Improving the Accuracy of a Hygrothermal Model for Wood-Frame Walls: A Cold-Climate Study
Abstract
:1. Introduction
2. Measurements
2.1. Overview of Field Measurements
2.2. Material Property Measurements
3. Hygrothermal Model: Initial Design Values
3.1. Database Material Properties
3.2. Boundary Conditions
3.3. Numerical Parameters
3.4. Results
4. Overview of Improvements to the Model
4.1. Customized Material Properties
4.1.1. Vinyl Siding
4.1.2. Extruded Polystyrene
4.1.3. Oriented Strand Board
4.1.4. Fiberglass
4.1.5. Asphalt-Coated Kraft Paper
4.1.6. Latex Paint on Gypsum Board
4.2. Changes in Simulation Results from Improvements
5. Comparison of Improved Simulations with Measurements
5.1. Model Adjustments to Facilitate Comparison
5.2. OSB Moisture Content
5.3. Temperature and Relative Humidity
5.4. Quantitative Comparison of Simulations with Measurements
6. Sensitivity Analysis
6.1. Vinyl Siding
6.1.1. Effective Vapor Permeance
6.1.2. Ventilated Air Cavity
6.2. Short-Wave Radiation Absorptivity
6.3. Exterior Surface Heat Transfer Coefficient
6.4. Fiberglass
6.5. Asphalt-Coated Kraft Paper
6.6. Oriented Strand Board
6.7. Extruded Polystyrene
6.8. Discussion
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Property Data Used in Hygrothermal Simulations
Appendix A.1. Vinyl Siding—Installed Directly on Sheathing or Insulation—Effective Permeance
Property | Value | Design |
---|---|---|
Thickness, mm | 1.11 | |
Bulk density, kg/m3 | 829 | |
Porosity, m3/m3 | 1 | 0.001 |
Specific heat capacity (dry), J/(kg·K) | 2299 | |
Thermal conductivity, W/(m·K) | 0.17 | |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 | |
Water vapor diffusion resistance factor | 700 | 76 |
RH | Water Content, kg/m3 | RH | Water Content, kg/m3 |
---|---|---|---|
0 | 0 | 0.93 | 5.72 |
0.5 | 0.485 | 0.94 | 6.6 |
0.6 | 0.724 | 0.95 | 7.77 |
0.7 | 1.12 | 0.96 | 9.41 |
0.8 | 1.88 | 0.97 | 11.9 |
0.85 | 2.62 | 0.98 | 15.9 |
0.9 | 4.03 | 0.99 | 23.9 |
0.91 | 4.48 | 0.995 | 31.8 |
0.92 | 5.03 | 1 | 47.1 |
Appendix A.2. Extruded Polystyrene (XPS) Insulation
Property | Value | Design |
---|---|---|
Thickness, mm | 25.4 | |
Bulk density, kg/m3 | 28.6 | |
Porosity, m3/m3 | 0.99 | |
Specific heat capacity (dry), J/(kg·K) | 1470 | |
Thermal conductivity, W/(m·K) | 0.025 | |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 | |
Water vapor diffusion resistance factor | 79 | 170.56 |
RH | Water Content, kg/m3 |
---|---|
0 | 0 |
0.1 | 0.009 |
0.5 | 0.08 |
0.8 | 0.31 |
0.9 | 0.66 |
0.97 | 1.95 |
0.99 | 3.94 |
0.999 | 7.09 |
1 | 7.77 |
Appendix A.3. Expanded Polystyrene (EPS) Insulation
Property | Value |
---|---|
Thickness, mm | 38.1 |
Bulk density, kg/m3 | 14.8 |
Porosity, m3/m3 | 0.99 |
Specific heat capacity (dry), J/(kg·K) | 1470 |
Thermal conductivity, W/(m·K) | 0.036 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 73.01 |
RH | Water Content, kg/m3 |
---|---|
0 | 0 |
0.1 | 0.004 |
0.5 | 0.031 |
0.8 | 0.12 |
0.9 | 0.26 |
0.97 | 0.77 |
0.99 | 1.55 |
0.999 | 2.78 |
1 | 3.05 |
RH | µ-Value |
---|---|
0 | 73.01 |
0.1 | 73 |
0.2 | 67.34 |
0.3 | 61.93 |
0.4 | 57.17 |
0.5 | 52.55 |
0.6 | 48.39 |
0.7 | 44.65 |
0.8 | 41.04 |
0.9 | 37.83 |
1 | 34.8 |
Appendix A.4. Mineral Wool (MW) Insulation
Property | Value |
---|---|
Thickness, mm | 38.1 |
Bulk density, kg/m3 | 128 |
Porosity, m3/m3 | 0.954 |
Specific heat capacity (dry), J/(kg·K) | 850 |
Thermal conductivity, W/(m·K) | 0.0322 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 1.3 |
RH | Water Content, kg/m3 | RH | Water Content, kg/m3 |
---|---|---|---|
0 | 0 | 0.99 | 33.43 |
0.65 | 0.4 | 0.995 | 87.9 |
0.8 | 0.7 | 0.999 | 269.26 |
0.93 | 2.2 | 0.9995 | 298.73 |
0.97 | 5.9 | 0.9999 | 312.96 |
0.98 | 12 | 1 | 314 |
Water Content, kg/m3 | Thermal Conductivity, W/(m·K) |
---|---|
0 | 0.0322 |
10 | 0.033 |
20 | 0.034 |
50 | 0.038 |
100 | 0.043 |
200 | 0.062 |
300 | 0.09 |
400 | 0.13 |
500 | 0.18 |
600 | 0.24 |
700 | 0.32 |
800 | 0.42 |
900 | 0.54 |
954 | 0.6 |
Appendix A.5. Spun Bonded Polyolefin Membrane (SBP)
Property | Value |
---|---|
Thickness, mm | 1 |
Bulk density, kg/m3 | 65 |
Porosity, m3/m3 | 0.001 |
Specific heat capacity (dry), J/(kg·K) | 1500 |
Thermal conductivity, W/(m·K) | 2.3 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 49.3 |
Appendix A.6. Spun Bonded Polyolefin Membrane with Crinkled Surface (SBPC)
Property | Value |
---|---|
Thickness, mm | 1 |
Bulk density, kg/m3 | 67 |
Porosity, m3/m3 | 0.001 |
Specific heat capacity (dry), J/(kg·K) | 1500 |
Thermal conductivity, W/(m·K) | 2.3 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 65.6 |
Appendix A.7. Oriented Strand Board (OSB)
Appendix A.7.1. Improved Model
Property | Value | Design |
---|---|---|
Thickness, mm | 11.1 | |
Bulk density, kg/m3 | 534 | 575 |
Porosity, m3/m3 | 0.64 | 0.8625 |
Specific heat capacity (dry), J/(kg·K) | 1280 | 1880 |
Thermal conductivity, W/(m·K) | 0.0806 | 0.084 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 | |
Water vapor diffusion resistance factor | 195 | 1182 |
RH | Water Content, kg/m3 | RH | Water Content, kg/m3 |
---|---|---|---|
0 | 0 | 0.7 | 57.1 |
0.1 | 12.7 | 0.8 | 71.9 |
0.2 | 20.1 | 0.9 | 95.1 |
0.3 | 26.1 | 0.95 | 112.7 |
0.4 | 32 | 0.98 | 126.6 |
0.5 | 38.6 | 1 | 333 |
0.6 | 46.6 | - | - |
RH | µ-Value |
---|---|
0 | 195 |
0.25 | 195 |
0.75 | 47 |
0.8 | 40.8 |
1 | 40.8 |
Water Content, kg/m3 | D (Suction), m2/s | D (Redistribution), m2/s |
---|---|---|
0 | 0 | 0 |
71.9 | 7.37 × 10−13 | 7.37 × 10−13 |
333 | 1.66 × 10−10 | 1.66 × 10−11 |
Appendix A.7.2. WUFI Database Low Density (575 kg/m3) OSB Entries
RH | Water Content, kg/m3 |
---|---|
0 | 0 |
0.49 | 29.6 |
0.695 | 55.2 |
0.905 | 87.4 |
1 | 333.5 |
RH | µ-Value |
---|---|
0 | 1182 |
0.1 | 1182 |
0.2 | 1182 |
0.3 | 525.5 |
0.4 | 295.5 |
0.5 | 187.5 |
0.6 | 130 |
0.7 | 95 |
0.8 | 72.3 |
0.9 | 56.9 |
1 | 45.6 |
Water Content, kg/m3 | D (Suction), m2/s | D (Redistribution), m2/s |
---|---|---|
0 | 0 | 0 |
71.3 | 7.24 × 10−13 | 7.24 × 10−13 |
333.5 | 1.65 × 10−10 | 1.65 × 10−11 |
Appendix A.8. Fiberglass Batt Cavity Insulation (Used with Additional 5 mm Air Gap)
Property | Value | Design |
---|---|---|
Thickness, mm | 135 | 140 |
Bulk density, kg/m3 | 30 | |
Porosity, m3/m3 | 0.008 | 0.99 |
Specific heat capacity (dry), J/(kg·K) | 840 | |
Thermal conductivity, W/(m·K) | 0.0398 | 0.035 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 | |
Water vapor diffusion resistance factor | 1.3 |
Water Content, kg/m3 | Thermal Conductivity, W/(m·K) | Design |
---|---|---|
0 | 0.0398 | 0.035 |
50 | 0.05 | 0.043 |
100 | 0.05 | 0.049 |
Appendix A.9. Kraft Paper Facing
Property | Value | Design |
---|---|---|
Thickness, mm | 1 | |
Bulk density, kg/m3 | 120 | |
Porosity, m3/m3 | 0.6 | |
Specific heat capacity (dry), J/(kg·K) | 1500 | |
Thermal conductivity, W/(m·K) | 0.42 | |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 | |
Water vapor diffusion resistance factor | 1919 | 3000 |
RH | Water Content, kg/m3 |
---|---|
0 | 0 |
0.5 | 0.6 |
0.8 | 1.8 |
0.9 | 2.6 |
0.97 | 3.5 |
1 | 11.2 |
RH | µ-Value |
---|---|
0 | 1919 |
0.25 | 1919 |
0.75 | 609 |
1 | 609 |
Appendix A.10. Polyethylene Membrane (PE)
Property | Value |
---|---|
Thickness, mm | 1 |
Bulk density, kg/m3 | 130 |
Porosity, m3/m3 | 0.001 |
Specific heat capacity (dry), J/(kg·K) | 2300 |
Thermal conductivity, W/(m·K) | 2.3 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 50,000 |
Appendix A.11. Interior Gypsum Board
Property | Value |
---|---|
Thickness, mm | 12.5 |
Bulk density, kg/m3 | 625 |
Porosity, m3/m3 | 0.706 |
Specific heat capacity (dry), J/(kg·K) | 870 |
Thermal conductivity, W/(m·K) | 0.16 |
Thermal conductivity temperature coefficient, W/(m·K2) | 0.0002 |
Water vapor diffusion resistance factor | 7.03 |
RH | Water Content, kg/m3 |
---|---|
0 | 0 |
0.505 | 4.34275 |
0.71 | 6.15625 |
0.896 | 11.3125 |
0.99 | 93 |
1 | 430.625 |
RH | µ-Value |
---|---|
0 | 7.03 |
0.1 | 7.03 |
0.2 | 6.48 |
0.3 | 5.98 |
0.4 | 5.5 |
0.5 | 5.05 |
0.6 | 4.63 |
0.7 | 4.24 |
0.8 | 3.87 |
0.9 | 3.52 |
1 | 3.19 |
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Wall | Interior Vapor Retarder | House Wrap | Exterior Insulation | Label |
---|---|---|---|---|
1 | Kraft paper | Flat polyolefin | None | No CI, kraft |
2 | Polyethylene | Flat polyolefin | None | No CI, poly |
3 | Kraft paper | Flat polyolefin | 38 mm Mineral Wool | MW, kraft |
4 | Polyethylene | Flat polyolefin | 38 mm Mineral Wool | MW, poly |
5 | Kraft paper | Flat polyolefin | 38 mm Expanded Polystyrene | EPS, kraft |
6 | Kraft paper | Flat polyolefin | 25.4 mm Extruded Polystyrene | XPS, kraft |
7 | Polyethylene | Flat polyolefin | 25.4 mm Extruded Polystyrene | XPS, poly |
8 | Kraft paper | Crinkled polyolefin | 25.4 mm Extruded Polystyrene | XPS, kraft, crinkled |
Material | Relative Humidity (%) | Water Vapor Permeance | Literature a | ||
---|---|---|---|---|---|
Boundary Conditions | Mean | (ng Pa−1 s−1 m−2) | (US perm) | (ng Pa−1 s−1 m−2) | |
Oriented strand board | 0–50 | 25 | 92 ± 30 | 1.6 ± 0.5 | 13–190 |
50–100 | 75 | 380 ± 89 | 6.6 ± 1.6 | 160–520 | |
Asphalt-coated kraft paper | 0–50 | 25 | 103 ± 21 | 1.8 ± 0.4 | 9–195 |
50–100 | 75 | 325 ± 128 | 5.6 ± 2.2 | 9–240 | |
Gypsum board with latex paint | 0–62 | 31 | 1140 ± 170 | 19.8 ± 3.0 | 208–2300 |
27–75 | 51 | 1820 ± 280 | 31.7 ± 4.8 | 404–2300 |
Wall | Label | S | N | Average |
1 | No CI, kraft | 117 | 172 | 145 |
2 | No CI, poly | 106 | 101 | 103 |
3 | MW, kraft | 83 | 97 | 90 |
4 | MW, poly | 105 | 122 | 114 |
5 | EPS, kraft | 113 | 91 | 102 |
6 | XPS, kraft | 98 | 92 | 95 |
7 | XPS, poly | 103 | 156 | 129 |
8 | XPS, kraft, crinkled | 98 | 102 | 100 |
- | Average | 103 | 116 | - |
RMSE | 1S | 2S | 3S | 4S | 5S | 6S | 7S | 8S |
OSB MC | 1.50 | 0.93 | 0.78 | 0.99 | 1.49 | 1.03 | 0.83 | 0.99 |
T | 1.52 | 1.53 | 1.01 | 1.26 | 1.10 | 1.05 | 1.34 | 1.04 |
RH | 5.53 | 7.63 | 6.39 | 8.16 | 6.50 | 7.38 | 8.68 | 7.71 |
Scaled Error | 117 | 106 | 83 | 105 | 113 | 98 | 103 | 98 |
Bias T | −0.18 | −0.15 | 0.36 | −0.23 | −0.25 | 0.11 | −0.09 | 0.31 |
Bias RH | 3.40 | 0.83 | 3.17 | 6.95 | 4.10 | 3.97 | 7.41 | 4.53 |
Wall | Label | Base | Wind | Diff |
1N | No CI, kraft N | 172 | 175 | 1.7% |
1S | No CI, kraft S | 117 | 119 | 1.7% |
2N | No CI, poly N | 101 | 101 | 0.0% |
2S | No CI, poly S | 106 | 106 | 0.0% |
3N | MW, kraft N | 97 | 97 | 0.0% |
3S | MW, kraft S | 83 | 83 | 0.0% |
4N | MW, poly N | 122 | 119 | −2.5% |
4S | MW, poly S | 105 | 101 | −3.8% |
6N | XPS, kraft N | 92 | 92 | 0.0% |
6S | XPS, kraft S | 98 | 99 | 1.0% |
7N | XPS, poly N | 156 | 152 | −2.6% |
7S | XPS, poly S | 103 | 102 | −1.0% |
- | Average | - | - | −0.4% |
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Boardman, C.R.; Glass, S.V. Improving the Accuracy of a Hygrothermal Model for Wood-Frame Walls: A Cold-Climate Study. Buildings 2020, 10, 236. https://doi.org/10.3390/buildings10120236
Boardman CR, Glass SV. Improving the Accuracy of a Hygrothermal Model for Wood-Frame Walls: A Cold-Climate Study. Buildings. 2020; 10(12):236. https://doi.org/10.3390/buildings10120236
Chicago/Turabian StyleBoardman, Charles R., and Samuel V. Glass. 2020. "Improving the Accuracy of a Hygrothermal Model for Wood-Frame Walls: A Cold-Climate Study" Buildings 10, no. 12: 236. https://doi.org/10.3390/buildings10120236