# Application of Semi-Circular Double-Skin Facades in Auditoriums in Winter Conditions

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## Abstract

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## 1. Introduction

- What is the thermal behaviour of semi-circular DSFs installed in curved envelopes and their thermal impact on adjacent compartments?
- How can variation in the solar orientation of semi-circular DSFs on the same facade throughout the day contribute to an improvement in the thermal behaviour of the compartments associated with them?
- How can these semi-circular DSFs, associated with a mechanical ventilation system, contribute to improving the comfort of interior spaces, simultaneously guaranteeing thermal comfort and the quality of the air provided to occupants?

## 2. Methodology

#### 2.1. Building Geometrical Design

- Opaque bodies, namely the interior and exterior walls, ceiling, and floor;
- Transparent bodies, namely the glass of the windows and the DSF;
- The volume of the indoor occupied space and the DSF spaces.

- The radius of the semi-circle;
- The angular coordinates, i.e., the angular position or the azimuth;
- The height or altitude.

#### 2.2. Building Thermal Dynamics

- Mass balance integral equations used to calculate the carbon dioxide concentration and the water vapour inside the space;
- Energy balance integral equations used to calculate the air temperature inside the space and the temperature of the opaque, transparent, and interior bodies.

_{2}, c, and i represent the water vapour; carbon dioxide concentration; number of compartments; and number of phenomena considered, namely the mass flux due to convection, diffusion, and other factors.

- The air temperature inside the space;
- The air relative humidity inside the space;
- The air velocity inside the space;
- The mean radiant temperature (MRT) inside the space;
- The clothing level of the occupants;
- The activity level of the occupants.

_{2}concentration value below 1800 mg/m

^{3}(1000 ppm).

## 3. Cases Studied

#### 3.1. Inputs

- Until 08:00, between 12:00 and 14:00, and after 18:00, one air exchange rate was used;
- In the morning, between 08:00 and 12:00, and in the afternoon, between 14:00 and 18:00, 35 m
^{3}/h per occupant was used.

- 26 spaces, namely 1 occupied auditorium space and 25 smooth DSFs turned south;
- 922 opaque bodies, namely surrounding walls, floor, ceiling, and others;
- 50 transparent surfaces, namely 25 transparent surfaces installed in the semi-circular DSF turned south and 25 windows located in the auditorium turned north.

- Outside air temperature between 4.5 °C and 13.5 °C;
- Outside air relative humidity between 37.2% and 65%;
- Wind speed between 0.01 m/s and 6.25 m/s.

- For the double bricks, used as a boundary with the external environment, eleven layers were considered;
- For the single bricks, used as a boundary with the semi-circular DSF, seven layers were considered;
- For the ground, used as a border with the soil, ten layers were considered;
- For the roof, used as a boundary with the external environment, nine layers were considered.

#### 3.2. Construction Elements and Materials

#### 3.3. Building Geometry

- The two-dimensional vertical section repetition over all opening angles of the DSF system. The two-dimensional vertical section is presented in Figure 2. Figure 3 and Figure 4 show the opening angles of the DSF system considered in the six cases studied. The two-dimensional vertical section repetition over all opening angles of the DSF system for the six cases studied is presented in Figure 5 and Figure 6.

## 4. Results and Discussion

_{2}measured therein. Figure 21 presents the evolution of the CO

_{2}concentration numerically obtained for each of the six cases studied. As can be seen, it was verified for all cases that the CO

_{2}concentration values were below the acceptable limit (that is, below 1800 mg/m

^{3}, ASHRAE-62 [34]); thus, the indoor air quality could be considered suitable for the number of occupants in the auditorium. These results showed that the ventilation system was properly designed to guarantee acceptable indoor air quality for the 100 occupants of the auditorium, depending on the variation in the volume of the space. Note that the smallest auditorium volume was obtained in Case C, and the largest auditorium volume was obtained in Case D. When the auditorium was unoccupied, the CO

_{2}concentration was higher for Case D and lower for Case C, because it depended on the air exchange rate. However, during occupancy, the CO

_{2}concentration depended on the airflow rate and the number of occupants, so its value could almost always be held constant regardless of the volume of the auditorium, that is, around 1400 mg/m

^{3}for all cases.

## 5. Conclusions

_{2}concentration.

- The results obtained regarding the daily evolution of solar radiation allowed us to conclude that the semi-circular DSF system received incident solar radiation from different directions throughout the day (between 7:30 and 16:30), considering a typical winter day with a clear sky. This made it possible to increase the available solar heating power, distributing it more effectively throughout the day. The results also showed that this heating power depended on the area of the glazed surface. Therefore, Case D (radius of 15 m and DSF opening angle of 180°) presented the highest available heating power values, and Case C (radius of 5 m and DSF opening angle of 45°) presented the smallest available heating power values. These values directly influenced the evolution of the indoor air temperature and, consequently, the PMV index obtained. Thus, the greater the opening angle of the DSF system and the radius of the semi-circular DSF system, the greater the available solar heating power.
- The indoor air temperature in the auditorium throughout the day had higher values when the radius was 15 m than when the radius was 5 m: the difference varied between 3 °C and 5 °C. For the smallest radius of the semi-circular DSF system, the temperature difference was not significant when the opening angle of the DSF system varied. For the largest radius of the semi-circular DSF system, the temperature was slightly higher when the opening angle of the DSF system was smaller (Case F, 45°), because the volume of air to be heated inside the auditorium was smaller.
- The evolution of the PMV index showed that, when the opening angle of the DSF system varied, the differences between the values of the PMV index were not very significant, regardless of the radius of the semi-circular DSF system used, although it was noted that better PMV index values were obtained for the smallest DSF opening angle. When comparing the values of the PMV index, it was verified that the best results were obtained for the largest radius of the semi-circular DSF (15 m). In this case, it was possible to obtain an acceptable level of thermal comfort for the occupants, according to Category C of ISO 7730 [28], from mid-morning to late afternoon. During the occupation period, until mid-morning, the PMV index values were close to acceptable. In the case of the smallest radius (5 m), it was not possible to obtain an acceptable level of thermal comfort for the occupants. In this case, it was necessary to resort to the support of an additional heating system, which led to higher energy consumption.

^{3}, ASHRAE-62 [34]. Therefore, it can be seen that the ventilation system was properly designed to provide adequate airflow rates for the number of occupants and the volume of air inside the auditorium.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Main symbols | |

Clo | Clothing level |

CO_{2} | Carbon dioxide concentration |

Cp | Specific heat at a constant pressure (J kg/°C) |

DSF | Double-skin facade |

$\dot{m}$ | Mass flux (kg/s) |

m | Mass (kg) |

Met | Activity level |

PMV | Predicted Mean Vote |

$\dot{Q}$ | Heat flux (kg/s) |

T | Temperature (°C) |

t | Time (s) |

Sub-indexes | |

air | The air in the compartments |

c | The number of compartments |

CO_{2} | The carbon dioxide concentration |

i | The number of mass phenomena |

j | The number of energy phenomena |

l | The number of opaque body layers |

o | The number of opaque bodies |

Op | The opaque bodies |

t | The number of transparent bodies |

Tr | The transparent bodies |

w | The water vapor |

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**Figure 1.**Details of the auditorium construction elements. (

**a**) DSF system, (

**b**) single-brick scheme, and (

**c**) double-brick scheme.

**Figure 2.**Scheme of a section of the auditorium and the respective dimensions. (

**a**) Two-dimensional vertical section, (

**b**) identification of the bodies and areas, (

**c**) horizontal dimensions, and (

**d**) vertical dimensions.

**Figure 3.**Scheme of the auditorium and details of the opening angle of the DSF system. (

**a**) Case A, (

**b**) Case B, and (

**c**) Case C. Three-dimensional top view.

**Figure 4.**Scheme of the auditorium and the details of the opening angle of the DSF system. (

**a**) Case D, (

**b**) Case E, and (

**c**) Case F. Three-dimensional top view.

**Figure 5.**Scheme of the auditorium construction methodology, using a two-dimensional vertical section, and the semi-circular DSF solar radiation. (

**a1**,

**a2**) Case A, (

**b1**,

**b2**) Case B, and (

**c1**,

**c2**) Case C. Figures with index 1 represent the three-dimensional southeast view of the semi-circular DSF and the auditorium, while Figures with index 2 represent the top view.

**Figure 6.**Scheme of the auditorium construction methodology, using a two-dimensional vertical section, and the semi-circular DSF solar radiation. (

**a1**,

**a2**) Case D, (

**b1**,

**b2**) Case E, and (

**c1**,

**c2**) Case F. Figures with index 1 represent the three-dimensional southeast view of the semi-circular DSF and the auditorium, while Figures with index 2 represent the top view.

**Figure 7.**Scheme of the auditorium construction methodology, using a two-dimensional horizontal section. (

**a**) Case A, (

**b**) Case B, and (

**c**) Case C.

**Figure 8.**Scheme of the auditorium construction methodology, using a two-dimensional horizontal section. (

**a**) Case D, (

**b**) Case E, and (

**c**) Case F.

**Figure 9.**Virtual auditorium developed in Case A. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 10.**Virtual auditorium developed in Case B. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 11.**Virtual auditorium developed in Case C. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 12.**Virtual auditorium developed in Case D. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 13.**Virtual auditorium developed in Case E. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 14.**Virtual auditorium developed in the Case F. (

**a**) Top view of the auditorium and the semi-circular DSF, (

**b**) tri-dimensional southeast view of the auditorium and the semi-circular DSF, and (

**c**) tri-dimensional southeast view of the semi-circular DSF.

**Figure 15.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case A).

**Figure 16.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case B).

**Figure 17.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case C).

**Figure 18.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case D).

**Figure 19.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case E).

**Figure 20.**Evolution of transmitted solar radiation for the different smooth DSF glass components (Case F).

**Figure 23.**Evolution of PMV index for the six cases studied. The comfort zone according to Category C of ISO 7730 [28] is shaded.

Opening Angle of the DSF System (°) | Radius of the Semi-Circular DSF System (m) | |
---|---|---|

Case A | 180 | 5 |

Case B | 135 | 5 |

Case C | 90 | 5 |

Case D | 180 | 15 |

Case E | 135 | 15 |

Case F | 90 | 15 |

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## Share and Cite

**MDPI and ACS Style**

Conceição, M.I.; Conceição, E.; Lúcio, M.M.; Gomes, J.; Awbi, H.
Application of Semi-Circular Double-Skin Facades in Auditoriums in Winter Conditions. *Inventions* **2023**, *8*, 60.
https://doi.org/10.3390/inventions8020060

**AMA Style**

Conceição MI, Conceição E, Lúcio MM, Gomes J, Awbi H.
Application of Semi-Circular Double-Skin Facades in Auditoriums in Winter Conditions. *Inventions*. 2023; 8(2):60.
https://doi.org/10.3390/inventions8020060

**Chicago/Turabian Style**

Conceição, Maria Inês, Eusébio Conceição, Maria Manuela Lúcio, João Gomes, and Hazim Awbi.
2023. "Application of Semi-Circular Double-Skin Facades in Auditoriums in Winter Conditions" *Inventions* 8, no. 2: 60.
https://doi.org/10.3390/inventions8020060