# Optimization of Window Positions for Wind-Driven Natural Ventilation Performance

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Optimization of Opening Specifications for Natural Ventilation Performance

#### 1.2. Optimization Method Integrated into the Design Process

## 2. Methodology

#### 2.1. Overview

^{3}was created as shown in Figure 2. The target zone to investigate was the second floor with seven windows on each façade, 28 windows per floor. Windows had identical areas of 1.43 m

^{2}, with the opening area of the 0.7 m

^{2}. In the optimization process, when a pair of two openings was investigated, the other 26 openings were assumed to be closed.

#### 2.2. Development of a Methodology for Optimizing Opening Positions for Wind-Driven Natural Ventilation

#### 2.2.1. Overview of the Optimization Process

#### 2.2.2. Climate Analysis

#### 2.2.3. Pressure Input from CFD Simulations

^{3}/s], ${C}_{\mathrm{d}}$ is a discharge coefficient that is considered a constant (~0.61 for sliding windows), ${A}_{\mathrm{eff}}$ is the effective opening area [m

^{2}], ${v}_{0}$ is the far-field wind velocity [m

^{2}/s], and $\mathsf{\Delta}{C}_{\mathrm{p}}$ is the pressure coefficient difference between two opening positions. Assuming sliding windows, the effective area (${A}_{\mathrm{eff}}$) of two operable windows is calculated by Equation (2) per [23]:

^{3}], and ${v}_{0}$ is the far-field wind velocity [m

^{2}/s], all of which were obtained from the CFD simulation.

#### 2.2.4. Mapping the Pressure Data

#### 2.2.5. Finding the Optimal Pair of Two Openings

^{th}pair when the wind is coming from the j

^{th}wind direction, ${\overline{v}}_{j}$ is the annual average wind speed of the j

^{th}wind direction, and ${f}_{j}$ is the normalized frequency of the j

^{th}wind direction. Mathematically speaking, the sum of ${\overline{v}}_{j}\xb7{f}_{j}$ is the average wind speed of the given climate. Since ${\phi}_{i}$ is the sum of ${\overline{v}}_{j}\xb7{f}_{j}\text{}\sqrt{\mathsf{\Delta}{C}_{p}{}_{i,j}}$, the magnitude of ${\phi}_{i}$ depends on the pressure coefficient differences and the average wind speed. With the minimum value being zero, there is no specific upper boundary in $\phi $. The scores made the evaluation convenient because each pair no longer had to carry eight sets of pressure coefficient differences corresponding to eight wind directions, but only one comprehensive score. In the codes, the scores were assigned to their pairs and were visualized in different colors. With eight wind directions and 27 pairs applied to Equation (5), the integrated score was calculated by Equation (6):

#### 2.3. Simulations for Validation

#### 2.3.1. Overview of Simulations for Validation

- Does the optimal pair perform better than the other pairs?
- How is the decision made differently in various cities with different wind profiles?

#### 2.3.2. Evaluation Metric: Natural Ventilation Effectiveness (NVE)

^{3}/s) calculated in Equation (1), and $V$ is the volume of the room (m

^{2}).

^{3}/s) for ventilation, ${Q}_{\mathrm{p}}$ is the outdoor airflow required per person (m

^{3}/s-ppl), $p$ is the number of people in the room (ppl), ${Q}_{\mathrm{a}}$ is the outdoor airflow required per unit area (m

^{3}/s-m

^{2}), and $A$ is the floor area of the room (m

^{2}). The values for ${R}_{\mathrm{p}}$ and ${R}_{\mathrm{a}}$ in Equation (9) are provided in [34].

^{3}/s), $\dot{q}$ is the cooling energy needed when natural ventilation was not used (kW), $\rho $ is air density (kg/m

^{3}), $c$ is the specific heat of air (kJ/kg-K), ${T}_{1}$ is the indoor setpoint temperature (K), and ${T}_{0}$ is the outdoor temperature (K). When ${T}_{1}-{T}_{0}\le 0$, ${Q}_{\mathrm{req},\text{}\mathrm{cool}}$ and $AC{H}_{\mathrm{req},\mathrm{cool}}$ are set to infinite as natural ventilation cannot provide cooling, hence the “+” sign in Equation (11). In this paper, $\dot{q}$ was obtained from running energy simulations in Honeybee.

## 3. Results

#### 3.1. Results of Optimization

- In San Francisco, the optimization identified openings on the west wall as ${\mathrm{N}}_{1}$ and ${\mathrm{E}}_{1}$ (optimal), and openings on the south wall as ${\mathrm{N}}_{0}$ and ${\mathrm{E}}_{0}$ (least optimal).
- In Nashville, the optimization identified openings on the south as ${\mathrm{N}}_{1}$ and ${\mathrm{E}}_{1}$, an opening on the east wall as ${\mathrm{N}}_{0}$, and the opening on the west wall as ${\mathrm{E}}_{0}$.
- In Boston, the optimization identified openings on the west wall as ${\mathrm{N}}_{1}$ and ${\mathrm{E}}_{1}$, an opening on the east wall for ${\mathrm{N}}_{0}$, and an opening on the north wall for ${\mathrm{E}}_{0}$.

#### 3.2. Validation

#### 3.2.1. Natural Ventilation Effectiveness for Ventilation only ($NV{E}_{\mathrm{vent}}$)

#### 3.2.2. Natural Ventilation Effectiveness for both Ventilation and Cooling (NVE).

#### 3.3. Sensitivity Analysis

^{2}in the validation, which was about 50% of the glazing area. For sensitivity analysis, various opening-to-glazing ratios were tested from 17%, 33%, 50%, 67%, 83%, to 100%, and the results are shown in Figure 13, In some cases, the performance is less sensitive with a greater opening area. For example, ${\mathrm{E}}_{1}$ and ${\mathrm{E}}_{0}$ of San Francisco, ${\mathrm{N}}_{1}$ and ${\mathrm{N}}_{0}$ of Nashville, and all cases of Boston had less than two percentage point difference when the opening-to-glazing ratio was 100%. However, in other cases, the performance difference between the optimal and non-optimal solutions was greater with an enlarged opening area. Such cases are ${\mathrm{N}}_{1}$ and ${\mathrm{N}}_{0}$ of San Francisco, and ${\mathrm{E}}_{1}$ and ${\mathrm{E}}_{0}$ of Nashville. The result data are appended to Table A3, Table A4 and Table A5.

## 4. Discussion

#### 4.1. Finding the Optimal Opening Positions

- The optimal pairs identified by the proposed methodology significantly varied by climates.
- Placing two openings on the opposite walls, which is typical for cross ventilation, may not always offer the best performance, and may even present the least performance depending on climate conditions.
- The determination of the optimal positions is influenced by multiple wind directions and speed, in addition to the dominant wind direction.
- If a simulation is not available, the safest guess is to place one opening on the windward wall.

#### 4.2. The Impact of the Optimal Opening Positions on Natural Ventilation Effectiveness

#### 4.3. Expandatility to a more Complex Building in an Urban Setting

#### 4.4. Expandability to an Existing Buildings

#### 4.5. BES-Integrated Design Workflow

#### 4.6. Limitation and Future Development

#### 4.6.1. Limitation

- As the title of this paper clarified, the opening pairs were examined based on the given wind conditions. To consider buoyancy-driven ventilation, the optimization function needs to be modified.
- The optimization function was based on a steady-state condition and does not explain the effect of thermal mass. Further research is needed to consider the relationship between opening positions and the transient behavior of buildings.
- The optimization assumed that the maximum airflow would lead to the greatest cooling energy savings; however, the optimal solution might miss a ‘better’ solution due to the indoor air distribution or flow pattern. There might be a pair that might have less potential score ($\phi $) but would distribute the air more efficiently thus improving the air circulation.
- In the CFD simulations, no surrounding condition was considered. For a local-specific analysis, immediate surrounding conditions including buildings and large trees should be modeled in CFD simulations.
- The test cases used eight wind directions. The number of directions is adjustable that one can use fewer or more directions if desired; however, this paper did not test on the minimum number of wind directions to be considered for the optimization.
- Natural ventilation’s availability is not solely determined by wind and temperature. Realistic constraints that were not examined in this paper include noise, pollution, and pollen.

#### 4.6.2. Future Development

- Validation with experimental measurements with fluctuating wind directions will enhance the methodology and help better understand the performance of the optimal solutions.
- Tool development to make the optimization program available to the public will encourage architects and BES professionals to consider natural ventilation in their practice.

## 5. Conclusions

- The effectiveness of wind-driven natural ventilation is greatly influenced by how windows are positioned in addition to outdoors conditions.
- The optimized window positions were shown to be effective, and some optimal solutions contradicted the typical cross-ventilation strategy.

- The proposed optimization methodology helps designers utilize outsourced pressure data during the preliminary design phase.
- The optimized solutions reduced the need for iterating design alternatives to maximize the natural ventilation’s cooling effect.
- The connectivity of the proposed framework to the existing airflow analysis method in CFD enables the comprehensive interpretation of the CFD results to be used in a seasonal analysis as opposed to a point-in-time analysis.
- With further examination of surrounding buildings and operation schedules, this optimization method can also be expanded to existing buildings with multiple windows.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Seasonal Wind Profiles of Three Cities

**Table A1.**Frequency of seasonal (May 15–Oct 15) wind direction and average wind speed extracted from EnergyPlus Weather (EPW) files of three different cities, San Francisco, CA; Nashville, TN; Boston, MA. Values in bold text represent the most frequent wind direction.

Wind Angle θ* | San Francisco, CA | Nashville, TN | Boston, MA | |||
---|---|---|---|---|---|---|

Frequency | Average Wind Speed | Frequency | Average Wind Speed | Frequency | Average Wind Speed | |

N | 4.38% | 3.99 m/s | 14.83% | 3.16 m/s | 7.93% | 4.30 m/s |

NE | 3.17% | 2.82 m/s | 13.50% | 3.28 m/s | 7.71% | 5.21 m/s |

E | 1.27% | 2.83 m/s | 5.74% | 2.46 m/s | 9.50% | 4.28 m/s |

SE | 1.33% | 3.06 m/s | 4.79% | 2.62 m/s | 8.63% | 3.92 m/s |

S | 3.71% | 4.31 m/s | 23.19% | 3.01 m/s | 15.04% | 4.65 m/s |

SW | 8.41% | 4.89 m/s | 10.63% | 3.42 m/s | 21.46% | 5.04 m/s |

W | 47.48% | 6.60 m/s | 8.98% | 3.38 m/s | 17.56% | 5.23 m/s |

NW | 26.46% | 6.10 m/s | 5.76% | 3.22 m/s | 11.69% | 4.96 m/s |

No wind | 3.79% | 0 m/s | 12.58% | 0 m/s | 0.49% | 0 m/s |

Total | 100% | 5.66 m/s | 100% | 2.73 m/s | 100% | 4.77 m/s |

**Figure A1.**Seasonal (May 15–Oct 15) wind distributions in three cities categorized in eight wind directions visualized by Ladybug. Each octagonal line represents the wind direction frequency of 5%, while the color represents wind speed: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, MA.

## Appendix B. Result of Optimal Pairs

**Table A2.**The integrated potential score of pairs ($\phi $) with various fixed opening positions in three different cities. Optimal and the least optimal pairs are displayed as thick lines. Other candidate pairs are displayed as thin lines.

San Francisco | Nashville | Boston |
---|---|---|

## Appendix C. Validation Results

Opening-to-Glazing Ratio | N_{1} | N_{0} | E_{1} | E_{0} | |
---|---|---|---|---|---|

NVE_{vent} | 16.7% | 0.62 | 0.34 | 0.71 | 0.33 |

33.3% | 0.81 | 0.47 | 0.86 | 0.63 | |

50.0% | 0.89 | 0.51 | 0.91 | 0.81 | |

66.7% | 0.92 | 0.54 | 0.92 | 0.88 | |

83.3% | 0.94 | 0.56 | 0.94 | 0.92 | |

100.0% | 0.95 | 0.57 | 0.94 | 0.94 | |

NVE | 16.7% | 0.58 | 0.30 | 0.66 | 0.30 |

33.3% | 0.76 | 0.43 | 0.82 | 0.58 | |

50.0% | 0.84^{1} | 0.48^{1} | 0.87 | 0.75 | |

66.7% | 0.88 | 0.51 | 0.89 | 0.83 | |

83.3% | 0.90 | 0.53 | 0.90 | 0.87 | |

100.0% | 0.91 | 0.54 | 0.91 | 0.89 |

^{1}Pairs with the bold text: NVE plots of these pairs are appended in Appendix C, Figure A2.

Opening-to-Glazing Ratio | N_{1} | N_{0} | E_{1} | E_{0} | |
---|---|---|---|---|---|

NVE_{vent} | 16.7% | 0.36 | 0.26 | 0.35 | 0.23 |

33.3% | 0.61 | 0.46 | 0.61 | 0.39 | |

50.0% | 0.73 | 0.61 | 0.73 | 0.47 | |

66.7% | 0.78 | 0.70 | 0.80 | 0.51 | |

83.3% | 0.80 | 0.77 | 0.83 | 0.52 | |

100.0% | 0.82 | 0.81 | 0.85 | 0.53 | |

NVE | 16.7% | 0.14 | 0.10 | 0.13 | 0.08 |

33.3% | 0.26 | 0.19 | 0.24 | 0.14 | |

50.0% | 0.32 | 0.24 | 0.31^{1} | 0.17^{1} | |

66.7% | 0.35 | 0.29 | 0.34 | 0.19 | |

83.3% | 0.37 | 0.32 | 0.37 | 0.21 | |

100.0% | 0.38 | 0.34 | 0.38 | 0.21 |

^{1}Pairs with the bold text: NVE plots of these pairs are appended in Appendix C, Figure A3.

Opening-to-Glazing Ratio | N_{1} | N_{0} | E_{1} | E_{0} | |
---|---|---|---|---|---|

NVE_{vent} | 16.7% | 0.59 | 0.44 | 0.58 | 0.45 |

33.3% | 0.85 | 0.73 | 0.83 | 0.73 | |

50.0% | 0.94 | 0.87 | 0.91 | 0.87 | |

66.7% | 0.97 | 0.94 | 0.95 | 0.93 | |

83.3% | 0.98 | 0.97 | 0.97 | 0.96 | |

100.0% | 0.99 | 0.98 | 0.98 | 0.98 | |

NVE | 16.7% | 0.41 | 0.30 | 0.39 | 0.31 |

33.3% | 0.61 | 0.51 | 0.60 | 0.51 | |

50.0% | 0.69^{1} | 0.63^{1} | 0.68 | 0.62 | |

66.7% | 0.73 | 0.69 | 0.72 | 0.68 | |

83.3% | 0.75 | 0.72 | 0.74 | 0.71 | |

100.0% | 0.76 | 0.74 | 0.76 | 0.74 |

^{1}Pairs with the bold text: NVE plots of these pairs are appended in Appendix C, Figure A4.

**Figure A2.**Seasonal NVE plot with an opening-to-glazing ratio of 50% in San Francisco: (

**a**) pair N

_{1}; (

**b**) pair N

_{0}.

**Figure A3.**Seasonal NVE plot with an opening-to-glazing ratio of 50% in Nashville: (

**a**) pair E

_{1}; (

**b**) pair E

_{0}.

**Figure A4.**Seasonal NVE plot with an opening-to-glazing ratio of 50% in Boston: (

**a**) pair N

_{1}; (

**b**) pair N

_{0}.

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**Figure 3.**Annual wind distributions in three cities categorized in eight wind directions visualized by Ladybug. Each octagonal line represents the wind direction frequency of 5%, while the color represents wind speed: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, MA.

**Figure 4.**Pressure coefficient distribution on building façades when the wind comes from eight directions: (

**a**) North wind; (

**b**) Northeast wind; (

**c**) East wind; (

**d**) Southeast wind; (

**e**) South wind; (

**f**) Southwest wind; (

**g**) West wind; (

**h**) Northwest wind.

**Figure 5.**Pressure data mapping process from computational fluid dynamics (CFD) to 3D environment: (

**a**) data reading from CFD; (

**b**) data grouping; (

**c**) data interpretation based on one wind direction.

**Figure 6.**Opening pairs created: (

**a**) when a fixed opening was on the north wall; (

**b**) when a fixed opening was on the east wall.

**Figure 7.**Evaluation and optimization of pairs of a case in San Francisco, CA: (

**a**) when a fixed opening was on the north wall; (

**b**) when a fixed opening was on the east wall.

**Figure 8.**The optimal pairs and the least optimal pairs identified by Equation (6), when a fixed window on the north wall: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, NA.

**Figure 9.**The optimal pairs and the least optimal pairs identified by Equation (6), when a fixed window on the east wall: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, NA.

**Figure 10.**Validation result: $NV{E}_{vent}$ of San Francisco, Nashville, and Boston with the selected pairs.

**Figure 11.**Validation result: $NVE$ of San Francisco, Nashville, and Boston with the selected pairs.

**Figure 12.**Validation results of $NVE$ compared to $NV{E}_{vent}$: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, MA.

**Figure 13.**Natural ventilation effectiveness of with opening-to-glazing ratios of 12.5%, 25%, 37.5%, 50%, 62.5%, 75%, 87.5%, and 100%: (

**a**) San Francisco, CA; (

**b**) Nashville, TN; (

**c**) Boston, MA.

**Table 1.**Frequency of annual wind direction and average wind speed of three different cities, San Francisco, CA; Nashville, TN; Boston, MA. Values in bold texts represent the most frequent wind direction.

Wind Angle θ* | San Francisco, CA | Nashville, TN | Boston, MA | |||
---|---|---|---|---|---|---|

Frequency | Average Wind Speed | Frequency | Average Wind Speed | Frequency | Average Wind Speed | |

N | 7.43% | 4.13 m/s | 15.79% | 3.67 m/s | 11.44% | 5.12 m/s |

NE | 5.63% | 3.21 m/s | 10.42% | 3.19 m/s | 5.92% | 5.08 m/s |

E | 4.46% | 3.20 m/s | 5.88% | 2.50 m/s | 9.66% | 5.32 m/s |

SE | 4.37% | 3.61 m/s | 4.90% | 2.77 m/s | 7.84% | 4.33 m/s |

S | 6.32% | 3.54 m/s | 27.15% | 3.85 m/s | 12.23% | 4.88 m/s |

SW | 7.26% | 4.41 m/s | 10.17% | 4.06 m/s | 15.53% | 5.36 m/s |

W | 37.66% | 6.15 m/s | 9.16% | 4.11 m/s | 18.49% | 6.18 m/s |

NW | 17.98% | 5.68 m/s | 7.89% | 4.15 m/s | 18.39% | 6.02 m/s |

No wind | 8.88% | 0 m/s | 8.65% | 0 m/s | 0.50% | 0 m/s |

Total | 100% | 4.67 m/s | 100% | 3.35 m/s | 100% | 5.43 m/s |

Floor area | 100 | [m^{2}] |

Overall heat transmission coefficient of walls (U-value with air) | 0.429 | [W/m^{2}-K] |

Overall heat transmission coefficient of glazing (U-value with air) | 2.720 | [W/m^{2}-K] |

Glazing ratio (wall-to-window) | 0.3 | |

Solar Heat Gain Coefficient (SHGC) of glass | 0.761 | |

Single glazing area | 1.43 | [m^{2}] |

Single opening area (assumed to be close at all times) | 0 | [m^{2}] |

Equipment load | 15 | [W/m^{2}] |

Infiltration rate per area | 0.0004 | [m^{3}/s-m^{2}] |

Lighting density per area | 3 | [W/m^{2}] |

Number of occupancy per area | 0.1 | [ppl/m^{2}] |

Cooling setpoint with HVAC (Ideal air loads) | 25 | [℃] |

Occupancy type | Open office |

**Table 3.**Validation result: $NV{E}_{vent}$ of San Francisco, Nashville, and Boston with the selected pairs. NVE: natural ventilation effectiveness.

${\mathbf{N}}_{1}$ | ${\mathbf{N}}_{0}$ | ${\mathbf{N}}_{1}-{\mathbf{N}}_{0}$ | ${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{0}$ | ${\mathbf{E}}_{1}-{\mathbf{E}}_{0}$ | |
---|---|---|---|---|---|---|

San Francisco, CA | 0.89 | 0.51 | 0.38 | 0.91 | 0.81 | 0.10 |

Nashville, TN | 0.73 | 0.61 | 0.12 | 0.73 | 0.47 | 0.26 |

Boston, MA | 0.94 | 0.87 | 0.07 | 0.91 | 0.87 | 0.04 |

${\mathbf{N}}_{1}$ | ${\mathbf{N}}_{0}$ | ${\mathbf{N}}_{1}-{\mathbf{N}}_{0}$ | ${\mathbf{E}}_{1}$ | ${\mathbf{E}}_{0}$ | ${\mathbf{E}}_{1}-{\mathbf{E}}_{0}$ | |
---|---|---|---|---|---|---|

San Francisco, CA | 0.84^{1} | 0.48^{1} | 0.36 | 0.87 | 0.75 | 0.12 |

Nashville, TN | 0.32 | 0.24 | 0.08 | 0.31^{1} | 0.17^{1} | 0.14 |

Boston, MA | 0.69^{1} | 0.63^{1} | 0.06 | 0.68 | 0.62 | 0.06 |

^{1}Pairs with the bold text: NVE plots of these pairs are appended in Appendix C, Figure A2, Figure A3 and Figure A4.

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**MDPI and ACS Style**

Yoon, N.; Piette, M.A.; Han, J.M.; Wu, W.; Malkawi, A. Optimization of Window Positions for Wind-Driven Natural Ventilation Performance. *Energies* **2020**, *13*, 2464.
https://doi.org/10.3390/en13102464

**AMA Style**

Yoon N, Piette MA, Han JM, Wu W, Malkawi A. Optimization of Window Positions for Wind-Driven Natural Ventilation Performance. *Energies*. 2020; 13(10):2464.
https://doi.org/10.3390/en13102464

**Chicago/Turabian Style**

Yoon, Nari, Mary Ann Piette, Jung Min Han, Wentao Wu, and Ali Malkawi. 2020. "Optimization of Window Positions for Wind-Driven Natural Ventilation Performance" *Energies* 13, no. 10: 2464.
https://doi.org/10.3390/en13102464