Heat and Moisture Transfer Model
In this thesis, the building envelope transient heat and moisture transfer model is developed
based on MOIST 3.0 (Burch and Chi, 1997) in order to analyze the moisture performance of
building materials. This model incorporates the following assumptions:
1. Heat and moisture transfer are one-dimensional;
2. The construction is airtight, and the transport of moisture by air movement is neglected;
18
3. Snow accumulation on horizontal surfaces, and its effect on the solar absorptance and
thermal resistance is neglected;
Other specific assumptions will be discussed later.
2.1.2. Mathematical Description of the Heat and Moisture Transfer Model
The migration of moisture is primarily the result of vapor diffusion and capillary transfer of
liquid. It turns out that the laws describing the migration of heat, vapor, and liquid look very
similar. Temperature is used as the potential or driving force for heat flow, water vapor pressure
is the driving force for the vapor transfer, and capillary suction pressure is the driving force for
liquid flow. For a wall assembly, the following equations can be used to represent these three
mechanisms for one-dimensional transport:
1. Law of Fourier (for heat conduction)
(2.1)
where q is the heat flux, k is the thermal conductivity of the material, T is temperature, and y is
the length.
2. Ficks Law (for vapor diffusion)
(2.2a)
where nA is the amount of flux for substance A, is the density, DAB is diffusion coefficient of
substance A in substance B, and uA is the concentration of substance A. The diffusion flux is
usually expressed as a mass flux, so that Eqn. (2.2a) can be transformed to:
where mv is the mass flux for vapor, is the water vapor permeability, and Pv is water vapor
pressure.
(2.2b)
" Tq ky
=
" AA ABun Dy
=
" vvPmy
=
19
3. Darcys Law (for capillary transfer):
where mw is the mass flux for liquid water, K is the hydraulic conductivity for liquid, and Pl is
capillary pressure.
It should be noted that the signs of the equations for Ficks law and Darcys law are
different. This is because water vapor flows in the opposite direction of the gradient in water
vapor pressure, whereas capillary water flows in the same direction of the gradient in capillary
pressure (typically called capillary suction pressure).
Mass balance:
Figure 2.1 depicts the mass transfers within a differential element of a wall having a source
generation. For a given phase k (vapor, liquid, or solid), a transient mass balance on the water
yields:
where d is the building material density for dry conditions (subscript d means dry condition), is
the moisture content in kg/kg or lbm/lbm, t is time, and S is the source term. In subsequent
developments, the subscript k will be replaced with v for vapor, w for water and ice for ice.
Figure 2.1 The schematic for the moisture balance.
(2.3)
(2.4a)
" lwPm Ky
=
k kd k
m St y
= +
dy
Sk
k kkmmy +
km
20
v vd v
m It y
= +
w wd w
m It y
= +
, ,
0kice w v
I =
For the moisture transfer problem within a building envelope, there is no source term, but
there is phase change, so it is reasonable to change Eqn. (2.4a) to:
where Ik represents a transfer of moisture from the phase k due to phase change.
1. For vapor, the application of Eqn. (2.4b) gives:
2. For liquid water:
3. For ice, there is no ice flow so that:
The summation of Eqn. (2.5a, b, and c) gives:
However, the individual transfers associated with the phase changes must balance internally, so
that:
Thus, Eqn. (2.6) can be simplified to:
(2.4b)
(2.5a)
(2.5b)
(2.5c)
(2.6)
(2.7)
(2.8)
k kd k
m It y
= +
iced iceIt
=
( ) ( ), ,
v w ice v wd k
ice w v
m mI
t y
+ + +
= +
( )v wd
m mt y
+=
21
tyPK
yyP
y dlv
=
After plugging Eqn. (2.2b) and (2.3) into Eqn. (2.8), the overall moisture balance is:
Energy balance:
The energy flow for a differential element within a wall is depicted in Figure 2.2 There is no
energy generation within the envelope, and in the absence of freezing or thawing, the primary
energy flows are heat conduction and enthalpy flow caused by liquid water transfer and water
vapor transfer. An overall energy balance on the wall material and moisture within the differential
element can be written as:
Figure 2.2 The schematic for the energy balance.
(2.9)
dy
mv"hv
mw"hw
q"
v vv v v v
m " hm " h "h dy m dyy y
+ +
w ww w w w
m " hm " h "h dy m dyy y
+ +
q"q" dyy
+
T, = w+v
22
where h is the enthalpy, and hfg is the heat of vaporization. Since v is much smaller than w, it is
reasonable to assume that =w. Furthermore, because cp,v is much smaller than cp,w, the sensible
heat of the water vapor within the building material is negligible and Eqn. (2.10a) can be
simplified as:
Eqn. (2.10b) can be simplified by eliminating common terms, so that:
In addition, the enthalpy for vapor at its given temperature can be expressed in term of heat of
fusion and liquid enthalpy for the same temperature:
(2.12)
Eqn. (2.12) can be substituted into Eqn. (2.11) to yield:
( ) ( )( ), ,v w v wfg w v wm " m " h h q"- " " d p d p w d v fgwc c T h
h h h m my y y y y t
+ + + =
(2.13a)
and then rewritten as:
( )( ), ,v w v v wfg w v w
m " m " m " h h q"- " "d p d p w d v fgc c T h
h h m my y y y y y t
+ + + =
(2.13b)
Substituting the mass balance of Eqn. (2.8):
(2.10a)
(2.10b)
( )( ), ,v v w wv v w w
m " h m " h q"- " "d p d p w d v fgc c T h
h m h my y y y y t
+ + =
(2.11)
( )( )
v vv v v v v v
w ww w w w w w
, ,
m " hm " h - (m " h " )
m " hm " h - (m " h " )
q"q"- (q" )d p d p w d v fg
h dy m dyy y
h dy m dyy y
c c T hdy dy
y t
+ + +
+ + +
+ + + =
( )( )
v vv v v v v v
w ww w w w w w
, , ,
m " hm " h - (m " h " )
m " hm " h - (m " h " )
q"q"- (q" )d p d w p w v p v d v fg
h dy m dyy y
h dy m dyy y
c c c T hdy dy
y t
+ + +
+ + +
+ + + + =
v fg wh =h +h
23
( )( ), ,v v wfg w v w
m " h h q"" "d p d p w d v fg
d
c c T hh h m m
y t y y y t
+ +
+ =
(2.13c)
The mechanistic equations for heat conduction and mass transfer can then be inserted to give:
( )( ), ,v ww v w
h h" "d p d p w d v fgv
fg d
c c T hPTk h h m my y y y t y y t
+ +
+ + =
(2.14a)
Rearranging:
( )( ), , v ww v w
h h" "d p d p w d v fgv
fg d
c c T hPTk h h m my y y y t t y y
+ +
+ = + +
(2.14b)
and expanding the energy change rate term on the right-hand side for T and assuming constant
specific heats for the wall material and liquid water:
(2.15)
which results in:
(2.16)
An order of magnitude analysis can be used to show that the last three terms on the right-
hand side of this equation are negligible compared to the other terms. Even though the heat of
vaporization is large, the second term on the right-hand side is small because water vapor transfer
occurs over a long period of time leading to a very small rate of change in vapor content. The last
two terms are small because the liquid water and vapor fluxes, water vapor and liquid specific
heats, and temperature gradients within a building envelope are all small. As a result, Eqn. (2.16)
can be simplified as:
(2.17)
Eqn. (2.9) and (2.17) are the resulting governing equations that need to be solved in order to
evaluate moisture and energy transport in a wall. However, in order to facilitate the numerical
solution, the vapor diffusion and capillary transfer equations are decoupled to give the following:
( ) v w, , , p,w v wh h" "v vfg d p d p w d fg d p w dPT Tk h c c h c T c T m my y y y t t t t y y
+ = + + + + +
( ) v w, , v wh h" "v vfg d p d p w d fgPT Tk h c c h m my y y y t t y y
+ = + + + +
( ), ,vfg d p d p wPT Tk h c cy y y y t
+ = +
24
(2.18a)
(2.18b)
(2.18c)
(2.18d)
These equations are non-linear (due to variable properties for , K, and k) and strongly coupled
and have time-varying boundary conditions. The boundary conditions and numerical solution are
described in later sections.
2.1.3. Comparison of Moisture Transfer Modeling Tools
There are several models that have been developed for modeling moisture transport in walls
that are reviewed briefly below.
1) MATCH - Moisture and Temperature Calculations for Constructions of Hygroscopic
Materials, was developed at Technical University of Denmark (Peterson, 1990). This
is a one-dimensional transient heat and moisture transfer model that was the basis for
the model incorporated in MOIST 3.0;
2) MOIST 3.0 was developed at NIST in the mid 1990s, and there has been no further
development since 1997. It utilizes a 1-dimensional model for transient heat and
moisture transfer that was briefly described in the previous section. A comprehensive
laboratory experiment was conducted by Zarr et al. (1995) to verify the accuracy of
the MOIST 3.0 in the hygroscopic regime. Good agreement between predictions and
measured results for the moisture content and surface heat flux was found. However,
a separate validation by Sipes et al. (2000) did not show as good results, possibly due
to two-dimensional transfer phenomena and the assumption of negligible sky
radiation in the model. MOIST was applied to assess the moisture performance of
building envelops under constant indoor conditions (Burch et al. 1995), variable
indoor relative humidity (Tsongas et al. 1995) and roofs (Burch et al. 1996 and
v v vd
P my y y t
= =
( ), ,vfg d p d p wPT Tk h c cy y y y t
+ = +
l w wd
P mK
y y y t
= = v w = +
25
Tsongas et al. 1996) in terms of building material surface relative humidities and
internal moisture contents.
3) HygIRC-1D is a one-dimensional hygrothermal computer model developed at the
Institute for Research in Construction in Canada for the aim of heat and moisture
analysis of building materials in Canadian climates. Compared to MOIST, moisture
migration due to air flow within the porous wall materials is included. A series of
research papers was published that covers modeling (Maref et al., 2004), parametric
studies for the moisture management (Kumaran et al., 2002 and 2003), and mid-scale
and large-scale measurements (Maref et al., 2002 and 2004). In addition to the one-
dimensional analysis, hygIRC was extended to a two-dimensional model, which is
called hygIRC-2D. HygIRC-2D can treat both air and water leakage for the building
materials, and considers gravity effects for problems related to the capillary transfer.
This model has been used for moisture performance analysis of building components
(Mukhopadhyaya et al., 2004).
4) MEWS - Moisture management for Exterior Wall Systems, was developed at
National Research Council Canada in 1998 (NEWS Project reports Task 2~8, 2002).
Its simulation model is based on hygIRC ;
5) HAM, for Heat, Air and Moisture transport, is a building simulation program that
provides one-dimensional calculations of heat, air and moisture transport processes in
a building enclosure. The program is based on the finite difference technique with
explicit forward differences in time. Analytical solutions for the coupling between
the computational cells for a given air flow through the construction are used.
Moisture is transferred by diffusion and convection in vapor phase. No liquid water
transport is considered. HAM was initiated in the European Union and sponsored by
IEA-Annex 24. It is has developed as part of HAM-Tools, an integrated simulation
tool for heat, air and moisture analyses for whole buildings (Sasic Kalagasidis, 2003).
The HAM-Tools wall block was compared with other models within the HAMSTAD
project (Heat Air and Moisture Standardization) and had reasonable agreement.
6) WUFI (Wrme und Feuchte instationr German for Transient Heat and Moisture)
was developed at IBP (Institute for Building Physics, Germany) for calculation of the
transient hygrothermal behavior of multi-layer building components exposed to
natural climate conditions. WUFI considers the influence of wind-driven rain, solar
26
radiation, and night sky radiation on the hygrothermal performance of wall systems.
It has both one-dimensional and two-dimensional options for analysis. WUFI was
validated through experiments and excellent agreement in total water content
between experiments and predictions was found (Knzel, 1995). WUFI has been
used to calculate overall moisture transfer for the drying of single layer brick walls
after impregnation (the impregnation could be assumed to be the effect of long term
rain) and good agreement was found between the predicted values and the results of
field test (Knzel et al. 1996).
WUFI has an international cooperation with the Oak Ridge National Laboratory
(USA) to develop a hygrothermal design tool named WUFI-ORNL/IBP. A complete
data set (including temperature, relative humidity, wind speed and orientation,
driving rain, and solar radiation) for more then 50 North American locations is
included in the model. This hygrothermal design model can assess the response of
building envelope systems in terms of heat and moisture loads and can also provide a
very useful and fair method for evaluating and optimizing building envelope designs
(Karagiozis et al., 2001). This software has hundreds of users in North America, and
John Straube, from the University of Waterloo, stated that: WUFI-ORNL/IBP could
well put an end to some of the controversies that have persisted in the building design
community.
7) UMIDUS is a tool to model coupled heat and moisture transfer within porous media
in Brazil. In order to analyze hygrothermal performance of building elements when
subjected to any kind of climate conditions, both diffusion and capillary regimes are
taken into account. UMIDUS has been built in an OOP language to be a fast and
precise easy-to-use software (Mendes et al., 1999).
8) CHAMPS, Coupled Heat, Air, Moisture, and Pollutant Simulations, is being
designed at Syracuse University, USA (Zhang, 2005) to allow one-, two- and three-
dimensional modeling of coupled heat and moisture transport. CHAMPS will include
the ability to predict contaminant transfer through building materials in addition to
heat and moisture transfer,
There are also some other codes that have been developed for heat and moisture transfer
calculations. For detailed comparison of these codes, please refer to:
27
http://www.cmhc-schl.gc.ca/publications/en/rh-pr/tech/03-128-e.htm
After careful study of the publications related to the leading and active software in this field
(e.g., MOIST, HygIRC, HAM, WUFI and UMIDUS), it can be concluded that the basic
governing equations for moisture and energy transport in the building envelope are the same
under the assumptions of one-dimensional transfer and no internal air flow. However, they do
differ in terms of the surface boundary conditions, material property correlations, and numerical
solution schemes.
In hygIRC, WUFI, UMIDUS and CHAMPS, capillary transfer for the liquid water is
included, so that they have the ability to handle a wetted surface condition caused by wind driven
rain. In addition, some validation of wetted surface moisture transfer in single layer materials has
been performed. However, no one has performed validation with wetted surface boundary
conditions in combination with solar heating effects or considered multiple layers. In addition,
previous validation studies involving capillary transfer have not provided transient moisture
distribution comparisons. Although some research groups have tried to realize whole building
heat and moisture analysis, e.g., HAM-Tools and UMIDUS, they utilized some simplifying
assumptions such as neglecting liquid water capillary transfer,, not accurately considering
infiltration, or neglecting differences in moisture concentrations in different parts of the building.
2.1.4. Properties of Building Material
One of the most important aspects of moisture transport modeling is material properties. In
this project, material property co
