Thermal Modeling of a Historical Building Wall: Using Long-Term Monitoring Data to Understand the Reliability and the Robustness of Numerical Simulations
Abstract
:1. Introduction
2. Methodology
- The first step consists of setting up the monitoring system that provides a long-term analysis of the thermal behavior of the historic wall under analysis.
- The software Delphin 6.1 [35] is used to set up the numerical model of the wall (at the component level). Since several input parameters of the simulation are unknown at this stage, several simulations were carried out by varying the materials in the database and choosing those that reduced the difference between the simulation values and those obtained from the monitoring system. The simulation with the optimal materials identified in this way was identified as the first optimized simulation.
- The definition of the variation range with each unknown input parameter of the numerical model. This process is done using different sources such as scientific literature, datasheets and software databases, national and international standards, and laboratory measurements. The outcome of this step is a variation range for each unknown input parameter.
- Use of sensitivity analyses (SA) to identify which of the input parameters are the most influential (or are negligible) for the calibration of the numerical model. In particular, the differential sensitivity analysis (DSA) is applied.
- Model calibration using the optimization program GenOpt. The optimization algorithm is set to reduce the discrepancy between simulated and monitored data. The final output of the optimization process is the calibrated model and the definition of all the unknown input parameters.
2.1. The Case Study
2.2. Monitoring System
- denotes the position of the sensors located on the outermost side of the stratigraphy, between the pre-existing old plaster and the new plaster.
- indicates the position of the sensors placed in the layer of glue used for the installation of the insulation.
- specifies the position of the sensors closest to the inside of the house. These have been fixed above the insulation and are located under the plaster layer applied to the interior surfaces.
2.3. Thermal Wall Modeling in Delphin
2.3.1. Statistical Index
- is the temperature recorded by the sensors;
- is the hourly outcome in terms of temperature from the simulation;
- is the measurement uncertainty calculated as the maximum value between the instrument accuracy (±0.3 °C) and the standard deviation () between sensors placed in the same layer.
2.3.2. Materials and Parameters Selection for the First Optimized Simulation
2.4. Differential Sensitivity Analysis (DSA)
2.4.1. Range Selection of Materials Parameters
- Uncertainty in the measurement result (typically not expressed in the datasheet);
- Uncertainty in the source used to provide the number in the datasheet (often datasheet reports a number without a reference standard or methodology and in some cases, the number might not even correspond to a measured value);
- Uncertainty in the installation procedure which might influence the material property;
- Uncertainty associated with the effect of ageing, moisture, and temperature.
- Commercial technical datasheets (if available);
- International standards;
- Databases of hygrothermal simulation software;
- Scientific literature;
- Laboratory measurements.
- Specific heat () equal to 700 J/kgK (with the error of ±20%);
- Density () equal to 2450 kg/m3 (with the error of ±100 kg/m3);
- Thermal conductivity () equal to 2.65 W/mK (with the error of ±10%).
- For density, a weighted average based on volume percentages is used
- For specific heat capacity, a weighted average based on mass percentages is used [45]
- For thermal conductivity, the weighted average is not the correct approach and in general an accurate derivation would require dedicated simulations [45]. However, in this context, there are already several other uncertainties and since the methodology is applied for the definition of variation ranges, a volume-weighted average approach is considered suitable. Based on the results obtained in [45], it has been assessed that this simplified methodology can lead to an overestimation of the thermal conductivity of the homogenized porous medium by approximately 22%. This effect is taken into account by decreasing the lower limit of the variation range by 22%.
2.4.2. Range Selection of Boundary Coefficients
2.5. Thermal Optimization
3. Results and Discussion
3.1. Sensitivity Analysis
3.2. Results of the second Optimization
- The temperature of the indoor sensor is measured toward the interior of the room, a few meters away from the analyzed perimeter wall. As a result, the air temperature measured by the sensor may be higher than the air temperature close to the wall. A higher temperature would then cause the internal convective heat transfer coefficient to be overestimated in order to rebalance the model.
- The measured outside temperature may also be overestimated when solar radiation is present. In fact, although a radiation shield has been applied, it is known that it is very difficult to obtain a perfect screening. Therefore, with higher external air temperature, the model will underestimate the solar radiation and thus reduce the value of the radiation absorption coefficient.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Symbol | Title | Unit of Measure |
External convective heat transfer coefficient | W/m2K | |
Internal convective heat transfer coefficient | W/m2K | |
Heat capacity | J/kgK | |
Position of sensors in the stratigraphy (behind the external plaster) | - | |
Position of sensors in the stratigraphy (behind the insulation) | - | |
Position of sensors in the stratigraphy (behind the internal plaster) | - | |
Temperature recorded by the sensors | °C | |
Hourly outcome in terms of temperature from the simulation | °C | |
Volumetric heat capacity | kJ/m3K | |
Measurement uncertainty calculated as the maximum value between the instrument accuracy (± 0.3 °C) and the standard deviation (σ) between sensors placed in the same layer | °C | |
Absorption coefficient for short waves radiation | - | |
Statistical index (equation 1) | - | |
Statistical index related to the position | - | |
Statistical index related to the position | - | |
Statistical index related to the position | - | |
Average of the three calculated indices (, ) | - | |
DSA | Differential sensitivity analysis | - |
SA | Sensitivity analysis | - |
Thermal conductivity | W/mK | |
Density | kg/m3 |
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Input Parameters | Known/Unknown | Sources (“First Optimized Simulation”) | |
---|---|---|---|
External climatic conditions | Temperature | Known | Monitoring System |
Short Wave Solar Radiation | Known | Monitoring System | |
Indoor climatic conditions | Temperature | Known | Monitoring System |
Wall Model | Thermal Conductivity (5 materials) | Unknown | Delphin Database + Preliminary Optimization |
Specific Heat Capacity (5 materials) | Unknown | Delphin Database + Preliminary Optimization | |
Density (5 materials) | Unknown | Delphin Database + Preliminary Optimization | |
Boundary coefficients | Convective heat transfer coefficient (Internal) | Unknown | WTA Recommendations 6.2 [37] |
Convective heat transfer coefficient (External) | Unknown | WTA Recommendations 6.2 [37] | |
The solar absorption coefficient for short wave radiation | Unknown | DIN 18599 [38] |
Materials | New Plaster | Old Plaster | Glue | Stonemasonry | Insulation | |
---|---|---|---|---|---|---|
(J/kgK) | Initial | 999.2 | 1417.7 | 889 | 708 | 2000 |
min/max | 630/1500 [35] | 630/1500 [35] | 772.2/1461.2 [35] | 531/1348 [35], (Lab measures) | 1000/2100 [42], (Datasheet) | |
Step-size | 30 | 30 | 23.8 | 28.2 | 37.9 | |
(kg/m3) | Initial | 1200 | 1520 | 1673 | 1919 | 150 |
min/max | 1035/1600 (Datasheet), [35],[46] | 600/1800 [46] | 561/1753 [35] | 1494/2443 [45],[35] (Lab measures) | 40/250 [46] | |
Step-size | 19.5 | 41.3 | 41.1 | 32.7 | 7.2 | |
(W/mK) | Initial | 0.28 | 0.62 | 0.72 | 2.00 | 0.042 |
min/max | 0.18/0.80 [46] | 0.28/0.82 [35],[29] | 0.12/1.10 [35], (Datasheet) | 1.13/2.62 [45],[44],[43], (Lab measures) | 0.038/0.061 [41],[42] | |
Step-size | 0.02 | 0.02 | 0.03 | 0.05 | 0.001 |
Boundary Coefficients | Initial | (-) | ||
---|---|---|---|---|
8 | 17 | 0.4 | ||
min/max | 4/10.6 [37],[47] | 11.9/17 [37],[47] | 0.2/0.6 [35],[48] | |
Step-size | 0.34 | 0.26 | 0.02 |
Materials | λ [W/mK] | |||||||
---|---|---|---|---|---|---|---|---|
First Optimized Simulation (Initial Value) | Range (min-max) | Second Optimized Value | Datasheet/Lab Value | First Optimized Simulation (Initial Value) | Range (min-max) | Second Optimized Value | Datasheet/Lab Value | |
New Plaster | 0.28 | 0.18 | 0.32 | <0.63/- | 1199 | - | - | - |
0.80 | - | |||||||
Old Plaster | 0.62 | 0.28 | 0.79 | -/- | 2155 | 378 | 2631 | -/- |
0.82 | 2700 | |||||||
Stone masonry | 2.00 | 1.13 | 1.18 | -/2.65 (only stone) | 1359 | 793 | 1272 | -/1691 (only stone) |
2.60 | 3293 | |||||||
Insulation | 0.042 | 0.038 | 0.040 | 0.043/- | 300 | - | - | - |
0.061 | - |
Materials | Boundary Coefficients | |||
---|---|---|---|---|
First Optimized Simulation | Range (min-max) | Second Optimized Value | Guidelines [37] | |
[W/m2K] | 8 | 4 | 4.14 | 8 |
10.6 | ||||
[W/m2K] | 17.0 | 11.9 | 17 | 17 |
17 | ||||
[-] | 0.4 | 0.2 | 0.205 | 0.4 |
0.6 |
Statistical index | Position | First Optimized Simulation | Second Optimized Simulation | Limit for lv1 Quality According [39] | ||
---|---|---|---|---|---|---|
Index Value | Average Value | Index Value | Average Value | |||
[°C] | Tbip | 0.60 | 0.75 | 0.39 | 0.48 | <1 |
Tbi | 0.60 | 0.34 | ||||
Tbep | 1.06 | 0.70 | ||||
[°C] | Tbip | 0.54 | 0.65 | 0.33 | 0.38 | <1 |
Tbi | 0.48 | 0.23 | ||||
Tbep | 0.92 | 0.57 | ||||
[-] | Tbip | 2.01 | 2.51 | 1.30 | 1.59 | |
Tbi | 2.00 | 1.14 | ||||
Tbep | 3.51 | 2.33 |
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Panico, S.; Larcher, M.; Troi, A.; Baglivo, C.; Congedo, P.M. Thermal Modeling of a Historical Building Wall: Using Long-Term Monitoring Data to Understand the Reliability and the Robustness of Numerical Simulations. Buildings 2022, 12, 1258. https://doi.org/10.3390/buildings12081258
Panico S, Larcher M, Troi A, Baglivo C, Congedo PM. Thermal Modeling of a Historical Building Wall: Using Long-Term Monitoring Data to Understand the Reliability and the Robustness of Numerical Simulations. Buildings. 2022; 12(8):1258. https://doi.org/10.3390/buildings12081258
Chicago/Turabian StylePanico, Simone, Marco Larcher, Alexandra Troi, Cristina Baglivo, and Paolo Maria Congedo. 2022. "Thermal Modeling of a Historical Building Wall: Using Long-Term Monitoring Data to Understand the Reliability and the Robustness of Numerical Simulations" Buildings 12, no. 8: 1258. https://doi.org/10.3390/buildings12081258