This study focuses on an office space situated in the Hefei area. The office has dimensions of 3.6 m in length, 4.0 m in width, and 3.0 m in height. It features a south-facing opening measuring 0.6 m × 1.2 m and a north-facing opening measuring 0.9 m × 2.1 m. Notably, the north-south opening is situated directly opposite. During the transitional season and summer in Hefei, the prevailing natural ventilation wind direction is from the southeast, with an average wind speed of 3.2 m/s in the southern direction.

The apparatus used in the experiment included a 5 mm thick acrylic plate model, an electric fan and a thermosensitive anemometer, as shown in Figure 1. The thermosensitive anemometer used is the SMART SENSOR AR866A model, with a measurement accuracy of ±1% and a resolution of 0.01 m/s. The probe diameter is 11 mm, which can be stretched to 920 mm, and the instrument and the line are about 2.1 m long. Additionally, the instrument featured a USB interface enabling real-time measurement and data recording on a computer. It also had the capacity to store data for up to 500 sets.

In this test, the medium used in the model and the prototype is air, and the air flow is turbulent, non-isothermal, incompressible, viscous three-dimensional steady flow, and the basic differential equations of the viscous fluid are dimensionally-processed to obtain the following functional equations. F Pr , R e , F r , E u = 0 (1) Where Pr is the Prandtl number; R e is the Reynolds number; F r is the Froude number; E u is the Euler number.

Since the medium used in both the model and the prototype is air (Xie et al., 2021), i.e., Pr ⁡ = 0.73 , E u is a non-qualitative characteristic number, E u = f Pr ⁡ , R e , thus, Eq. 1 can be rewritten as. F R e , F r = 0 (2)

In practical engineering and modeling tests, air flow is generally in the drag square region, the Reynolds number R e is generally greater than 4,000. The air flow along the drag coefficient λ is only related to the equivalent roughness k , but not related to R e , that is, the flow into the Reynolds self-simulating region (Walker et al., 2011). The reduced-scale model experiments in this paper satisfy this condition, and the R e number need not be considered in the simulation process. Therefore Eq. 2 can be transformed into. F F r = 0 (3)

The Froude number ( F r ) in Eq. 3 is defined as: F r = v 2 g l (4) Where v is the air supply velocity, m/s; g is the free fall acceleration, m/s²; l is the characteristic length, m.

When designing using the Froude criterion, it is required that the rooms and models have equal Froude numbers, which can be expressed according to Eq. 4 as follows: (Xie et al., 2021). v 2 g l = v ′ 2 g ′ l ′ (5) where the mark "′" is added to indicate the corresponding parameter of the prototype. Let the free-fall acceleration scale C g = g / g ′ , geometric scale C l = l / l ′ , and velocity scale C v = v / v ′.

When the model test conditions are basically similar to the prototype conditions, C g = 1 can be assumed, and the velocity scale can be derived from Eq. 5 as follows. C v = C l 1 2 (6)

In the experiment of this paper, the geometric scale C l = 1 / 10 , and the actual incoming wind speed is 3.2 m/s. According to Eq. 6, the inlet wind speed can be calculated as v = v ′ C l 1 / 2 . Therefore, the southward inlet wind speed in this reduced-scale model experiment is 1.0 m/s.

The reduced-scale model experiment employs a room model with dimensions of 36 cm in length, 40 cm in width, and 30 cm in height, as depicted in Figure 2. The size of the south-facing opening of the model is 6 cm × 12 cm, the height from the bottom is 9 cm, the size of the north-facing opening is 9 cm × 21 cm, and the size of the indoor set deflector is 12 cm × 12 cm, the height from the bottom is 9 cm, and the distance from the south-facing opening is 14 cm, which is scaled down by 10 times. Geometric similarity between the model and the prototype is upheld, with the model crafted from specially treated plexiglass acrylic plate of 5 mm thickness. The chosen acrylic plate boasts notable advantages, including robust impact resistance, high recyclability, ample rigidity and strength, ease of processing and molding, and simple maintenance. Importantly, the acrylic plate remains resilient against significant vibrations and deformations throughout the experimental course.

The arrangement of measurement points for the experimental model is illustrated in Figure 2. At the top of the model, a circular hole with a diameter of 15 mm (11 mm diameter of the thermosensitive anemometer probe) serves as the designated measurement point. These measurement points are symmetrically positioned along the centerline of the building model, as depicted in Figure 3. The total count of measurement points corresponds to 14.

To investigate the impact of varying width-to-height ratios and distinct shapes of deflector plate openings on the indoor velocity partitioning ratio within the context of natural ventilation, this paper introduces the subsequent experimental plan: 1) a hole was opened in the deflector plate, and eight deflector plates with different width to height ratio openings were set, the opening sizes of the deflector plates were shown in Table 1, and the schematic diagram of the openings was shown in Figure 4; 2) A hole is opened in the deflector plate with the same opening area, and the opening shapes are circular, 4.00 cm × 9.00 cm rhombic, square and 9.00 cm × 4.00 cm rhombic. The shape and size of the specific deflector opening is shown in Table 2, and the schematic diagram of the opening is shown in Figure 5.

The experimental protocol commenced by establishing the model’s fixed position, followed by meticulous adjustments to both the distance and height between the fan and the window opening. Drawing from similarity theory (Han and Li, 2021), a hot-wire anemometer was deployed to gauge the wind speed at the entrance, thereby maintaining a constant inflow velocity of 1.0 m/s. The experiment aims to measure the wind speed at a 15 cm height within the model. To minimize experimental errors, it is essential to maintain the thermal probe of the thermosensitive anemometer perpendicular to the incoming flow direction. The experimental measurement diagram is shown in Figure 6. Then, use the anemometer to test the wind speed at 14 measurement points. To ensure the accuracy of the measurement results, take 10 consecutive instantaneous velocity values for each measurement point and calculate the average value as the final velocity value at each measurement point.

Airpak software is now widely used to simulate indoor and airflow organization distribution (Zhang and Ryu, 2021; Zhang et al., 2023). In this study, we employed the Airpak software to construct a scaled-down numerical model of a room, measuring 36 cm in length, 40 cm in width, and 30 cm in height. During the simulation, all doors and windows remained open. The room model is depicted in Figure 7, with the x-axis denoting the depth direction, the y-axis representing height, and the z-axis indicating width. The arrangement of numerical simulation measurement points is the same as that of the reduced-scale model experiment. The velocity values of each measurement point were calculated directly by Airpak software when the deflectors with different opening width to height ratio and different opening shapes were set in the room.

In order to study the flow of indoor air in the real state, a 1:1 full-scale modeling was conducted, and the room model size was 3.6 m × 4.0 m × 3.0 m (length × width × height). The natural ventilation of the room with all windows and doors open is simulated. The airflow distribution in the cross-section at the height of y = 1.5 m (height of human activity) was investigated by numerical simulation of the room without deflector, with deflectors with different opening width-to-height ratios and deflectors with different opening shapes.

Indoor air flow is incompressible and low-speed turbulent. This paper employs the indoor zero-equation model for its extensive validation, characterized by rapid computational speed and stable convergence when predicting various airflow scenarios, including natural convection (Vera et al., 2010), forced convection, mixed convection, and displacement ventilation within a room. This model is well-suited for forecasting indoor airflow distribution and has demonstrated its effectiveness, particularly under mixed convection conditions (Ling et al., 2015). In this study, the SIMPLE (semi-implicit method for pressure dependent equations) pressure-velocity coupling algorithm is used (Fan et al., 2022; Liu et al., 2022; Mohamed et al., 2022).

The boundary conditions of the reduced-scale model are determined based on the full-size working conditions as well as similar scales. The boundary conditions of this simulation are as follows: the pressure boundary is chosen, and the southward inlet wind pressure of the room is determined according to Δ p = ρ v 2 / 2 . The wind pressure at the northward opening is negligible. The boundary conditions of the full-size and reduced-scale models are set as shown in Table 3.

The simulation was conducted using the Airpak software to mesh the computational region with a hexahedral unstructured grid. As an example, five different grid schemes were selected for the simulation when a circular hole was opened in the deflector of the reduced-scale model. The number of divisions for these schemes was 14,520, 17,664, 22,818, 34,210, and 44,404 grid cells, respectively. To investigate the grid independence (Strasszer and Xydis, 2020; Yuan et al., 2020; Wang Z. et al., 2021), the measurement point was chosen at the center of the deflector opening. Figure 8 illustrates the wind speed variations at the measurement point for different grid numbers. When the number of grids is less than 22,818, there is a noticeable difference in air velocity at the measurement point. However, when the number of grids is equal to or greater than 22,818, the air velocity at the measurement point remains relatively stable. The air velocities at the measurement point for grid counts of 22,818, 34,210, and 44,404 are recorded as 0.66 m/s, 0.66 m/s, and 0.67 m/s, respectively. The air velocity deviation among the three grid schemes is within 5%. Therefore, 22,818 grid cells were selected as the meshing scheme for this study, as shown in Figure 9. The meshing quality is good and meets the requirements for the simulation.

As depicted in Figure 11, the velocity distribution at a height of y = 1.5 m in the absence of a deflector is illustrated. Outdoor air enters the room through the southern entrance and exits through the northern air vent, establishing cross-ventilation. The air velocity is highest at the south side inlet, and localized areas in the middle section have higher air velocities due to cross ventilation.

As indicated in Table 5, in the absence of a deflector within the room, the velocity cloud diagram of the cross-section at a height of y = 1.5 m comprises 3.06% in the low wind speed zone, 62.11% in the comfort speed zone, and 34.83% in the high wind speed zone.

Illustrated in Figure 12, outdoor air flows into the room through the southern entrance, with the highest wind speed observed at this inlet. Encountering the obstruction at the unopened place of the deflector plate, vortex will be generated at the back of the deflector plate, resulting in the value of the air velocity at the back of the deflector plate in a large area close to zero. Through the openings in the room deflector, air flows from one side of the room to the other, creating cross ventilation and resulting in higher air velocities in localized areas. As the width-to-height ratio of the deflector opening increases, the percentage of the low-wind-speed zone in the velocity cloud diagram at the cross-section of y = 1.5 m height decreases, while the proportion of the comfortable-speed zone and high-wind-speed zone increases.

Figure 13 illustrates the effect of variations in the width-to-height ratio of the deflector openings on the percentage of indoor velocity partitioning. As the width-to-height ratio increases from 3/6 to 7/6, there is a continuous reduction in the proportion of the low wind speed zone, decreasing from 11.79% to 3.75%, representing an 8.04% decrease. Concurrently, there is an increase in the proportion of the speed comfort zone, rising from 72.38% to 75.98%, indicating a 3.60% increase. Additionally, the proportion of the high wind speed zone rises from 15.83% to 20.27%, reflecting a 4.44% increase. Subsequently, when the width-to-height ratio of the deflector opening increases from 7/6 to 8/6, the percentage of the low wind speed zone experiences an increase from 3.75% to 7.33%, a growth of 3.58%. Simultaneously, the percentage of the speed comfort zone decreases from 75.98% to 71.38%, representing a 4.60% decrease. Additionally, the percentage of the high wind speed zone increases from 20.27% to 21.29%, signifying a 1.02% increase. Lastly, when the width-to-height ratio of the deflector opening is increased from 8/6 to 10/6, the percentage of the low wind speed zone decreases from 7.33% to 2.98%, indicating a 4.35% decrease. Correspondingly, the percentage of the speed comfort zone increases from 71.38% to 73.01%, reflecting a 1.63% increase. Furthermore, the percentage of the high wind speed zone increases from 21.29% to 24.01%, representing a 2.72% increase.

As shown in Figure 14, the flow state and the reason for its formation are in general agreement with Figure 12. The different shapes of the deflector opening have a greater influence on the proportion of each wind speed zone in the velocity cloud map of the cross-section at the height of y = 1.5 m.

In Figure 15, we observe changes in wind speed zones related to different deflector opening shapes. When the deflector opening has a 9.00 cm × 4.00 cm rhombus shape, the percentage of the low wind speed zone measures 13.78%, while with a square deflector opening, it decreases to 6.04%. The highest percentage of the speed comfort zone, at 75.56%, is recorded when the deflector opening takes the form of a 4.00 cm × 9.00 cm rhombus, and the lowest percentage, 66.83%, is observed when the deflector opening is in the shape of a 9.00 cm × 4.00 cm rhombus. The percentage of the high wind speed zone shows relatively little variation.

The effects of the above three scenarios on the indoor airflow distribution under natural ventilation conditions are simulated and analyzed, keeping the wind pressure at the entrances and exits constant and the position of the deflector plate constant. In the absence of a deflector plate in the room, the indoor speed comfort zone occupies the smallest proportion, accounting for 62.11%. The percentage of indoor speed comfort zone increased significantly when deflectors with different opening width-to-height ratios and deflectors with different opening shapes were installed indoors. The percentage of the indoor speed comfort zone varied with changes in the opening width-to-height ratio of the deflector plate. When the deflector plate had an opening width-to-height ratio of 7/6, it reached its highest value at 75.98%, marking a significant increase of 13.87%. The shape of the deflector opening had a more pronounced effect on the indoor speed comfort zone percentage. When the deflector opening took on a rhombus shape measuring 4.00 cm × 9.00 cm, it reached its highest value at 75.56%, reflecting a substantial increase of 13.45%.