Investigation on the Effect of Opening Size and Position on Wind-Driven Cross-Ventilation in an Isolated Gable Roof Building

Abstract

In this study, the influence of window opening sizes and positions on wind-induced cross ventilation performance in an isolated gable roof building was numerically investigated using the k-ω SST turbulence model. The results obtained from numerical analyses to evaluate the ventilation efficiency of different configurations show that larger inlet openings significantly increase the ventilation rates and the WO5 model reaches the highest ventilation rate of 0.004089 m³/s with an improvement of 37.27% compared to the reference model. As with the WO1 model, smaller inlet openings limited the air intake, reducing ventilation efficiency and indoor air quality. In terms of outlet window opening sizes, the LO5 model showed the highest ventilation efficiency, improving ventilation by 28% compared to reference model, while smaller outlet openings, as in the LO1 model, were associated with significantly lower performance. Additionally, when evaluating window opening locations, configurations with higher exit openings generally exhibited superior ventilation rates. The best overall ventilation performance was achieved in the Upper-Lower configuration at 0.003129 m³/s. The findings emphasized the critical role of window design in natural ventilation performance. Larger and strategically located window openings optimize airflow, increase ventilation efficiency and improve indoor air quality, providing valuable information for energy-efficient building design.

1. Introduction

Due to the growth in the world population, the need for energy demand is increasing day by day. This increase in non-renewable energy consumption accelerates the release of greenhouse gases into the atmosphere, climate change, and leads to environmental impacts that will adversely affect air quality and thus human health. Buildings are one of the main sources of global energy consumption and maintenance and operation procedures are responsible for 20–40% of total energy use [1]. Most of the energy consumed by buildings is used by heating, ventilation and air conditioning (HVAC) systems for space conditioning [2]. Especially in developed countries, HVAC systems in buildings consume more than two thirds of the energy supplied to buildings [3]. This ratio is predicted to increase up to 64% by 2100 [4]. In order to reduce this high energy consumption in buildings, environmentally friendly sustainable methods should be researched and developed. To reduce the amount of energy consumed for indoor ventilation and thermal comfort, passive cooling systems, i.e., natural ventilation systems, should be utilized instead of mechanical ventilation systems. Compared to mechanically ventilated buildings, it has been observed that energy use in naturally ventilated buildings is reduced by 30–40% [5,6,7].

Natural ventilation systems, which are divided into cross ventilation and chimney ventilation, rely on natural driving forces like wind and the temperature difference between the building and its surroundings to provide fresh air flow from a building [8]. By using wind-driven natural cross ventilation, indoor air quality and thermal comfort can be improved without energy consumption. Although cross ventilation is an effective ventilation method for buildings, its analysis is a complex process. This complexity arises from the fact that it is affected by many factors such as building geometry, location and dimensions of ventilation openings, internal obstructions, urban density, wind direction. This situation has attracted the attention of researchers and has led to an increase in the number of experimental and numerical studies to investigate natural ventilation processes in buildings. Table 1 presents an overview of the computational fluid dynamics and experimental studies reported to date on cross-ventilation in buildings, classifying these studies according to the type of research, turbulence models used, key physical variables and performance metrics.

Studies examining the influence of opening position, one of the key variables affecting ventilation efficiency, reveal notable findings. Karava et al. [9] found that the relative position of openings in the building façade and the inlet–outlet ratio were the critical parameters for accurate natural ventilation modelling and design. Shetabivash [8] numerically investigated the effect of opening position and shape on natural cross ventilation and found that both opening shapes and positions were critical elements of the building and significantly affected airflow pattern within the building. Kasim et al. [10] evaluated nine distinct cross-opening arrangements, situated on both the downwind and upwind facades of a building, to assess the impact of various opening locations on wind-driven ventilation efficiency using k-ϵ turbulence model. Derakhshan and Shaker [11] stated that small changes in the lateral and vertical positions of the windows affected the natural ventilation flow by increasing the volume flow. On the other hand, Perén et al. [12] emphasized that the influence on the volumetric flow rate of placing the outlet openings vertically was relatively small.

Another important issue that has been studied extensively by researchers is the role of opening sizes on ventilation efficiency. Yi et al. [13] performed an experimental study on the impact of sidewall opening size on the discharge coefficient of a windward opening. The research found that the discharge coefficient was significantly influenced by the opening size. Moreover, Chu et al. [14] reported that the discharge coefficients were sensitive to wind direction, Reynolds number and the type of airflow, whereas external turbulence intensity played a negligible role. Zhang et al. [15] indicated that larger openings on either windward or leeward surfaces increased ventilation rates and promoted better interior air circulation. Hwang and Gorlé [16] revealed that wind direction exerted a more pronounced influence on ventilation performance than opening size or location. When analyzing the cross-ventilation effectiveness of roof geometry and angle on isolated buildings, it was reported that a steeper roof pitch (30°) resulted in a significant increase in the pressure difference, especially for a shed roof orientated downwind [17]. Perén et al. [12,18,19] stated that increasing roof inclination angles led to improved ventilation efficiency, with a 22% rise in volumetric flow rate for the 45° roof in comparison to a flat roof also convex-straight roof geometries significantly enhanced ventilation performance by increasing the under-pressure in the wake of building, causing a 13% increase in airflow compared to concave geometries.

A number of studies were also undertaken in order to ascertain the performance of natural ventilation in relation to wind direction [11,14,16,20,21]. Ohba et al. [20] stated that ventilation flow rates increased for wind directions between 40° and 60° due to changes in dynamic pressure at the inlet. Derakhshan and Shaker [11] found that ventilation efficiency decreased as wind direction deviated from perpendicular, becoming independent of window dimensions beyond 45°. Nikas et al. [21] revealed that wind incidence angle significantly affected ventilation performance, with perpendicular wind directions yielding higher air exchange rates. Hwang and Gorlé [16] revealed that wind direction exerted a more pronounced influence on ventilation performance than opening size or location. Ramponi and Blocken [22] stated that, in terms of turbulence models for predicting indoor airflow patterns, the k-ω SST turbulence model demonstrated the optimal performance, followed by the RNG k-ε model. van Hooff et al. [23] demonstrated that Large Eddy Simulation (LES) provided superior accuracy, particularly in capturing transient features like jet flapping and shear instabilities, though at significantly higher computational costs. Among the Reynolds-averaged Navier-Stokes (RANS) models, the SST k-ω and RNG k-ε models performed relatively better. Kosutova et al. [24] conducted experimental and numerical studies to analyze cross-ventilation in a building with louvers. It was stated that buildings with louvered openings had the largest dimensionless volume flow rate. Tai et al. [25] performed a numerical analysis to examine the effects of changing louver slopes and opening positions on cross-ventilation in isolated buildings. The maximum dimensionless flow rate was found to be 0.719, which was recorded for the top-top configuration without louvers.

A review of the prevailing literature reveals that most studies on natural cross-ventilation have been conducted on generic isolated buildings, with a lack of research focusing on natural cross ventilation in gable-roofed buildings. This study aims to fill this gap in the literature and investigates the effects of window opening sizes and window opening positions on wind-induced natural cross-ventilation performance in isolated buildings with gable roofs. In the analysis performed for different configurations within the scope of the study, the velocity and pressure distributions and the indoor airflow structure are examined in detail.

Table 1. A summary of experimental and computational research on wind-driven natural cross-ventilation.

Authors	Study Type	Turbulence Model	Influential Physical Parameters	Performance Indicator
Yi et al. [13]	Exp	-	Opening size	V, Cp, DC, Q
Chu et al. [14]	Exp	-	Wind direction, Opening size	V, Cp, DC
Karava et al. [9]	Exp	-	Opening position	V, VF, Cp, Q
Tominaga & Blocken [26]	Exp	-	Urban density	V, TKE, Conc, TSF, Q
Ohba et al. [20]	Exp	-	Wind direction	V, VF, Q
Karava et al. [27]	Exp	-	Wall porosity, Opening ratio, Opening position	Cp, ACH, Q
Tominaga & Blocken [28]	Exp	-	Opening position, Opening size	V, TKE, Conc, Q
Tominaga et al. [17]	Exp	-	Roof geometry, Roof angle, Roof eave	V, Cp, Q
Sudirman et al. [29]	Exp	-	Wind direction, Internal partition	V, Q
Golubić et al. [30]	Exp	-	Urban density, Wind direction, Wind speed	V, Cp, ACH, Q
Evola & Popov [31]	CFD	RANS (Standard k-ε, RNG)	Opening position	V, Cp, Q
Hu, Ohba & Yoshie [32]	CFD	LES (Smagorinsky SGS)	Wind direction	V, Cp, TKE, Q
Ramponi & Blocken [22]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG k-ε, SST k-ω, RSM)	Computational domain size, Grid resolution, Turbulence model, Discretization scheme	V, TKE, VF
Shetabivash [8]	CFD	RANS (Standard k-ε)	Opening geometry, Opening position	V, VF, Q
Kasim et al. [10]	CFD	RANS (RNG k-ε)	Opening position	V, Q
Derakhshan & Shaker [11]	CFD	RANS (SST k-ω)	Opening geometry, Opening position, Wind direction	V, Cp, Q
van Hooff et al. [23]	CFD	RANS (Standard k-ε, RNG k-ε, Realizable k-ε, RSM, SST k-ω), LES (Dynamic Smagorinsky SGS)	Turbulence model	V, TKE, IJA, Q
Shirzadi et al. [33]	CFD	RANS (Standard k-ε, RNG k-ε, SST k-ω, RSM)	Urban density	V, Cp
Shirzadi, et al. [34]	CFD	RANS (Standard k-ε, SST k-ω)	Wind direction, Urban density	V, Cp, TKE, Q
Gautam et al. [35]	CFD	RANS (SST k-ω)	Wall porosity, Wind direction	V, Cp, TKE, DC, TD, Q
Hwang and Gorlé [16]	CFD	LES (Smagorinsky SGS)	Opening position, Opening size, Wall porosity, Wind direction	V, AA, Q
Kurabuchi et al. [36]	CFD	LES (Standard Smagorinsky)	Opening position, Wind direction	VF, Cp, TKE
Hu et al. [32]	CFD	LES (Standard Smagorinsky)	Wind direction	VF, Cp, TKE, Q
Kobayashi et al. [37]	CFD	RANS (RSM)	Opening size	Cp, DC, Q
Meroney [38]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG, Standard k-ω, RSM), LES (Standard Smagorinsky), DES	Opening position, Turbulence model	V, VF, Cp, DFR
Nikas et al. [21]	CFD	RANS (Standard k-ω)	Wind direction, Wind speed	V, VF, Q
Cheung and Liu [39]	CFD	RANS (Standard k-ε)	Wind direction, Building disposition	V, VF, Q
Peren et al. [12,18,19]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG k-ε, Standard k-ω, SST k-ω, RSM)	Roof angle, Opening position, Turbulence model, Roof geometry, Roof eave, Opening ratio	V, VF, Cp, Q
Tong et al. [40]	CFD	LES (Dynamic Smagorinsky)	Wind direction, Urban density	V, ACH
Zhang et al. [15]	CFD	RANS (Standard k-ε, RNG k-ε, Realizable k-ε)	Number of external openings, Opening size, Opening position, Position and geometry of internal wall	V, Q
Fu et al. [41]	CFD	RANS (Realizable k-ε)	Opening position, Building level	V, VF, Cp, TKE, DFR, AEE
Tai et al. [34]	CFD	RANS (RNG k-ε)	Louver angle, Opening position, Effective opening area	V, Cp, TKE, DFR, AEE, AA
Li et al. [42]	CFD	RANS (Standard k-ε)	Planar area ratio, Opening position	V, Cp, TKE, DFR, AEE, AA
Kosutova et al. [26]	Exp, CFD	RANS (RNG k-ε, SST k-ω, RSM)	Turbulence model, Opening position, Louver	V, VF, TKE, AA, AEE, DFR, Q
Jiang et al. [43]	Exp, CFD	LES (Smagorinsky SGS, Filtered dynamic SGS)	Opening position	V, VF, Cp, Q
Kato et al. [44]	Exp, CFD	LES (Standard Smagorinsky)	Opening size	V, VF, Cp, TKE, Q
Kobayashi et al. [45]	Exp, CFD	RANS (RSM)	Opening size	V, VF, Cp
Larsen et al. [46]	Exp, CFD	RANS (Standard k-ω)	Wind direction, Wind speed	V, ACH
Bangalee et al. [47]	Exp, CFD	RANS (RNG k-ε)	Opening position, Wind speed	V, VF, Q
Shirzadi et al. [48]	Exp, CFD	RANS (Standard k-ε, RNG k-ε, SST k-ω)	Wind direction, Urban density, Planar area ratio	V, Cp, TKE, Q

AA: Age of air, ACH: Air change rate, AEE: Air exchange efficiency, Conc: Concentration, Cp: Pressure coefficient, DC: Discharge coefficient, DFR: Dimensionless flow rate, IJA: Incoming jet angle, TKE: Turbulence kinetic energy, TSF: Turbulent scalar fluxes, V: Velocity, VF: Velocity vector fields, Q: Ventilation rate.

Table 1. A summary of experimental and computational research on wind-driven natural cross-ventilation.

Authors	Study Type	Turbulence Model	Influential Physical Parameters	Performance Indicator
Yi et al. [13]	Exp	-	Opening size	V, Cp, DC, Q
Chu et al. [14]	Exp	-	Wind direction, Opening size	V, Cp, DC
Karava et al. [9]	Exp	-	Opening position	V, VF, Cp, Q
Tominaga & Blocken [26]	Exp	-	Urban density	V, TKE, Conc, TSF, Q
Ohba et al. [20]	Exp	-	Wind direction	V, VF, Q
Karava et al. [27]	Exp	-	Wall porosity, Opening ratio, Opening position	Cp, ACH, Q
Tominaga & Blocken [28]	Exp	-	Opening position, Opening size	V, TKE, Conc, Q
Tominaga et al. [17]	Exp	-	Roof geometry, Roof angle, Roof eave	V, Cp, Q
Sudirman et al. [29]	Exp	-	Wind direction, Internal partition	V, Q
Golubić et al. [30]	Exp	-	Urban density, Wind direction, Wind speed	V, Cp, ACH, Q
Evola & Popov [31]	CFD	RANS (Standard k-ε, RNG)	Opening position	V, Cp, Q
Hu, Ohba & Yoshie [32]	CFD	LES (Smagorinsky SGS)	Wind direction	V, Cp, TKE, Q
Ramponi & Blocken [22]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG k-ε, SST k-ω, RSM)	Computational domain size, Grid resolution, Turbulence model, Discretization scheme	V, TKE, VF
Shetabivash [8]	CFD	RANS (Standard k-ε)	Opening geometry, Opening position	V, VF, Q
Kasim et al. [10]	CFD	RANS (RNG k-ε)	Opening position	V, Q
Derakhshan & Shaker [11]	CFD	RANS (SST k-ω)	Opening geometry, Opening position, Wind direction	V, Cp, Q
van Hooff et al. [23]	CFD	RANS (Standard k-ε, RNG k-ε, Realizable k-ε, RSM, SST k-ω), LES (Dynamic Smagorinsky SGS)	Turbulence model	V, TKE, IJA, Q
Shirzadi et al. [33]	CFD	RANS (Standard k-ε, RNG k-ε, SST k-ω, RSM)	Urban density	V, Cp
Shirzadi, et al. [34]	CFD	RANS (Standard k-ε, SST k-ω)	Wind direction, Urban density	V, Cp, TKE, Q
Gautam et al. [35]	CFD	RANS (SST k-ω)	Wall porosity, Wind direction	V, Cp, TKE, DC, TD, Q
Hwang and Gorlé [16]	CFD	LES (Smagorinsky SGS)	Opening position, Opening size, Wall porosity, Wind direction	V, AA, Q
Kurabuchi et al. [36]	CFD	LES (Standard Smagorinsky)	Opening position, Wind direction	VF, Cp, TKE
Hu et al. [32]	CFD	LES (Standard Smagorinsky)	Wind direction	VF, Cp, TKE, Q
Kobayashi et al. [37]	CFD	RANS (RSM)	Opening size	Cp, DC, Q
Meroney [38]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG, Standard k-ω, RSM), LES (Standard Smagorinsky), DES	Opening position, Turbulence model	V, VF, Cp, DFR
Nikas et al. [21]	CFD	RANS (Standard k-ω)	Wind direction, Wind speed	V, VF, Q
Cheung and Liu [39]	CFD	RANS (Standard k-ε)	Wind direction, Building disposition	V, VF, Q
Peren et al. [12,18,19]	CFD	RANS (Standard k-ε, Realizable k-ε, RNG k-ε, Standard k-ω, SST k-ω, RSM)	Roof angle, Opening position, Turbulence model, Roof geometry, Roof eave, Opening ratio	V, VF, Cp, Q
Tong et al. [40]	CFD	LES (Dynamic Smagorinsky)	Wind direction, Urban density	V, ACH
Zhang et al. [15]	CFD	RANS (Standard k-ε, RNG k-ε, Realizable k-ε)	Number of external openings, Opening size, Opening position, Position and geometry of internal wall	V, Q
Fu et al. [41]	CFD	RANS (Realizable k-ε)	Opening position, Building level	V, VF, Cp, TKE, DFR, AEE
Tai et al. [34]	CFD	RANS (RNG k-ε)	Louver angle, Opening position, Effective opening area	V, Cp, TKE, DFR, AEE, AA
Li et al. [42]	CFD	RANS (Standard k-ε)	Planar area ratio, Opening position	V, Cp, TKE, DFR, AEE, AA
Kosutova et al. [26]	Exp, CFD	RANS (RNG k-ε, SST k-ω, RSM)	Turbulence model, Opening position, Louver	V, VF, TKE, AA, AEE, DFR, Q
Jiang et al. [43]	Exp, CFD	LES (Smagorinsky SGS, Filtered dynamic SGS)	Opening position	V, VF, Cp, Q
Kato et al. [44]	Exp, CFD	LES (Standard Smagorinsky)	Opening size	V, VF, Cp, TKE, Q
Kobayashi et al. [45]	Exp, CFD	RANS (RSM)	Opening size	V, VF, Cp
Larsen et al. [46]	Exp, CFD	RANS (Standard k-ω)	Wind direction, Wind speed	V, ACH
Bangalee et al. [47]	Exp, CFD	RANS (RNG k-ε)	Opening position, Wind speed	V, VF, Q
Shirzadi et al. [48]	Exp, CFD	RANS (Standard k-ε, RNG k-ε, SST k-ω)	Wind direction, Urban density, Planar area ratio	V, Cp, TKE, Q

AA: Age of air, ACH: Air change rate, AEE: Air exchange efficiency, Conc: Concentration, Cp: Pressure coefficient, DC: Discharge coefficient, DFR: Dimensionless flow rate, IJA: Incoming jet angle, TKE: Turbulence kinetic energy, TSF: Turbulent scalar fluxes, V: Velocity, VF: Velocity vector fields, Q: Ventilation rate.

2. Numerical Methodology

2.1. Building Geometry and Configurations

In this study, the generic building geometry commonly used in research on natural ventilation, particularly in detailed analyses by Karava et al. [9], was taken as a basis. By preserving the original building dimensions, the roof was added to the building, and a gable roof structure with a slope of α = 26.6° was created, as shown in Figure 1. The building configurations created to examine the effects of both window opening sizes and locations on natural cross ventilation in this unique geometric model were given in

Table 2. Dimensions of different opening sizes for building models.

Building Model		Size of Opening (mm) (Width × Height)		Building Model		Size of Opening (mm) (Width × Height)
		Windward	Leeward			Windward	Leeward
WO1		15.33 × 6	46 × 18	LO1		46 × 18	15.33 × 6
WO2		30.67 × 12		LO2			30.67 × 12
WO3		46 × 18		LO3			46 × 18
WO4		61.3 × 24		LO4			61.3 × 24
WO5		92 × 36		LO5			92 × 36

and

Table 3. Dimensions of different opening positions for building models.

Case	Building Model	Opening Location	Opening Height (mm)
			Windward	Leeward
I		Lower-Lower	20	20
II		Lower-Middle		40
III		Lower-Upper		60
IV		Middle-Lower	40	20
V		Middle-Middle		40
VI		Middle-Upper		60
VII		Upper-Lower	60	20
VIII		Upper-Middle		40
IX		Upper-Upper		60

, respectively.

2.2. Computational Flow Domain and Grids

Figure 2 shows the isometric view of the rectangular computational domain, created based on the criteria proposed in the literature by Franke [49], Ramponi and Blocken [22], Tominaga et al. [50], and Demir and Aktepe [51]. When setting up the flow domain, the length between the building model and the inlet plane was set to 3H to prevent undesired flow conditions in the flow direction. The distance of the building model from the outlet plane was defined as 15H, and the distance to the top and side boundaries was defined as 5H, where H represented the model height, or 80 mm.

Figure 3 shows a detailed cross-sectional view and close-up views of the mesh structure taken from the vertical mid-plane in the X-Y directions. To obtain more accurate results in a shorter time for the calculations, a rectangular domain surrounding the building form was created. In addition, the flow around the building and the ground was detailed with a boundary layer mesh consisting of 10 layers, with the first layer having a thickness of 0.1 mm.

2.3. Boundary Conditions

The wind velocity profile at the inlet was determined on the basis of the logarithmic law, with a roughness length ($z_0$) of 0.025 mm, using Equation (1). In this equation, $u_{ABL}^{\ast }$ denotes the friction velocity of the atmospheric boundary layer (ABL), $\kappa$ represents the von Karman constant (0.42), and $z$ is the height coordinate. The turbulent kinetic energy ($k$) was estimated from the average wind velocity and the measured turbulence intensity by means of Equation (2), where $I_u$ represents the stream-wise turbulence intensity. The kinetic energy factor ($a$) was specified at 1, in accordance with the proposal of Tominaga et al. [50]. The turbulence dissipation rate, $\epsilon$ was determined by Equation (3) and the specific dissipation rate ($\omega$), by Equation (4), where $C_{\mu }$ is an empirical constant set to 0.09.

$$U(z)={\displaystyle \frac{u_{ABL}^{\ast }}{\kappa }}\ln \left[{\displaystyle \frac{z}{z_0}}+1\right]$$

(1)

$$k(z)=a{\left[I_u(z)U(z)\right]}^2$$

(2)

$$\epsilon (z)=\left[{\displaystyle \frac{{u_{ABL}^{\ast }}^3}{\kappa \left(z+z_0\right)}}\right]$$

(3)

$$\omega (z)={\displaystyle \frac{\epsilon (z)}{C_{\mu }k\left(z\right)}}$$

(4)

In the flow domain, the lateral and upper walls were defined as having zero specific shear stress. Besides, the outlet was described as a pressure outlet, and the entry plane was designated as a velocity inlet. The inlet parameters, including velocity magnitude, turbulent dissipation rate, and turbulent kinetic energy, were derived from the Atmospheric Boundary Layer (ABL) data file. The ground surface was defined as a boundary wall with a no-slip condition applied. The roughness constant ($C_s$) was assigned a value of 0.5, resulting in a roughness height of ground sand grain ($k_s$) of 0.0006 m when plugged into Equation (5) [25,27,52,53].

$$k_s={\displaystyle \frac{9.79z_0}{C_s}}$$

(5)

2.4. CFD Solver Settings

The three-dimensional, steady-state RANS equations were employed as the governing equations for the conservation of mass and momentum and were solved using ANSYS 18.2 software with the k-ω SST turbulence model. The selection of an appropriate turbulence model is crucial for achieving accurate results in numerical simulations across fields such as aerodynamics, hydrodynamics, and wind engineering, where the detailed behavior of flow physics is of interest. For pressure-velocity coupling, the equations were discretized and solved using the SIMPLE algorithm. The Green-Gaussian node-based scheme was chosen for spatial discretization to calculate the gradient, while a second-order upwind scheme was applied to all other variables. Convergence was achieved when all scaled residuals reached steady values, with thresholds of 10⁻⁷ for x, y, and z momentum components, and 10⁻⁴ for continuity, k, and ω.

2.5. Grid Sensitivity and Validation of the Model

In order to verify that the simulation results are not affected by grid resolution, a grid sensitivity analysis was conducted on the generic building model using three different grid structures consisting of 1,895,087 (coarse grid), 3,251,493 (medium grid), and 4,454,122 (fine grid) cells, respectively. In the simulations performed with these grid structures, the variable U represents the velocity vector in the flow field, while U_ref = 6.97 m/s refers to the reference wind speed measured at the building height. Figure 4 presents the wind speed ratio profiles (U/U_ref) along the flow direction on the centerline for each grid resolution, together with the results obtained from the PIV experiment conducted by Karava et al. [9]. The comparison clearly shows that the simulation results obtained with the fine grid (Grid C) provide the closest agreement with the experimental data. Therefore, the fine grid structure was adopted for all subsequent simulations in this study.

Before starting the natural ventilation analyses to be conducted within the scope of this study, a test model without window openings was created for model validation. The variation in pressure coefficient (C_p) values across the surfaces of this building model was compared with the experimental results obtained by Tominaga et al. [54], and this comparison is presented in Figure 5. On Wall I, the surface where the air first hits and slows down, C_p was positive in both studies and showed an increasing trend. As the flow moved from Wall I to Wall II, a sharp decrease in C_p was observed due to the flow separating from the corner, and it became negative. A slight increase in C_p was observed in Wall III, while no significant change was observed in Wall IV compared to other regions. When the regions are compared with each other, the C_p values obtained from the experimental results are slightly higher in Wall I and Wall II, while the numerical analysis results show higher values in Wall III and Wall IV. Overall, there is satisfactory agreement between the results obtained from CFD analysis and experimental data in terms of trends. Although some deviations in the absolute C_p values are observed, the basic flow characteristics and pressure change trends have been successfully captured by CFD. This indicates that the numerical modeling performed is generally consistent with the experimental findings in the literature and provides a reliable analysis. Figure 6 and Figure 7 present the results of the streamlines and pressure coefficient distributions obtained numerically in this study and Tominaga et al. [54], respectively. When the distribution of the streamline around the building in Figure 6 is analyzed, a large recirculation zone is detected at the rear of the building model. In addition, a smaller recirculation zone is formed at the lower corner of the building on the windward side. The pressure coefficient distributions in Figure 6 show a positive pressure region at the front of the building models, which is interpreted as the blocking effect of the building. As can be seen from the above results, the results obtained in this study are consistent with the results reported by Tominaga et al. [54]. Consequently, the validation of the model was considered satisfactory, and the solver settings were applied similarly to all scenarios created within the scope of the study.

2.6. Sensitivity Analysis

To evaluate the effects on simulation results, a parametric sensitivity analysis was conducted based on systematically changing a single parameter. In this context, analyses were carried out using the roughness constant (C_s) and turbulence models as a basis. The results obtained are presented in Figure 8 and Figure 9 to show the comparison of wind speed ratios (U/U_ref) along the horizontal centerline of the window openings in the flow direction relative to the reference case (C_s = 0.5 and k-ω SST). Additionally,

Table 4. Computational parameters examined in the sensitivity analysis and corresponding results.

Roughness Constant	Cs = 0.3	Cs = 0.4	Cs = 0.5	Cs = 0.6	Cs = 0.7
(U/Uref)max	0.78	0.76	0.77	0.74	0.76
(U/Uref)avg	0.40	0.39	0.39	0.35	0.36
Turbulence Model	SST k-ω	Standard k-ω	RNG k-ε	Standard k-ε	Realizable k-ε
(U/Uref)max	0.77	0.69	0.74	0.64	0.67
(U/Uref)avg	0.40	0.46	0.37	0.43	0.46

presents the parameters used in the sensitivity study and the data obtained.

2.6.1. Impact of Roughness Constant

In the parametric sensitivity analysis conducted, it is observed in Figure 8 that the U/U_ref value remains constant despite different C_s values as the approach to the building increases. However, the effect of changing this parameter is noticeable in the interior and exit areas of the building. To better understand this effect, the results obtained at different C_s values presented in Table 4 were examined. When the C_s value was reduced to 0.3, a 2.56% increase in the average U/U_ref value and a 1.3% increase in the maximum U/U_ref value were observed. At C_s = 0.4, a 1.3% decrease in the maximum U/U_ref was observed, while the average U/U_ref remained unchanged. At higher values, when C_s was 0.6, the maximum U/U_ref decreased by 3.89%, while the average U/U_ref decreased by a significant 10.25%. At C_s = 0.7, the maximum U/U_ref decreased by 1.3%, and the average U/U_ref value decreased by 7.69%. Based on these results, C_s = 0.5 was selected as the reference roughness coefficient, as it does not show excessive deviation in terms of both maximum (0.77) and average (0.39) U/U_ref values and is widely preferred in the literature.

2.6.2. Impact of Turbulence Model

The effects of turbulence models on indoor airflow are presented in Figure 9 in terms of the U/U_ref along the center line of the openings. As can be seen, the normalized velocity distributions obtained for different turbulence models show significant deviations when compared to the reference model, SST k-ω. These differences are observed in all regions from the entrance to the exit of the building and become even more pronounced in the interior regions of the building. When the quantitative data presented in Table 4 is examined, the (U/U_ref)_max value generally decreases in other turbulence models; the largest difference is 16.88% in the standard k-ε model, while the smallest difference is 3.89% in the RNG k-ε model. When examining the (U/U_ref)_avg value, an approximate 15% increase was observed in the standard k-ω and realizable k-ε models, while the RNG k-ε and standard k-ε models showed increases and decreases of 7.5%, respectively.

3. Results

3.1. Impact of Opening Sizes

3.1.1. Results for Building Models with Varying Windward Opening Sizes

The results obtained within the scope of the study are presented based on the mid-plane of the three-dimensional model, as exemplified in Figure 10. The dimensionless velocity and pressure contour results obtained for building models with fixed outlet opening size and varying inlet openings were shown in Figure 11 and Figure 12, respectively. The results showed that the building models with larger inlet openings had lower air velocities and higher internal pressures. This confirmed the inverse relationship between velocity and pressure in accordance with Bernoulli’s principle. As seen in the results of the WO5 building model, the changes in the air velocity entering the building with a larger inlet opening size are milder compared to those in a building with a smaller opening size. In the case of the WO1 model, the smaller inlet opening limited the volume of air entering the building, leading to a sudden drop in the air velocity striking the windward wall. This resulted in a significant pressure increase around the opening. This pressure growth caused the air to enter the building model at a higher speed, which gradually decreased as the inlet opening size increased. With the increment in the inlet opening size, a rise in indoor air pressure was observed. While the large inlet opening allowed more air mass to enter the building, the fixed outlet opening caused a significant increase in the indoor pressure, especially from the WO3 model onwards. This demonstrates the effect of the inlet opening size on indoor pressure.

Figure 13 shows the distribution of streamlines obtained for building models with fixed outlet opening sizes and variable inlet opening sizes. When examining the results, it is evident that a horseshoe vortex is formed in the lower part of all building models, regardless of the change in opening sizes. This result indicates the presence of a consistent flow pattern in front of the building. The airflow entering the building exhibited different flow structures in each model. In the WO1 building model, a counterclockwise vortex formed at the upper right corner of the building above the incoming jet, while a clockwise vortex formed at the lower right edge of the building. In the WO2 building model, the vortex that formed at the lower edge inside the building shifted to the left and became smaller. In the WO3 and WO4 building models, clockwise rotating vortices at the bottom of the incoming jet became more prominent. In the WO5 model, the large inlet opening allowed the incoming jet to reach the lower part of the building, thus preventing the formation of reverse flow in the lower region. Instead, a counterclockwise vortex formed at the upper part of the jet, near the center of the building. The air exiting the building formed a large reverse flow region after leaving it. The distribution in this reverse flow region was similar between the WO1 and WO2 building models, and similarities were also observed between the WO3 and WO4 models. In the WO5 building model, two large recirculation zones were prominent, both below and above the exiting jet.

Figure 14 shows the change in wind speed ratio (U/U_ref) along the horizontal line drawn along the windward and leeward window openings for building models with fixed outlet openings and different inlet openings, as a function of the distance ratio (x/D). Here, x/D = 0 represents the entrance point of the building, x/D = 0.5 represents the midpoint of the building, and x/D = 1 represents the exit point of the building. At x/D = 0, the highest normalized velocity value of 0.764274 is observed in WO1, which has the narrowest inlet opening, while the velocity values at this location decrease as the inlet opening increases, with the lowest velocity value of 0.305658 belonging to WO5. This demonstrates that narrow openings accelerate the flow at the entrance due to the nozzle effect, while wider openings result in slower but more widespread distribution of the flow throughout the volume.

For all building models, there is a decrease in the velocity of the air entering the building from the windward opening, with a notable distribution in the velocity profiles at the building’s midpoint (x/D = 0.5). The lowest velocity value is 0.0540731 in WO4, and the second lowest value is 0.136448 in WO5. In other models, the normalized velocity values at the midpoint are higher. This result illustrates that when the entrance opening exceeds a certain size, the airflow in the mid-section may weaken, meaning that very large entrance openings can create a stagnant zone in the mid-section. In the exit region (x/D = 1), WO5 achieved the highest normalized velocity at 0.832999. It was followed by WO4 at 0.800706 and WO3 at 0.648038. WO1 has the lowest exit velocity at 0.212390, and WO2 has the second lowest at 0.421573. This finding indicates that as the inlet opening increases, the amount of air evacuated from the building also increases, resulting in higher exit velocities despite the exit opening remaining constant.

3.1.2. Results for Building Models with Varying Leeward Opening Sizes

Figure 15 and Figure 16 illustrated the velocity and pressure contour distributions for gable roof buildings with fixed inlet opening and variable outlet opening sizes. According to the results obtained, the increase in the exit opening size directly affected the air velocity inside the building; in other words, as the exit opening size enlarged, the air velocity within the building increased. In the LO5 building model, which had a larger outlet opening size than the other models, the airflow entering the interior travelled at a higher velocity and left the building model without any sudden drop in velocity. This demonstrated that the airflow can be more easily discharged through the larger outlet opening, resulting in a smoother and faster flow profile within the building model. Besides, a rapid drop in air velocity occurred in building model LO1 with a smaller outlet opening. This sudden drop in air velocity limited the volume of air passing through the opening and caused the airflow to collect within the building. The accumulation of air inside caused a pressure increase directly inside the building and around the opening. The increased pressure affected the ventilation process by forcing the air out through the outlet opening. This explained why model LO1, which had a smaller opening size, had the maximum velocity at the exit point and the minimum velocity at the entry point. Consequently, in the LO1 model, the internal pressure reaches its highest value while the lowest velocity values are achieved. In contrast, the LO5 model exhibits the lowest pressure and the highest velocity values. These findings demonstrate that the size of outlet opening plays a decisive role in the airflow velocity and pressure distribution inside the building and that wider openings increase the indoor air velocity while decreasing the pressure.

Figure 17 presents the distribution of streamlines for building models with different outlet opening sizes. Upon examining the results, it is evident that a horseshoe vortex forms in the front lower part of all building models, regardless of changes in outlet opening dimensions. In each model, a counterclockwise flow motion occurs above the incoming jet, whereas in the LO5 model, an opposite flow direction is observed. This reverse flow direction may be interpreted as the large outlet opening makes the flow inside the building freer and reduces turbulence in the interior. Additionally, the center of the recirculation region formed behind the building moves farther from the building as the outlet opening size increases. This effect is particularly noticeable in the LO5 model; in this model with a larger opening size, the recirculation region forms farther from the building. This finding indicates that the outlet opening size exerts a direct influence on the flow structure at the rear of the building.

Figure 18 shows the change in U/U_ref along the horizontal line for five different models with a fixed inlet opening. Although the inlet opening was kept constant for all models, the normalized velocity values differ significantly. At x/D = 0, the U/U_ref value for LO1 is 0.202524, while for LO5 it reaches 0.833925. This indicates that an increase in the outlet opening not only affects the outlet performance but also influences the inlet flow through the pressure distribution within the internal space. In models with wider outlet openings, lower back-pressure is generated, allowing the inlet jet to start at higher speeds. Therefore, the airflow is shaped not only by the local effect of the opening configuration but also interactively throughout the entire volume.

As moving towards x/D = 0.5 (middle region) along the building, the normalized velocity value in LO1, which has the narrowest outlet, remains almost negligible (U/U_ref = 0.011056), indicating that the flow forms a dispersion and recirculation zone in the early stage due to high back pressure. This situation is also seen in the streamline distribution in Figure 17. The U/U_ref value reaches 0.482278 at LO5. This reveals that the pressure gradient in the internal volume is directly related to the outlet opening ratio, thus indicating that ventilation efficiency can be directly improved by increasing the air velocity in the middle zone. Such an effect is particularly important in natural ventilation scenarios for reducing dead zones within the volume and homogenizing indoor air quality. The trend is reversed in the outlet region (x/D = 1). LO1 reaches the highest normalized velocity value of 0.96 at the outlet, while LO5 drops to 0.330001. This indicates that narrow outlet openings create a jet-like nozzle effect, accelerating the airflow at the outlet point. In models with wide openings, however, the resistance in the exit region is very low, allowing the airflow to be discharged at a lower speed but in a more homogeneous manner.

3.2. Impact of Opening Positions

3.2.1. Results for Building Models with a Fixed 20 mm Inlet Position and Varying Outlet Positions

Figure 19 and Figure 20 present the velocity and pressure contours for three different cases in an isolated gable roof building with a fixed inlet opening height of 20 mm and variable outlet openings (20 mm, 40 mm, and 60 mm). Figure 20 shows the streamlines for these configurations. Due to the no-slip condition on the ground and the fixed inlet opening height of 20 mm in all building models, the inflow directed downward inside the building exhibits a similar flow pattern across all cases. In buildings with outlet openings at 40 mm (Lower-Middle) and 60 mm (Lower-Upper), the flow is observed to be directed upward within the building, and these configurations display a notably similar behavior. When examining all cases, it is observed that the highest inlet velocity occurs when the inlet and outlet openings are aligned (Lower-Lower). As the outlet opening height increases, there is a decrease in inlet velocity and internal velocity values, resulting in an increase in internal pressure within the building. These findings align with Bernoulli’s principle, which explains the inverse relationship between velocity and pressure. Additionally, the pressure distribution on the windward facade appears similar across all cases.

The streamline distributions in Figure 21 reveal that in the Lower-Lower, Lower-Middle, and Lower-Upper configurations, the flow distinctly enters the building with a downward inclination, then exits with an upward inclination. Notably, in the Lower-Middle and Lower-Upper cases, where the windward opening is positioned lower than the leeward opening, the outflow from the leeward opening shows an upward tendency. This upward tendency may enhance ventilation efficiency by creating a compatible air circulation with the airflow movement and wind effect within the building.

The horseshoe vortex in the front of the building generates a standing vortex, a phenomenon that has been reported in previously conducted studies (Karava et al. [9], Ramponi and Blocken [22]. The trajectory of the jet is evidently directed downwards, towards the floor of the building, as a consequence of the standing vortex upstream of the inlet opening, which functions as a downward direction for the incoming jet, as demonstrated in the findings of Karava et al. [9] and Ramponi and Blocken [22,55]. In all three cases (Lower-Lower, Lower-Middle, Lower-Upper), a vortex has formed in the upper part of the incoming jet, rotating in the opposite direction to the clock in the middle of the central building and covering almost the entire internal volume. The jet moving towards the outlet has left the building at a steeper angle due to the upward shift of the outlet opening.

3.2.2. Results for Building Models with a Fixed 40 mm Inlet Position and Varying Outlet Positions

In an isolated gable-roofed building model with cross ventilation, where the center of the inlet window opening is fixed at a distance of 40 mm from the ground, the velocity and pressure contours and the distribution of streamlines for the Middle-Lower, Middle-Middle, and Middle-Upper configurations (where the center of the outlet window opening is varied at 20, 40 and 60 mm) are presented in Figure 22, Figure 23 and Figure 24. Due to the downward inclination of the flow passing through the inlet opening and the lower positioning of the outlet opening, it is observed in the Middle-Lower configuration that the flow exits the building without a significant reduction in inlet velocity. In this model, higher inlet velocities and lower pressure values were obtained compared to the other configurations, which aligns with Bernoulli’s principle. Furthermore, the distribution of pressure across the windward façade remains consistent in all analyzed scenarios. In the isolated building models with Middle-Middle and Middle-Upper configurations, the flow exhibits an upward tendency due to the higher position of the recirculation region above the flow compared to the recirculation region below the flow. When examining the streamline distributions of configurations in which the windward opening is fixed at the middle height level of the building and the leeward opening is located at different heights, it is observed that the incoming jet generally tends to be downward. In all three cases, a clockwise recirculation vortex forms in the lower region of the jet. The center of this vortex is located in the middle section of the building in the Middle-Lower configuration, while it shifts towards the windward opening when the leeward opening is moved to the Middle-Upper level. While the flow structures in the upper region of the jet are similar in the Middle-Middle and Middle-Upper configurations, an additional vortex rotating counterclockwise is observed near the exit opening in the Middle-Lower configuration.

3.2.3. Results for Building Models with a Fixed 60 mm Inlet Position and Varying Outlet Positions

The velocity contours, pressure contours, and streamline distributions obtained from numerical analysis for the Upper-Lower, Upper-Middle, and Upper-Upper configurations, where the center of the inlet window opening in an isolated building with a single inlet and outlet is fixed at 60 mm from the ground and the outlet window opening varies at 20 mm, 40 mm, and 60 mm, are shown in Figure 25, Figure 26, and Figure 27, respectively. When examining the results, it is observed that, in all configurations, the air impacting the lower part of the building gains an upward motion after contacting the building wall, causing the inlet flow to be directed upward. Similarly, the outgoing airflow exhibits an upward movement, particularly in the Upper-Upper configuration where the inlet and outlet openings are aligned; this configuration displays the most stable velocity contours, and the highest velocity contour compared to the other two cases. Notably, the distribution of pressure on the windward facade is similar across all situations, indicating that different outlet opening ratios do not have a significant impact in this area. Examining the streamline distribution reveals that in cases where the windward opening is positioned higher than the leeward opening (Upper-Lower and Upper-Middle), the flow enters the building with an upward inclination, while the outflow from the leeward opening exhibits a downward pattern. This outcome highlights how the airflow path within the building and the exit direction are influenced by the positioning of the window openings. It can be stated that these scenarios, where the windward opening is positioned higher, have a significant impact on the direction and velocity distribution of indoor ventilation.

The incoming jet adheres to the ceiling surface and is directed upwards due to the Coanda effect, as emphasized by Tominaga and Blocken [28]. Unlike other configurations, setting the windward opening to the highest position creates counterclockwise vortices in the roof section.

Figure 28 illustrates the change in U/U_ref along the window openings for various configurations. Among the symmetric opening configurations, the highest non-dimensional velocity ratio was obtained in Upper-Upper, followed by Middle-Middle and Lower-Lower, respectively. This finding obtained in this study exhibits similar results to those reported in the PIV experiments conducted by Karava [9] and CFD study by Moey et al. [56].

When examining the Upper-Lower and Lower-Upper configurations, the U/U_ref is higher in the Upper-Lower configuration in both the windward and leeward openings. This indicates that the airflow speed in the upper part is better than the air intake in the lower part. This result is similar to the findings of Moey et al. [56].

Except for the Upper-Lower and Upper-Middle configurations, which had the highest speed ratio values of 0.656700 and 0.621798, respectively, an increase in speed ratios occurred at the x/D = 0 point for all configurations. Although there were significant decreases in the velocity ratio values of the air entering the building at the x/D = 0.5 point for all conditions, the decrease in velocity was slow in the Middle-Lower configuration, amounting to only a 3% decrease. This minimal decrease ensured that the highest velocity at the x/D = 1 point was also in the Middle-Lower configuration.

Unlike the literature, when the Middle-Lower, Middle-Middle and Middle-Upper configurations were examined, in the Middle-Lower case, when the exit opening was set to the highest position in the Middle-Upper case, the normalized velocity ratio decreased by 21% at x/D = 0; at x/D = 0.5, a 72% decrease, and at x/D = 1, a 20% decrease occurred.

3.3. Analysis of Ventilation Rate Results

The ventilation rate for a naturally cross ventilated low rise isolated building with one effective inlet and one effective outlet can be determined using the following equations [45].

The airflow coefficient, $C_Q$ was computed by Equation (6) with a reference velocity, $u_{ref}$ of 6.97 m/s and the discharge coefficient, $C_d$ of 0.62 [46].

$$C_Q=u_{ref}{C}_d\sqrt{\Delta C_p}$$

(6)

where, $\Delta C_p$ denotes the difference in pressure coefficients between the windward and leeward openings, as defined by Equation (7).

$$\Delta C_p=C_{p,windward}-C_{p,leeward}$$

(7)

Moreover, the flow coefficient, $C_Q$ was employed in Equation (8) for the purpose of calculating the actual flow coefficient, $C_a$.

$$C_a={\displaystyle \frac{C_Q}{1+C_Q}}$$

(8)

Lastly, the ventilation rate, $Q$ can be obtained by utilizing Equation (9).

$$Q=u_{ref}{A}_e{C}_a$$

(9)

where $A_e$ is the area of the opening and is calculated by Equation (10).

$$A_e={\displaystyle \frac{A_{inlet}·A_{outlet}}{\sqrt{A_{inlet}^2+A_2^{outlet}}}}$$

(10)

$A_{inlet}$ and $A_{outlet}$ are the area of the inlet and outlet openings respectively.

In Figure 29, the ventilation rate (Q) and normalized ventilation rate (Q/Q_ref) values for cross-ventilated isolated building models with fixed outlet window sizes and variable inlet window sizes were visualized using color intensities to facilitate quick understanding of the differences between models. When examining the ventilation rates calculated for the building models WO1, WO2, WO3, WO4, and WO5 used in the study, it is clear that an increase in inlet opening size directly affects ventilation efficiency. The WO5 building model with the highest ventilation rate of 0.004089 m³/s was the most efficient model in terms of natural ventilation. In fact, this value clearly indicated that a larger inlet opening size increased the indoor air circulation. The WO4 model ranks second with a ventilation rate of 0.003814 m³/s. The high ventilation performance of the WO4 and WO5 models showed that larger inlet openings enhanced the indoor air movement, thus promoting more fresh air circulation within the building. Therefore, it can be concluded that the performance of natural cross ventilation was sensitive to the size of the inlet opening and the airflow improved significantly with larger inlet sizes. The WO3 model, which ranked third with a ventilation rate of 0.003021 m³/s, showed a higher performance than the WO2 and WO1 models with smaller openings but a lower performance compared to the WO4 and WO5 models, showing a medium level of success. This result showed that medium sized inlet openings provided a certain level of ventilation efficiency, although insufficient to achieve maximum performance. The WO2 model ranked fourth with 0.001666 m³/s, while the WO1 model exhibited the lowest ventilation performance with 0.000418 m³/s. The narrow inlet opening in the WO1 model had a limiting effect on ventilation and prevented sufficient air intake. From this, it can be clearly stated that small inlet openings were insufficient for natural ventilation, which could reduce the indoor air quality. The WO1 model should be avoided where ventilation performance is a priority.

According to the results obtained above, it can be concluded that the size of the window opening has a critical importance in the natural ventilation performance of the building. Window openings need to be carefully designed if ventilation efficiency is to be improved. Since the WO5 model with a high ventilation rate is suitable for maximizing indoor air quality, it can be preferred for situations where optimum ventilation performance is targeted. However, depending on architectural requirements or aesthetic considerations, the WO4 or WO3 models can also be considered acceptable alternatives. On the other hand, WO1 and WO2 models with lower ventilation efficiency should not be selected for buildings where natural ventilation is prioritized. The normalized ventilation rate (Q/Q_ref) reached the highest value of 1.372670 in the WO5 model, providing a ventilation rate 37.27% higher than the reference condition. The Q/Q_ref value of the WO1 model was significantly below the reference level with 0.140321 and was the model with the lowest performance. Looking at the color intensity in the graph in Figure 22, models WO1 and WO2 were represented by low intensity colors and the color intensity increased from WO3 to WO5. With this color transition, it was easily understood that the models with higher ventilation rates provided more efficient ventilation.

Figure 30 provides a graphical comparison of the ventilation rates calculated for isolated building models with a fixed inlet window size and varying outlet window sizes. Upon examining the results, it is evident that the LO5 model achieves the highest ventilation rate. With a ventilation rate of 0.003814 m³/s, the LO5 model stands out as the most efficient option for natural cross ventilation. The LO4 model follows with a ventilation rate of 0.003547 m³/s. The larger outlet openings in these models facilitate airflow within the building, enhancing ventilation efficiency. The LO3 model, ranked third, has a ventilation rate of 0.003021 m³/s and exhibits moderate performance. While the LO3 model provides a higher ventilation rate than models LO2 and LO1, which have smaller outlet openings, it falls short of maximum performance. This finding highlights the significant role that the width of the outlet opening plays in the effectiveness of air circulation. The LO2 model, ranked fourth, has a ventilation rate of 0.001809 m³/s, performing better than the LO1 model. However, the LO1 model, with a ventilation rate of 0.000467 m³/s, demonstrates the lowest performance, indicating that a narrow outlet opening severely restricts airflow. The low ventilation rate of the LO1 model clearly shows that small outlet openings are inadequate for effective airflow in natural ventilation systems. Examining the normalized ventilation rate (Q/Q_ref) values for the building models from LO1 to LO5, the LO1 model performs at only 15.67% of the reference, indicating the lowest performance in terms of normalized ventilation rate. This suggests that the LO1 model is insufficient for natural ventilation performance when compared to the reference model, potentially lacking in energy efficiency or indoor air quality. The LO5 model, on the other hand, achieves the highest normalized ventilation rate, providing 128.03% of the reference ventilation rate. This indicates that the LO5 model delivers approximately 28% more ventilation than the reference model. The LO2 and LO3 models exhibit moderate efficiency, achieving 60.71% and 101.42% of reference ventilation performance, respectively. These models possess the potential to meet basic indoor air exchange requirements but deliver lower performance compared to the LO4 and LO5 models.

Figure 31 shows a comparison of the ventilation rates calculated for cross-ventilated isolated gable roofed building models with various inlet and outlet opening positions. The ventilation rates obtained for nine alternative building combinations show how the positions of both inlet and outlet openings have a decisive influence on the natural ventilation performance. When the results were examined, in the models where the inlet opening position was fixed at 20 mm, changing the outlet opening height at 20 mm, 40 mm, and 60 mm created differences in ventilation rates. Lower-Upper configuration with an outlet opening of 60 mm exhibited the highest performance with a ventilation rate of 0.003021 m³/s. In contrast, the Lower-Lower configuration with both inlet and outlet openings of 20 mm had the lowest ventilation rate of 0.002932 m³/s, colored in dark purple. This implied that a higher outlet opening increased the airflow while the inlet opening was constant. A similar trend was observed for the models with a fixed inlet opening position of 40 mm. The Middle-Upper building configuration achieved the highest ventilation rate of 0.003065 m³/s with an outlet opening height of 60 mm. On the other hand, the lowest ventilation rate of 0.002959 m³/s was recorded in the model with an outlet opening position of 20 mm (Middle-Lower). This result shows that a medium height inlet opening better supports the airflow when paired with higher outlet openings.

For the building models with the highest inlet opening position of 60 mm, the building model with a 20 mm outlet opening position (Upper-Lower) achieved the highest ventilation rate of 0.003129 m³/s, highlighted in yellow, while the model with a 60 mm outlet position (Upper-Upper) reached the lowest ventilation rate of 0.003012 m³/s. The best ventilation performance among all the configurations related to the opening positions was obtained in the Upper-Lower building model.

3.4. Limitations and Future Work

The limitations of this study are outlined below:

• This study considered an isolated building model.
• All simulations were performed under isothermal conditions.
• The study considered a constant wind perpendicular to the inlet openings.
• No internal obstacles were considered within the building model.

Future research will aim to conduct a detailed analysis of how varying wind directions and velocities, as well as non-isothermal conditions, affect the performance of natural ventilation. Additionally, in realistic design scenarios, the development of a more comprehensive configuration that accounts for the influence of interior furnishings, wall partitions, and physical obstructions is essential to enhance the practical applicability and reliability of natural cross-ventilation strategies.

4. Conclusions

In this study, the effects of window opening sizes and their positions on wind-induced natural cross-ventilation performance were numerically investigated using ANSYS software in an isolated building model with a gable roof. Given that the existing literature predominantly focused on simplified rectangular or cubic geometries with limited opening scenarios, this study provided a more comprehensive examination of various opening configurations within a gable-roofed building form. The primary findings obtained from the analyses were summarized below:

• It was observed that increasing the inlet opening has a strong but non-linear effect on the distribution and intensity of airflow throughout the volume. Although a significant increase in outlet velocity was observed as the inlet opening increased, the fact that the minimum velocity in the middle region occurred at WO4 and WO5 indicated a complex relationship between the opening size and the internal flow balance. The finding suggests that in natural ventilation systems, optimized opening ratios rather than simply larger openings may provide more effective performance.
• It was stated that an improvement in the exit opening had a significant effect on the air flow inside the building. Larger openings increase the air speed in the entrance and middle areas, thereby improving ventilation efficiency, while reducing the speed values in the exit area. Therefore, when optimizing the size of the openings, the aim should be to ensure balanced air flow throughout the entire volume rather than focusing on a single area.
• Among the cross-ventilated isolated building models with fixed outlet window opening size and varying inlet opening sizes, the lowest ventilation rate was calculated in the WO1 model with 0.000418 m³/s.
• The ventilation rate improved significantly from WO1 model to WO5 model, reaching 0.004089 m³/s.
• The normalized ventilation ratio (Q/Q_ref) reached the highest value of 1.372670 in the WO5 model, providing a ventilation ratio 37.27% higher than the reference building model.
• When the ventilation rates calculated for isolated building models with fixed inlet window size and varying outlet window sizes were analyzed, the LO5 model was the most efficient with a ventilation rate of 0.003814 m³/s.
• The LO1 model had the lowest performance in terms of normalized ventilation rate, providing approximately 28% more ventilation than the reference model.
• In the building models with the highest inlet opening of 60 mm, the Upper-Lower model reached the highest ventilation rate of 0.003129 m³/s. Among all configurations related to the opening positions, the best ventilation performance was obtained in the Upper-Lower building model.

The findings indicated that the size and position of window openings significantly influenced indoor airflow patterns, vortex formation, and thus, the effectiveness of wind-driven natural ventilation.