# Parametric Enhancement of a Window-Windcatcher for Enhanced Thermal Comfort and Natural Ventilation

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## Abstract

**:**

## 1. Introduction

**Figure 1.**Schematic function of windcatchers [33].

- The proposed window-windcatcher system, by virtue of its small size and integration into the building envelope as a constituent of the window assembly, enhances the utilization potential of the building roof, while concurrently freeing it from design and spatial limitations, including potential vertical expansion or roof garden
- The proposed windcatcher’s diminutive size could surmount the minimum wind velocity requirement, as the air’s path from outside to inside the building through the system is considerably shorter compared to conventional windcatchers.
- As the proposed system is affixed to the window, it can regulate the volumetric airflow entering the room by adjusting the window opening ratio.
- Due to the system’s design, small size, and installation location, all its components are easily accessible, making it easy to clean and impervious to dust and insects.

## 2. Materials and Methods

#### 2.1. The Baseline Design of the Proposed Window-Windcatcher

#### 2.2. Building Description

^{2}window, with a total window-to-wall ratio of 18%.

#### 2.3. Study Cases

#### 2.4. CFD Setup

^{5}, 6.9 × 10

^{5}, 9.4 × 10

^{5}, 1.4 × 10

^{6}, and 1.9 × 10

^{6}. At around 9.4 × 10

^{5}elements, the results start to be steady reaching the independently at 1.9 × 10

^{6}. Nevertheless, a much finer mesh with 2.19 × 10

^{6}elements was chosen to obtain a high level of confidence and accuracy.

#### 2.5. Optimization Criteria and Parametric Intervals

_{Q}(θ) = −0.029θ

^{3}+ 1.78θ

^{2}− 53.09θ + 641.61

_{Q,avg}=16 L/s

_{act,D}= −0.12θ

^{3}+ 7.14θ

^{2}− 205.49 + 2490

**Figure 7.**Optimization methodology for determining the optimal window-windcatcher geometrical parameters ${D}_{W-f}$ and $\theta $.

## 3. Results

#### 3.1. Fins Angle for the Maximum Actual-to-Required Ventilation Ratio (${\theta}_{{n}_{Qmax}}$)

_{act},

_{D}) subtracted by the ${S}_{Q}$ coefficient, and then ${Q}_{act}$ for Amman can be described using Equations (7) and (8). Inserting Equations (4)–(6) into Equation (7) yields a generic formula that approximates the ${Q}_{act}$ of the window-windcatcher for the fins angle.

#### 3.2. ${D}_{W-f}$ That Corresponds to the Maximum Actual-to-Required Ventilation Ratio (${{D}_{W-f}}_{{n}_{Qmax}}$)

#### 3.3. Turbulence Conditions for the Optimized Dimensional Parameters

#### 3.4. Qualitative Characterization

#### 3.5. Thermal Comfort

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${A}_{floor}$ | Floor area (${\mathrm{m}}^{2}$) |

${c}_{\mu}$ | k–ε model parameter |

${D}_{A-A}$ | Width of the window-windcatcher [cm] |

${D}_{W-f}$ | Fins-wall distance [cm] |

${{D}_{W-f}}_{{n}_{Qmax}}$ | Fins-wall distance with the maximum actual-to-required ventilation ratio [cm] |

$I$ | Initial turbulence intensity |

$k$ | Turbulence kinetic energy (J/kg) |

$l$ | Turbulence or eddy length scale |

${N}_{br}$ | Number of bedrooms |

${n}_{Q}$ | Actual-to-required ventilation ratio |

${n}_{Q,\theta i}$ | Actual-to-required ventilation ratio for each ith $\theta $ |

${n}_{Q,{D}_{W-f}i}$ | Actual to required ventilation rate for ith |

${Q}_{act.g}$ | Generic actual ventilation rate (mathematically obtained) [L/s] |

${Q}_{act.g,avg}$ | Average generic actual ventilation rate (mathematically obtained) [L/s] |

${Q}_{act}$ | Actual ventilation rate [L/s] |

Q_{act,D} | ${\mathrm{Q}}_{\mathrm{a}\mathrm{c}\mathrm{t}}$ for the Doha case study [L/s] |

${Q}_{act,{D}_{W-f},i}$ | Actual ventilation rate for ith [L/s] |

${Q}_{act,\theta i}$ | Actual ventilation rate ${Q}_{\mathrm{a}\mathrm{c}\mathrm{t}}$ for each ith $\theta $ [L/s] |

${Q}_{req}$ | Required ventilation rate (ASHRAE standards) [L/s] |

$Re$ | Reynolds number |

S_{Qavg} | Average actual ventilation rate shift [L/s] |

${S}_{Q}$ | Actual ventilation rate shift from one case study to another [L/s] |

${T}_{avg}$ | Average annual temperature [$\mathrm{\mathbb{C}}$] |

$U$ | Initial velocity magnitude (m/s) |

${V}_{NW}$ | Normal component of wind velocity [m/s] |

${V}_{SW}$ | Shear component of wind velocity [m/s] |

${V}_{Tw}$ | The total wind velocity [m/s] |

$\epsilon $ | Turbulence Kinetic Energy Dissipation (J/kg) |

$\u03f4$ | Fins angle [$\xb0$] |

${\theta}_{{n}_{Qmax}}$ | Fins angle $\theta $ with the highest ventilation rate [$\xb0$] |

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**Figure 4.**(

**Left**): average temperature (${T}_{avg}$); (

**Right**): total wind velocity (${V}_{TW}$) in 2021 in Amman and Doha.

**Figure 5.**(

**Left**): Result planes at 1 m and 1.7 m; (

**Right**): Simulated temperature and wind velocity setups.

**Figure 6.**(

**A**) CFX mesh of the model; (

**B**) Mesh sensitivity analysis to the average velocity at 1.7 m offset (internal plane); (

**C**) the velocity contours at three mesh sizes (9.4 $\times {10}^{5}$ elements, 1.4 $\times {10}^{5}$ elements, and 1.9 $\times {10}^{6}$ elements); (

**D**) Three-dimensional computational domain clarifies boundary types (Inlet, Outlet, green surface is the open boundary condition).

**Figure 8.**(

**A**) Actual ventilation rate with respect to a variable fins angle ${(Q}_{act,\theta i})$; (

**B**) actual-to-required ventilation ratio with respect to a variable fins angle $\left({n}_{Q,\theta i}\right)$′; (

**C**) The velocity contours at the 1 m and 1.7 planes for ${\theta}_{{n}_{Qmax}}=80\xb0$, $\theta =40\xb0$ and $\theta =10\xb0$, at ${{D}_{W-f}}_{{n}_{Qmax}}=45$ cm.

**Figure 11.**(

**A**) Actual ventilation rate through the mathematical estimation; (

**B**) CFD-generated actual ventilation rate for Amman. (The estimated average error between (

**A**) and (

**B**) was approximately $1.2\times {10}^{-3}$).

**Figure 13.**(

**A**) Actual ventilation rate with respect to ${D}_{W-f}$. (

**B**) Actual-to-required ventilation ratio. The vertical lines correspond to the conditions at ${{D}_{W-f}}_{{n}_{Qmax}}$.

**Figure 14.**The average turbulence kinetic energy with respect to $\theta $ at ${{D}_{W-f}}_{{n}_{Qmax}}=45$ cm for (

**A**) the 1 m plane and (

**B**) the 1.7 plane.

**Figure 15.**The Average turbulence kinetic energy at the 1 m plane for ${\theta}_{{n}_{Qmax}}=80\xb0$, $\theta =40\xb0,$ and $\theta =10\xb0$, at ${{D}_{W-f}}_{{n}_{Qmax}}=45$ cm. (

**A**) High–turbulence regions for $\theta =10$ (

**B**) High–turbulence region for $\theta =40$ (

**C**) High–turbulence region for ${\theta}_{{n}_{Qmax}}=80$.

**Figure 16.**Average turbulence kinetic energy at the 1.7 m plane for ${\theta}_{{n}_{Qmax}}=80\xb0$, $\theta =40\xb0,$ and $\theta =10\xb0$, at ${{D}_{W-f}}_{{n}_{Qmax}}=45$ cm. Black box is a high–turbulence region.

Category | Property | Specification | Consistent with Reference |
---|---|---|---|

Mesh Quality | Elements maximum size (mm) | 500 | [30,39,40,41] |

Number of elements | 2,190,000 | ||

Growth rate | 1.2 | ||

Defeature size (mm) | 2.5 | ||

Curvature minimum size (mm) | 5 | ||

Curvature normal angle (degree) | 18 | ||

Skewness | 0.21188 | ||

Orthogonal quality | 0.78694 | ||

Inflation transition ratio | 0.75 | ||

Inflation number of layers | 5 | ||

The mesh sensitivity study was conducted in the Amman case study using average velocity across an interior plane with an offset of 1.7 m from the floor, which is approximately the average person’s height in the Middle East Region [42]. The velocity results converged with a relative error margin of 1%. | |||

Turbulence model | k − $\epsilon $ | $k=\frac{3}{2}{\left(UI\right)}^{2}$ | [30,39,40,41] |

$\epsilon ={c}_{\mu}^{\frac{3}{4}}{k}^{\frac{3}{2}}{l}^{-1}$ | |||

$I=0.16R{e}^{-\frac{1}{8}}$ | |||

$l=0.07L$ | |||

Solid Modeling | Domain | Boolean | [30] |

Solid-fluid | No-Slip Walls | ||

Inlet conditions | Velocity inlets; as per Figure 5, with a turbulence intensity of 5% | ||

Fluid Modeling and Boundary Conditions | Outlet condition | Pressure outlets of 1 bar | [30,37,38] |

The external surfaces of the computational domain | Openings An open boundary condition is a computational boundary that allows phenomena generated in the interior domain to pass through the artificial boundary without distortion and without affecting the interior solution. | ||

Computational performance | Computational performance | Computational performance | [30] |

Computational time | 12 h/case | ||

Software | Ansys CFX | ||

Residual targets | 1 × 10^{−3} | ||

Achieved residual level | Approximately 1 × 10^{−6} | ||

Boundary Wall | No slip wall | Smooth | |

Simulation | Steady state |

Parameter | Description | |
---|---|---|

Building area | 100 m^{2} | |

Shape | Square, 10 × 10 m | |

Living space area | 12 m^{2} | |

Building height | 3 m | |

Parapet height | 1 m | |

Living space shape | Rectangular 3 × 4 m | |

Orientation of living space | Long axis east-west | |

Windows | Two windows. South, West | |

Windows size | Four windows | |

Windows size | Two windows: Width = 1.5 Height = 1 | |

Two windows: Width = 1.0 Height = 1 | ||

Airtightness | 0.05 ac/h | |

Lighting | Fluorescent | 25 mm diam |

Power density | 10.20 W/m^{2} | |

Control | Stepped = 1 step ON/OFF dimming day lighting control | |

HVAC System | Heating | Off |

Cooling | Off | |

Natural Ventilation | On within ASHRAE limitations | |

Occupancy | Person | 5 |

Component | Thickness | U-Value | Layers | Thickness |
---|---|---|---|---|

External wall | 0.26 m | 1.736 | Cement Plaster | 0.03 |

Block | 0.20 | |||

Cement Plaster | 0.03 | |||

Internal wall | 0.16 m | 1.690 | Cement Plaster | 0.03 |

Block | 0.10 | |||

Cement Plaster | 0.03 | |||

Roof | 0.28 m | 2.004 | Cast Reinforced concrete | 0.10 |

Block + cast reinforced concrete | 0.15 | |||

Cement Plaster | 0.03 | |||

Floor | 0.35 m | 1.4 | Gravel-based Soil | 0.20 |

Sand | 0.05 | |||

Cast Reinforced concrete | 0.10 | |||

Windows | N/A | 1.4 | Sliding, Single clear glazing | 0.06 |

5.881 | Aluminum Framing | 0.05 |

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## Share and Cite

**MDPI and ACS Style**

Obeidat, L.M.; Alrebei, O.F.; Nouh Ma’bdeh, S.; Al-Radaideh, T.; Amhamed, A.I.
Parametric Enhancement of a Window-Windcatcher for Enhanced Thermal Comfort and Natural Ventilation. *Atmosphere* **2023**, *14*, 844.
https://doi.org/10.3390/atmos14050844

**AMA Style**

Obeidat LM, Alrebei OF, Nouh Ma’bdeh S, Al-Radaideh T, Amhamed AI.
Parametric Enhancement of a Window-Windcatcher for Enhanced Thermal Comfort and Natural Ventilation. *Atmosphere*. 2023; 14(5):844.
https://doi.org/10.3390/atmos14050844

**Chicago/Turabian Style**

Obeidat, Laith M., Odi Fawwaz Alrebei, Shouib Nouh Ma’bdeh, Tamer Al-Radaideh, and Abdulkarem I. Amhamed.
2023. "Parametric Enhancement of a Window-Windcatcher for Enhanced Thermal Comfort and Natural Ventilation" *Atmosphere* 14, no. 5: 844.
https://doi.org/10.3390/atmos14050844