# Numerical Analysis of Wind Effects on a Residential Building with a Focus on the Linings, Window Sills, and Lintel

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Research Method, Description of a Building and CFD Calculation Model

#### 3.1. Research Methods

#### 3.2. Residential Building and Input Parameters

#### 3.3. CFD Model Created in the Ansys Fluent Software

^{−1}according to [18,19].

_{0}equal to 0.7. It can be seen in Figure 5a,b that constant values up to 10 m above the ground were considered.

_{p}

_{e}are presented in the paper.

#### 3.4. Calculation of the External Pressure Coefficients and Wind Pressures

_{pe}[-] were calculated as follows:

_{e}= q

_{p}(z

_{e})c

_{pe},

_{e}[m] q

_{p}(z

_{e}) is defined as:

_{p}(z

_{e}) = [1 + 7l

_{v}(z

_{e})] 0.5ρ ν

^{2}

_{m}(z

_{e})

## 4. SILSOE Cube, Wind Tunnel Testing, and Verification of the CFD Simulation

#### 4.1. The SILSOE Cube in the Scale 1:1

_{0}was 0.006 to 0.01 m due to relatively flat terrain with periodic skipping. Therefore, it was impossible to consider the typical parameters for terrain category II. Other essential parameters: The Jensen number (h/z

_{0}) of the SILSOE cube was 600 to 1000, and the intensity of turbulence was 19–20% at the top of the cube. The walls and roof of the cube were smooth. Six pressure taps were placed in the middle of the wall in the horizontal and vertical directions. The top was divided into four quadrants. In each quadrant, 30 pressure taps were placed. The cube was rotated by increments of 15°. The reference velocity was measured at 6 m (the top of the cube).

#### 4.2. The Model of the SILSOE Cube in Scale 1:30

#### 4.3. BLWT in Bratislava and Methodology of the Testing of SILSOE Cube Model

^{3}(reference velocity 4.1 m/s), 1.01 × 10

^{4}(reference velocity 7.56 m/s), 1.53 × 10

^{4}(reference velocity 11.52 m/s). The barometric pressure was 99,160 Pa, and the air temperature was 16.8 °C during the test.

## 5. Validation of the CFD Model of the Residential Building Results with SILSOE Cube

#### 5.1. External Pressure Coefficients—Residential Building vs. SILSOE Cube

_{pe}obtained from the residential building CFD model (Figure 6a,b) were compared with the results of the SILSOE cube tested in situ [28] and in wind tunnels. The vertical profile, horizontal profile, and roof were compared for wind direction 45°. A good coincidence in the values was achieved (Figure 7, Figure 8 and Figure 9). Thus, this 3D computing model could be used for other calculations and detailed analysis—determination of wind pressures and suctions in the places of window sills and the lining. The dimensions of the window sills and linings were too small for their implementation in the 3D model tested in a wind tunnel.

#### 5.2. External Pressure Coefficients—Residential Building vs. STN EN 1991-1-4

_{pe}values determined for the 0° wind direction (Figure 10a) could also be compared with the values defined in standards [18,19] (Figure 10c). These values are defined for the entire wall. In the case of all walls, the total area was greater than 10 m

^{2}, so c

_{pe}

_{,10}was considered. For the windward side, c

_{pe}was equal to +0.8. For the leeward side, c

_{pe}was −0.5. In the case of side walls (parallel with wind direction), the walls were divided into two parts. For area A, c

_{pe}was −1.2 on a length of 6 m. In area B, c

_{pe}was −0.8 on the rest of the wall (14 m). From the comparison, it is evident that it is sufficiently safe to consider the values of external pressure coefficients according to the standards of the design or assessment of the structure.

_{pe}values on the roof defined in the standards [18,19] were significantly different (for the residential building and the SILSOE cube model). The values mentioned in the standards were more significant, making their use safer. In the cross section of the roof of a residential building, the importance of c

_{pe}was: −1.2 for area G (the length was 3 m), −0.7 for area H (the size was 12 m), ±0.2 for area I (the rest of the roof). In the corners (in the areas F, the length was 3 m), the values of c

_{pe}were −1.8.

## 6. Results and Discussion: Detailed Analysis—Window Sills, the Linings and Lintel

#### 6.1. Wind Direction 0°

_{pe}= 0.89. From the point of view of passive ventilation, we do not recommend the installation of these units in the extreme positive zone of pressure. The optimal position is in the site according to the labels from the green to the yellow area (Figure 12a). Zones where the pressure distribution on the window does not copy the façade pattern must be specially treated (Figure 12a,c). Negative values occur only near the corner. This negative zone is outside the windows (Figure 12a). The other three façades B, C, and D, are in the negative pressure zone. The extreme values are in the corners where the acceleration and separation of the flow occur c

_{pe}= −0.53 (Figure 12c). We recommend replacing passive ventilation in these zones with forced ventilation.

#### 6.2. Wind Direction 22.5°

_{pe}= 0.91. From the point of view of passive ventilation, we do not recommend the installation of these units in the extreme positive zone of pressure. The optimal position is in the site according to the labels from the green to the yellow area (Figure 13a). Zones where the pressure distribution on the window does not copy the façade pattern must be specially treated (Figure 13a,c). Negative values occur only near the corner. This negative zone interferes with the windows (Figure 13a). The other three façades B, C, and D, are in the negative pressure zone. The extreme values are in the corners, where the acceleration and separation of the flow occur c

_{pe}= −1.19 (Figure 13c). We recommend replacing passive ventilation in these zones with forced ventilation.

#### 6.3. Wind Direction 45°

_{pe}= 0.87. From the point of view of passive ventilation, we do not recommend the installation of these units in the extreme positive zone of pressure. The optimal position is in the site according to the labels from the green to yellow area (Figure 14a). Zones where the pressure distribution on the window does not copy the façade pattern must be specially treated (Figure 14a,c). Negative values occur only in façades B and D. The extreme values are near the corners, where the acceleration and separation of the flow occur c

_{pe}= −0.55 (Figure 14c). We recommend replacing passive ventilation in these zones with forced ventilation.

#### 6.4. Wind Direction 67.5°

_{pe}= 0.89. From the point of view of passive ventilation, we do not recommend the installation of these units in the extreme positive zone of pressure. The optimal position is at the site according to the labels from the green to the yellow area (Figure 15a). Zones where the pressure distribution on the window does not copy the façade pattern must be specially treated (Figure 15a,c). Negative values occur only near the upper part of the corner. The other three façades A, B, and D, are in the negative pressure zone. Extreme values are in the corners, where the acceleration and separation of the flow occur c

_{pe}= −1.04 (Figure 15c). We recommend replacing passive ventilation in these zones with forced ventilation.

#### 6.5. Wind Direction 90°

_{pe}= 0.89. From the point of view of passive ventilation, we do not recommend the installation of these units in the extreme positive zone of pressure. The optimal position is at the site according to the labels from green to yellow (Figure 16a). Zones must be specially treated where the pressure distribution on the window does not copy the façade pattern (Figure 16a,c). Minimum negative values occur only in close proximity to the lower part of the corner (Figure 16c). The other three façades A, B, and D, are in the negative pressure zone. Extreme values are in the corners, where the flow acceleration and separation occur c

_{pe}= −0.65 (Figure 12c). We recommend replacing passive ventilation in these zones with forced ventilation.

_{pe}for the façade compared with the window sill, lining and lintel. The pressure values also include the name of the façade, where the extreme occurs. Windows are partially protected from minimum negative pressure, which follows from Table 1. Because they are not located on the corners of the building. The distribution of positive pressure in the windows is similar to the façade. The window sill, lining, and lintel have the same extremes for the same wind directions. The same applies to the position on the façade. However, there are zones where the negative and positive pressure distribution on the window does not copy the façade pattern (Figure 12b,c, Figure 13b,c, Figure 14b,c, Figure 15b,c and Figure 16b,c). These zones must be specially treated.

## 7. Conclusions and Discussions

- Wind direction 0°: the windward side A was in the positive pressures; the air-conditioning devices should be placed from the 2nd to the 6th floor. Only negative pressure occurred on the leeward side B and the side walls C and D.
- Wind direction 22.5°: the windward side A was still in the zone of positive pressures. The side walls B and D, were in negative pressure zones. On wall C is where the low values of the forces were. The extreme values of the wind pressures were in the upper three floors.
- Wind direction 45°: the windward sides were A and C. The higher values were in the corner of these walls from the 7th to the 11th floor. Walls B and D were in the negative pressure zones.
- Wind direction 67.5°: the windward side was C. The maximum positive values of the wind pressures occurred in the upper left corner (in the upper three floors). Extreme negative values were in wall D from the 8th to the 11th floor.
- Wind direction 90°: the windward side was C. The maximum values of positive wind pressures were from the 7th to the 11th floor in the middle of the wall. Walls A, B, and D were in negative pressure zones.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

C_{1}ε, C_{2} | constants | [-] |

c_{o} | the coefficient of orography | [-] |

c_{pe} | external pressure coefficient | [-] |

c_{r}(z) | coefficient of roughness | [-] |

C_{μ} | the model constant | [-] |

G_{b} | the generation of turbulence kinetic energy due to buoyancy | |

G_{k} | generation of turbulence kinetic energy due to the mean velocity gradients | |

h | height | m |

k | turbulence kinetic energy | m^{2}/s^{2} |

l_{v}(z_{e}) | the turbulence intensity | [-] |

p_{CFD} | external static pressure at some point | Pa |

p_{ref} | static pressure of free stream at the reference height | Pa |

q_{p}(z_{e}) | the peak value velocity pressure | Pa |

S_{k}, S_{ε} | the user-defined source terms | |

t | time | s |

u | wind velocity | m/s |

v* | wind shear velocity | m/s |

v_{b} | basic wind velocity | m/s |

v_{m}(z) | mean wind velocity at height z | m/s |

v_{ref} | reference wind velocity | m/s |

w_{e} | the wind pressure | Pa |

Y_{M} | the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate | |

z_{0} | aerodynamic roughness length | m |

ε | dissipation rate | m^{2}/s^{3} |

κ | von Kármán constant | [-] |

μ_{t} | turbulence dynamic viscosity | kg/m·s |

ν | kinematic viscosity | m^{2}/s |

ρ | the air density | kg/m^{3} |

σ_{k} | Prandtl numbers for k | [-] |

σ_{ε} | Prandtl numbers for ε | [-] |

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**Figure 1.**Dimensions of the residential building model with wind directions, ground plan, section plan, and 3D.

**Figure 2.**Wind rose for Bratislava area (

**a**) Average values of wind velocity [m/s] in Bratislava—Mlynská dolina; (

**b**) Frequency of wind direction [‰] in Bratislava—Mlynská dolina; (

**c**) Average values of wind velocity [m/s] in Bratislava—the airport; (

**d**) Frequency of wind direction [‰] in Bratislava—the airport [20].

**Figure 5.**Atmospheric boundary layer properties (

**a**) The profile of the mean value of the wind velocity; (

**b**) The profile of the intensity of turbulence.

**Figure 6.**SILSOE cube (

**a**) Cube in scale 1:1 during the in situ test in England [28]; (

**b**) Model of the SILSOE cube in scale of 1:30 in detail; (

**c**) Model of the SILSOE cube during the wind tunnel testing.

**Figure 7.**Comparison of the external pressure coefficients—45°—vertical profile—CFD model vs. SILSOE cube.

**Figure 8.**Comparison of the external pressure coefficients—45°—horizontal profile—CFD model vs. SILSOE cube.

**Figure 9.**The roof—c

_{pe}—wind direction 45°—(

**a**) CFD model of the residential building; (

**b**) SILSOE cube model tested in BLWT Bratislava (wind velocity 15 m/s).

**Figure 10.**External pressure coefficients—(

**a**) CFD—wind direction 0°; (

**b**) CFD—wind direction 45°; (

**c**) STN EN 1991-1-4—wind direction 0° (walls and roof).

**Figure 11.**SIEGENIA passive ventilation units and examples of their placements (

**a**) Linings; (

**b**) Sills; (

**c**) Lintel [31].

**Figure 12.**Pressure distributions on the buildings for wind incidence 0° (

**a**) General view; (

**b**) Positive pressure; (

**c**) Negative pressure.

**Figure 13.**Pressure distributions on the buildings for wind incidence 22.5° (

**a**) General view; (

**b**) Positive pressure; (

**c**) Negative pressure.

**Figure 14.**Pressure distributions in the buildings for wind incidence 45° (

**a**) General view; (

**b**) Positive pressure; (

**c**) Negative pressure.

**Figure 15.**Building pressure distributions for wind incidence 67.5° (

**a**) General view; (

**b**) Positive pressure; (

**c**) Negative pressure.

**Figure 16.**Pressure distributions in the buildings for wind incidence 90° (

**a**) General view; (

**b**) Positive pressure; (

**c**) Negative pressure.

**Table 1.**Summarized table of the external pressure coefficient for various wind directions and the position of the passive ventilation units on the façades A, B, C or D according to the Figure 1.

Wind Direction [°] | External Pressure Coefficient c_{pe} [-] | |||||||
---|---|---|---|---|---|---|---|---|

Façade | Window Sill | Lining | Lintel | |||||

Pos. | Neg. | Pos. | Neg. | Pos. | Neg. | Pos. | Neg. | |

0 | 0.89_A | −0.53_C,D | 0.89_A | −0.45_C,D | 0.89_A | −0.45_C,D | 0.89_A | −0.45_C,D |

22.5 | 0.91_A | −1.19_C | 0.91_A | −0.64_C | 0.91_A | −0.64_C | 0.91_A | −0.64_C |

45 | 0.87_A,C | −0.55_B | 0.87_A | −0.55_B | 0.87_A,C | −0.55_B | 0.87_A,C | −0.55_B |

67.5 | 0.89_C | −1.04_A | 0.89_C | −0.40_B | 0.89_C | −0.40_B | 0.89_C | −0.40_B |

90 | 0.89_C | −0.65_A,B | 0.89_C | −0.56_A,B | 0.89_C | −0.56_A,B | 0.89_C | −0.56_A,B |

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## Share and Cite

**MDPI and ACS Style**

Hubová, O.; Macák, M.; Franek, M.; Lobotka, P.; Konečná, L.B.; Ivánková, O.
Numerical Analysis of Wind Effects on a Residential Building with a Focus on the Linings, Window Sills, and Lintel. *Buildings* **2023**, *13*, 183.
https://doi.org/10.3390/buildings13010183

**AMA Style**

Hubová O, Macák M, Franek M, Lobotka P, Konečná LB, Ivánková O.
Numerical Analysis of Wind Effects on a Residential Building with a Focus on the Linings, Window Sills, and Lintel. *Buildings*. 2023; 13(1):183.
https://doi.org/10.3390/buildings13010183

**Chicago/Turabian Style**

Hubová, Oľga, Marek Macák, Michal Franek, Peter Lobotka, Lenka Bujdáková Konečná, and Oľga Ivánková.
2023. "Numerical Analysis of Wind Effects on a Residential Building with a Focus on the Linings, Window Sills, and Lintel" *Buildings* 13, no. 1: 183.
https://doi.org/10.3390/buildings13010183