Comfort and discomfort indices
1. Introduction
Thermal comfort in the building is an essential requirement. What differentiates modern architecture in terms of the energy problem from the architecture of any era is not only the reduction in the availability of energy resources but rather the demand for thermal comfort.
Energy optimization in buildings is considered a major area of interest in the modern era of scientific research. Energy consumption in buildings has increased from \(24\%\) to \(40\%\) in developed countries. A significant amount of this energy is used to provide a sufficient level of comfort for the building’s occupants. Moreover, given recent increases in global temperatures due to climate change and the associated decrease in comfort levels, it is increasingly important to provide adequate levels of comfort in indoor spaces. However, finding a balance between reducing the energy consumption of buildings and providing adequate levels of comfort is a major challenge (cf.[Gilani2015])
According to ASHRAE Standard 55, thermal comfort is defined as the condition of mind that expresses satisfaction with the thermal environment and is estimated by subjective evaluation. The World Health Organization (WHO) also defines thermal comfort as the condition when people are satisfied with the thermal environment. There are two well-known thermal comfort models that are used internationally to establish the thermal comfort conditions in a building(cf.[Sarah2015]):
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Fanger Model
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Adaptive model .
During our internship, we became interested in the Fanger Model which is a static approach based on the thermal equilibrium of the human body by introducing two indices: the predicted mean Vote (PMV) and the predicted percentage of dissatisfied (PPD).
To get more informations about the comfort thermique, you can follow the link.
2. Model
In the framework of our internship, we are interested in the study of the thermal comfort of the building located in Illkirch.
To carry out this study we implemented a model in which we calculated the thermal comfort indices PMV and PPD. The PMV index depends on several parameters unlike the PPD index which depends only on PMV.
2.1. Validation
As a first step, we implemented a script for the general thermal comfort model where the PMV parameters are chosen according to the norm [ISO-7730].
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\(M\) [\(\text{W}/\text{m}^2\)] : the metabolic rate.
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\(W\) [\(\text{W}/\text{m}^2\)] : the effective mechanical power ( W=0).
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\(I_{cl}\) [\(\text{m}^2\text{K}/\text{W}\)] : the clothing insulation
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\(f_{cl}\) [–] : the clothing surface area factor :
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\(T_a\) [°C] : the air temperature
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\(T_{mr}\) [°C] : the mean radiant temperature
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\(v_{ar}\) [m/s] : the relative air velocity
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\(p_a\) [Pa] : the water vapor partial pressure
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\(h_c\) [\(\text{W}\,\text{m}^{-2}\text{K}^{-1}\)] : the convective heat transfer coefficient with :
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\(T_{cl}\) [°C] : the clothing surface temperature
In order to verify the performance of this model, we compared the results we obtained with results given according to the norm [ISO-7730].
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| Run no. | \(T_a\) (°C) | \(T_{mr}\) (°C) | \(v_{ar}\) (m/s) | RH (%) | M (met) | \(I_{cl}\) (clo) | PMV | PPD | Calculated PMV | Calculated PPD | Verify |
|---|---|---|---|---|---|---|---|---|---|---|---|
1 |
22.0 |
22.0 |
0.1 |
60 |
1.2 |
0.5 |
-0.75 |
17 |
-0.75 |
16.85 |
correct value |
2 |
27.0 |
27.0 |
0.1 |
60 |
1.2 |
0.5 |
0.77 |
17 |
0.76 |
17.17 |
correct value |
3 |
27.0 |
27.0 |
0.3 |
60 |
1.2 |
0.5 |
0.44 |
9 |
0.43 |
8.86 |
correct value |
4 |
23.5 |
25.5 |
0.1 |
60 |
1.2 |
0.5 |
-0.01 |
5 |
-0.02 |
5.01 |
correct value |
5 |
23.5 |
25.5 |
0.3 |
60 |
1.2 |
0.5 |
-0.55 |
11 |
-0.56 |
11.57 |
correct value |
6 |
19.0 |
19.0 |
0.1 |
40 |
1.2 |
1.0 |
-0.6 |
13 |
-0.61 |
12.80 |
correct value |
7 |
23.5 |
23.5 |
0.1 |
40 |
1.2 |
1.0 |
0.5 |
10 |
0.36 |
7.70 |
incorrect value |
8 |
23.5 |
23.5 |
0.3 |
40 |
1.2 |
1.0 |
0.12 |
5 |
0.11 |
5.25 |
correct value |
9 |
23.0 |
21.0 |
0.1 |
40 |
1.2 |
1.0 |
0.05 |
5 |
0.05 |
5.05 |
correct value |
10 |
23.0 |
21.0 |
0.3 |
40 |
1.2 |
1.0 |
-0.16 |
6 |
-.17 |
5.60 |
correct value |
11 |
22.0 |
22.0 |
0.1 |
60 |
1.6 |
0.5 |
0.05 |
5 |
0.04 |
5.03 |
correct value |
12 |
27.0 |
27.0 |
0.1 |
60 |
1.6 |
0.5 |
1.17 |
34 |
1.17 |
33.79 |
correct value |
13 |
27.0 |
27.0 |
0.3 |
60 |
1.6 |
0.5 |
0.95 |
24 |
0.95 |
24.06 |
correct value |
|
For the case 7, we did not find the same results, it could be a typing error in the results of the table given by the norm [ISO-7730]. |
2.2. Application
Once the general model was validated, we adapted it to our problem, which is to calculate the thermal comfort of the building under study. To do this, we took certain parameters for the PMV calculation from the values obtained by the captors installed in the building, and the rest of the parameters were modified so that they were consistent with the configuration of the building.
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Metabolic rate (\(M\)) [Candas2000]
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Effective mechanical power (W=0).
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Clothing insulation (\(I_{cl}\)) equal to \(0.5\) clo in summer and \(1.0\) clo in winter.
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Clothing surface area factor (\(f_{cl}\))
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Air temperature (\(T_a\)) (calculated by captors)
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Mean radiant temperature (\(T_{mr}\))
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Relative air velocity (\(v_{ar}\))
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Water vapor partial pressure (\(p_a\))
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Convective heat transfer coefficient(\(h_c\) )
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Clothing surface temperature (\(T_{cl}\))
In order to calculate the thermal comfort of a given zone we have aggregated the data stored in the "export_comfort" file by fields. We used an area-weighted average : for a given zone, and for a given field, an average is computed, weighted by the rooms’ areas associated to each node in the zone of interest.
The script of the model previously implemented allows us to calculate the thermal comfort of zone 13 for the month of January 2019 or July 2019 with an average radiant temperature equivalent to the air temperature, air velocity equal to 0.1(m/s), M=1.2(met) and W=0.
The figures below represent the results obtained for :
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Month of January
The figures above show that :
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thermal comfort is satisfied according to the norm [ISO-7730] when the PPD is less than \(10\%\), which corresponds to a PMV between \(-0.5\) and \(-0.369\). However this satisfaction can be spread out up to the sensation of a slight coolness (\(-1\)) with a dissatisfaction rate equal to \(25\%\) among people exposed to the same conditions.
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During the month of January the most dominant values of pmv (resp PPD) ranges between \(-1\) and \(-0.5\) (resp \(10\%\) and \(25\%\))
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For a PMV between \(-1.26\) and \(-1\) the PPD is comprised between \(25\%\) and \(38\%\).
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Thermal comfort is ensured for a temperature of \(20(°C)\) with a humidity between \(18\%\) and \(30\%\)
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A negative PMV value means that the temperature is lower than the ideal temperature.
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Month of July
The figures shows that:
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for PMV=0 (neither warmter nor colder) the PPD value equals \(5\%\) which represents an optimal thermal comfort state according to the norm [ISO-7730].
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the thermal comfort is satisfied for a PMV between \(-0.2\) and \(0.5\) and a PPD lower than \(10\%\), This satisfaction is reached for a temperature (humidity) between \(24.7(°C)\) and \(26(°C)\)(resp \(28\%\) and \(43\%\)).
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For a PMV between \(1\) and \(1.26\) the dissatisfaction value is comprised between \(25\%\) and \(43\%\).
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the thermal comfort is satisfied from the july \(7^{th}\) at \(21h \) to july \(25^{th}\) at \(10h\) for a temperature (resp humidity) between \(26.96(°C)\) and \(24.7(°C)\)(resp \(27\%\) and \(37\%\) )
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A positive PMV value means that the temperature is higher than the ideal temperature.
Other results are available here
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References
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[Allab17] Allab, Yacine. Building ventilation performance assessement : ventilation efficiency and thermal comforT. PhD thesis, École nationale supérieure d’arts et métiers, 2017
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[ASHRAE2004] ANSI/ASHRAE Standard 55. Thermal Environment Conditions for Human Occupancy, 2004.
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[Candas2000] Candas, V., Traité Génie énergeétique, Techniques de l’Ingénieur, Doc. BE 9 085, 2000.
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[Cannistraro1992] Cannistraro, G., Franzitta, G., and Giaconia, C., Algorithms for the calculation of the view factors between human body and rectangular surfaces in parallelepiped environments, Energy and Buildings, 19(1992) 51-60
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[Djongyang2010] Djongyang, N., Tchinda, R., and Njomo, D. Thermal comfort: A review paper, Renewable and Sustainable Energy Reviews 14 (2010) 2626–2640.
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[Gilani2015] Syed Ihtsham ul Haq Gilani, Muhammad Hammad Khan and William Pao, Thermal comfort analysis of PMV model Prediction in Air conditioned and Naturally Ventilated Buildings,2015.
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[Hensen1991] Hensen J. L. M., On the thermal interaction of building structure and heating and ventilating system, PhD thesis, Technische Universiteit Eindhoven; 1991. Download PDF
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[ISO-7730] Ergonomics of the thermal environment — Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria
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[Sarah2015] Sarah Benharkat and Djamila Rouag-Saffidine, Approche adaptative du confort thermique dans les espaces d’enseignement universitaire à Constantine,2015