Research on the Impact of Air Temperature and Wind Speed on Ventilation in University Dormitories under Different Wind Directions (Northeast China)

Abstract

This study employs computational fluid dynamics to analyze the natural ventilation conditions of university student dormitories in the northeastern region of China under various outdoor wind directions, wind speeds, and temperature conditions. By separately simulating room natural ventilation efficiency under four different outdoor wind speeds (1.5 m/s, 3.3 m/s, 5.4 m/s and 7.9 m/s) at different outdoor temperatures (−10 °C, 0 °C, 10 °C and 20 ℃), curves of indoor pollutant removal rates (VOA-Time) are established for different wind directions. The study also determines the minimum ventilation time required for rooms under different environmental conditions (T_VOA=70%). The data indicate that, despite the promotion of ventilation efficiency with increasing wind speed or indoor-outdoor temperature difference, the wind direction determines the extent to which these factors enhance room ventilation efficiency. Furthermore, there are corresponding mathematical relationships between T_VOA=70%, outdoor temperature, wind speed, and different wind directions, allowing for predictions related to the rate of indoor carbon dioxide change. The research findings will assist students in formulating more effective ventilation strategies under complex outdoor environmental conditions.

1. Introduction

With the continuous popularization of higher education, the number of college students in Northeast China has been increasing. Following the coronavirus pandemic, people have realized that sufficient attention must be paid to the health issues of university students [1]. Since the dormitory is the place where the students spend most of their time while attending school, how to build a safer and healthy place for students is a meaningful topic. The research [2,3,4] reveals that the air quality within dormitories has a direct impact on the physical health of students. A poorly ventilated living space [5,6,7,8,9] can result in compromised sleep quality among students and even heighten the risk of infection.

In Northeast China, natural ventilation is the predominant method of ventilation employed in university dormitories. Natural ventilation is an energy-saving and environmentally friendly way, while its ventilation efficiency is closely related to the outdoor environment. However, this may not be the most effective ventilation strategy because outdoor environmental conditions will largely affect ventilation efficiency, and it is difficult to maintain pollutant concentrations below specified standards by relying solely on students’ subjective judgment [10,11,12,13].

In order to assess the relationship between indoor air quality and outdoor environment, scholars have proposed various research methods. Lei et al. [14] explored the relationship by monitoring indoor carbon dioxide levels and analyzing the ventilation area’s correlation with indoor pollutant concentrations based on the winter outdoor environment in Beijing. Li et al. [15] established an empirical equation for the ventilation status and indoor air quality in university dormitories by monitoring the carbon dioxide concentration. Sun et al. [16] conducted a series of measurements in the academic buildings of Tianjin, China, revealing that changes in the outdoor environment significantly impact the health of students on campus. Although these studies utilized experiments to demonstrate the relationship between natural ventilation and air quality, the inability to precisely control various environmental variables often affecting experimental factors necessitates extended experimental periods, and the conclusions drawn may be subject to noticeable regional limitations.

With the continuous development of computational fluid dynamics (CFD), CFD technology has gradually found applications in this field, becoming a crucial method for analyzing the relationship between indoor air quality and the outdoor environment [17,18,19]. In this context, Dai et al. [20] simulated different wind directions to identify critical pollution areas within university dormitory buildings. Meanwhile, Kai et al. [21] conducted a simulation analysis of the dispersion of droplet pollutants inside dormitories and discovered a significant correlation between wind direction and the distribution of indoor pollutants. Additionally, Wang et al. [22], based on the thermal environment in Chongqing, China, analyzed the impact of thermal effects on dormitory ventilation efficiency and established the relationship between thermal effects and natural ventilation efficiency. Overall, in relevant simulation studies, the variations in airflow environments caused by outdoor wind conditions and temperature have been the focal points of such research. It is widely known that in real-world scenarios, the natural ventilation efficiency of a room is typically determined by multiple factors. These primarily include outdoor wind direction [23,24,25], wind speed [26,27,28], air temperature [29,30,31], and so on. However, current research on indoor natural ventilation tends to analyze the impact of specific single variables on indoor ventilation efficiency. Neglecting the influence of changes in multiple factors on indoor natural ventilation efficiency may lead to significant limitations in research conclusions. Therefore, quantitatively calculating the mathematical relationship between outdoor wind speed and temperature and indoor natural ventilation, as well as analyzing the degree of influence of various environmental factors on indoor ventilation efficiency, contributes to the construction of a room’s natural ventilation model under complex environmental conditions. Furthermore, influenced by the climate, student dormitories in the northeastern region of China utilize smaller casement windows. Although this design enhances the insulation of the dormitories, it restricts the ventilation area. Currently, there is no research on room natural ventilation based on models of university dormitories in this region.

According to the above perspectives, this paper utilizes CFD to analyze the ventilation efficiency of rooms within a linear-shaped dormitory building under different outdoor wind directions, wind speeds, and air temperatures. The paper establishes functional relationships among multiple variables. Additionally, the study combines on-site experiments to further validate the universality and reliability of the obtained conclusions. The research aims to quantitatively analyze the impact of the outdoor environment around the dormitory building on indoor natural ventilation through theoretical calculations and practical measurements. The results of this study will assist students in formulating reasonable and effective ventilation strategies under different outdoor environmental conditions. It can also serve as a reference for the relationship between room ventilation efficiency and prevalent winds in the region, providing guidance for architectural design.

2. Model and Methods

The Ansys-Fluent 2020R2 CFD software was utilized in this study, with a server core count of 64 and the CPU was AMD-EPYC-7061.

The nomenclature can be found in the Nomenclature section.

2.1. Theoretical Equations

The simulation calculation method employed in this study is RNG-k-ε, with the standard wall equation utilized for the wall boundary condition. This approach has sufficient accuracy when applied to simulate indoor ventilation [32,33]. The k and ε equations are as follows:

$$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{{\partial x}_i}\left(\rho k{u}_i\right)=\frac{\partial }{{\partial x}_j}\left(a_k{u}_{eff}\frac{\partial k}{{\partial x}_j}\right)+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(1)

$$\frac{\partial }{\partial t}\left(\rho \epsilon \right)+\frac{\partial }{{\partial x}_i}\left(\rho \epsilon u_i\right)=\frac{\partial }{{\partial x}_j}\left(a_{\epsilon }{u}_{eff}\frac{\partial \epsilon }{{\partial x}_j}\right)+C_{1\epsilon }\frac{\epsilon }{k}\left(G_k+C_{3\epsilon }{G}_b\right)-C_{2\epsilon }\rho \frac{{\epsilon }^2}{k}-R_{\epsilon }+S_{\epsilon }$$

(2)

where

$$R_{\epsilon }=\frac{C_{\mu }\rho {\eta }^3\left(1-\frac{\eta }{{\eta }_0}\right){\epsilon }^2}{k\left(1+\beta {\eta }^3\right)}$$

(3)

$$\eta =\frac{Sk}{\epsilon }$$

(4)

The equation below is utilized for the computation of viscosity:

$$d\left(\frac{{\rho }^{2}k}{\sqrt{\epsilon \mu }}\right)=1.72\frac{\tilde{v}}{\sqrt{{\tilde{v}}^3-1-Cv}}d\tilde{v}$$

(5)

$$\tilde{v}=\frac{u_{eff}}{u}$$

(6)

In the regime of high Reynolds numbers, the viscosity coefficient governing air turbulence is formulated as follows:

$${\mu }_t=\rho C_{\mu }\frac{k^2}{\epsilon }$$

(7)

$$C_{\mu }=0.0845$$

(8)

The logarithmic distribution of the dimensionless velocity predicted by the standard wall function is as follows:

$$u^{+}=\left\{\begin{array}{c}{y}^{+}, y^{+}<11.25 \\ \frac{1}{k}\ln \left(E{y}^{+}\right),y^{+}>11.25 \end{array}\right.$$

(9)

Additionally, the tensor expression utilized to solve the governing equation of air age definition is as follows:

$$\frac{\partial }{\partial x_i}\left(A\rho u_i\right)=\frac{\partial }{\partial x_i}\left({\mathsf{\Gamma }}_A\frac{\partial }{\partial x_i}\right)+\rho$$

(10)

$${\mathsf{\Gamma }}_A=\frac{\mu }{Sc}+\frac{{\mu }_t}{S{c}_t}$$

(11)

2.2. Physical Model

The design specifications for university dormitories can be found in “Several Opinions on the Construction Standards of College Students’ Apartments [2001]” [34] and “GB 55025-2022” [35]. Northeast Electric Power University is situated on the outskirts of Jilin City, and there are no high-rise buildings around the corresponding dormitory building in the experiment. The physical model employed in this study is based on a four-student room at Northeast Electric Power University. In this model, the window is the only ventilation opening for the room. The selected room for the study is situated in the middle of the third floor of the dormitory building. Ventilation issues in the other rooms within the dormitory building are not considered in this study; therefore, all sides of the dormitory building are defined as Wall in the model. Furthermore, relevant experimental work was also conducted within the dormitory rooms of the same university.

The construction of the outdoor fluid domain is crucial. Inadequate space within the fluid domain can lead to deviations in calculations, as air pressure rises due to wind influence, while an excessively large outdoor fluid domain can reduce calculation efficiency. Assuming the height of the corresponding building in the experiment as H (H = 20 m), a minimum distance of 5H is necessitated between the building and the boundary of the fluid domain, according to the construction recommendations for outdoor fluid domains provided by relevant research [36,37]. The model utilized in this study is illustrated in Figure 1a, and the length of each boundary of the fluid domain (length × width × height = 380 m × 207 m × 135 m) is ensured to be five times the corresponding building height, and the outlet blockage rate is guaranteed to remain below 3%.

The Polyhedral mesh generation method is employed for mesh generation. In order to balance the accuracy and efficiency of the simulation, the turbulent kinetic energy of the connection between points A (2, 1.8, 1.6) and B (5, 1.8, 1.6) in the dormitory is utilized as an evaluation metric to verify grid independence. The assumed wind speed is 1 m/s with a westerly direction. Figure 1b displays the grid independence verification, where the range of the error bar is 5%. Four sets of grid models were compared through calculations, and it has been observed that the difference in turbulent kinetic energy calculated is less than 5% when the number of grids reaches 3,671,977. The model with a grid size of 3,671,977 will be selected for subsequent calculations.

The flow field in the room is the focus of this study, so the number of grids is 1,095,331, and the grid size is 5 cm. In addition, the growth rate of grid size is set to 1.03, and the upper limit of the mesh size in the fluid domain is 3.5 m. The minimum orthogonal quality is 0.51.

2.3. Evaluation Method

The “air age” is defined as the time duration required for air particles to enter a room and reach a specific location [38]. Although the “air age” can accurately reflect the freshness of air at a specific location in a room, it is challenging to comprehensively evaluate the overall air quality of the entire space. Liu [39] and Yang [40] have proposed a novel concept, namely area ratio of age of air (AOA), for assessing overall air quality in a classroom. The calculation formula is as follows:

$$\mathit{AOA}\left(\%\right)=\frac{X\left(\mathit{the}\mathit{area}\mathit{of}\mathit{age}\mathit{of}\mathit{air}\mathit{in}a\mathit{time}\right)}{Y\left(\mathit{the}\mathit{area}\mathit{of}\mathit{age}\mathit{of}\mathit{air}\mathit{in}a\mathit{whole}\mathit{time}\right)}$$

(12)

The calculation of AOA is based on the air age values’ area coverage in each part of the contour map. However, it should be noted that the flow field studied in this work is three-dimensional, and using the air age above the cross-section to reflect the overall indoor air quality may reduce the accuracy of the conclusion. Therefore, this study has extended the AOA indicator to three dimensions and proposed a novel concept of the volume ratio of air age (VOA). This study was inspired by the Rosin-Rammler distribution (Equation (13)), which characterizes particle size in materials [41,42] as below.

$$Y_d=e^{{-\left(d/\overline{d}\right)}^n}$$

(13)

$$n=\frac{ln(-ln{Y}_d)}{\mathit{ln}\left(d/\overline{d}\right)}$$

(14)

The following introduces the numerical sampling method for VOA. Given that each air particle corresponds to a unique air age value, and the air age values of adjacent air particles are nearly identical. Since the grid cells constituting the dormitory room are sufficiently small, it can be assumed that the air age values of all air particles within the grid cell are exactly the same (as shown in Figure 2). In addition, to ensure the accuracy of the fitted curve, it is recommended to average at least 15 values within the overall calculated range of environmental air age and calculate the corresponding grid volumes for each of these values. The volume size corresponding to different values can indicate the number of air particles associated with those values. Equation (15) shows the fitting approach for the VOA curve.

$$VOA\left(\%\right)=\frac{V_i}{V_m}$$

(15)

$$V_i=\sum _{z=1}^i{v}_z\left(z<m;\mathit{Accuracy}\mathit{requirement}:i\ge 15\right)$$

(16)

where $V_i$ is the total volume of the grids of which the air age is less than a certain value, $V_m$ is the total volume of the grid contained in the selected value.

The numerical value of VOA represents the exchange ratio between the original air inside the room and the outdoor air, indicating the freshness or air quality inside the room. When the VOA value is 0, it means that the air inside the room has not exchanged with the outdoor air, indicating no ventilation. When the VOA value is 100%, it indicates a complete exchange between the original air inside the room and the outdoor air, resulting in excellent indoor air quality. The relationship between VOA value and time is illustrated in Figure 2, showing the correlation between the duration of ventilation and indoor air quality. Due to the noticeable slow-growth region (decline area) in the curve, prolonged ventilation may not necessarily lead to higher ventilation efficiency and may even fail to meet residents’ comfort [43,44]. Therefore, according to “GB/T 50378-2019” [45] and the study by Liu [39], it is known that when the continuous ventilation time of the room ensures that the value of VOA exceeds 70% (i.e., VOA > 70%), the indoor air quality reaches an acceptable level. The time corresponding to the VOA value of 70%, i.e., T_VOA=70%, is the minimum ventilation time that the room should maintain under such conditions.

2.4. Settings

The essential data for computation and the solution settings are presented in

Table 1. Values and Model Settings.

Feature	Value	Note
Room air temperature	Average 22 °C	Measurements.
Body temperature	36.5 °C	Replace the human body with a bed surface and emit heat.
Ambient mean air pressure	99,342 Pa
Initial air pressure difference between indoor and outdoor	−5 Pa~0 Pa
Ambient wind direction	W (0°); SW (45°); S (90°)	Due to the geometric symmetry of the building and considering people’s habits of using the basic wind direction, the focus is on these three wind directions.
Ambient wind speed	1.5 m/s; 3.3 m/s; 5.4 m/s; 7.9 m/s	The Beaufort Wind Scale ranges from wind force 1 to 4.
Outdoor temperature	−10 °C; 0 °C; 10 °C; 20 °C	Assume.
Calculation scheme	Coupled
Pressure solution	PRESTO!
Momentum and energy discretization scheme	Second order upwind
Gas definition	Incompressible-ideal-gas	Ideal for thermal diffusion.

. Convergence of the computational results should be determined by user-defined scale (UDS) iteration <0.0001 and a fluctuation rate of calculation results <5%.

The relationship between wind speed and height above ground is shown by Equation (17), where $h$ represents the height position at the velocity-inlet surface and $V_0$ is the velocity at this height. The dormitory building is situated in a suburban area, with a roughness index of approximately 0.2. This equation is incorporated into the model through a user-defined function (UDF).

$$V_h=V_0\ast {\left(\frac{h}{h_0}\right)}^a$$

(17)

2.5. CFD Verification

The value of the air age is dependent on the velocity of airflow, and validation of the model can be achieved by comparing the velocity of airflow at sampling points [46,47]. The sampling point is set outdoors at 0.5 m from the window. In addition, the indoor temperature is subject to external environmental factors and human body heat, leading to the formation of temperature gradients. We conducted air temperature monitoring at sampling points located at heights of 0.2 m and 1.5 m within the indoor space, from which we obtained the average air temperature for each height. Three sets of validation experiments were conducted on the model, with each set lasting approximately 30 min. Validate the precision of the simulation model through a comparison between the initial simulation data and experimental findings.

The experimental instruments include an anemometer (Brand: Aicevoos; Accuracy ±0.1 m/s) (Brand: Smart-Sensor; Accuracy ±0.02 m/s) and a hygrometer (Brand: Sensirion-sensor; Temperature accuracy: ±0.2 °C). The experiment was conducted starting from 10 May 2023. During the experiment, the air temperature in the outdoor environment was 9 °C, and the average wind speed was 1.8 m/s. The wind direction is perpendicular to the window surface.

The variation of airflow velocity is shown in Figure 3a. To streamline data analysis, we normalized both the collected and simulated data (Equation (18)). The Y value serves as an indicator of the discrepancy between theoretical calculations and actual results across different time periods. As shown in Figure 3b, with an increase in monitoring time, the Y value gradually converges toward zero and exhibits slight fluctuations near the X-axis. In these three experiments, the Y value remained below 5% after a sampling time of 25 min, and the highest Y value was 3.3% at 30 min. Therefore, the discrepancy between experimental and simulated results is acceptable.

$$Y=\frac{\left|\sum _{i=1}^{time=30}{(V}_i-\overline{{\overline{V}}_{rel}})\right|}{i\overline{V}}$$

(18)

It was recommended that dormitory students remain in bed during the experiments to evaluate the potential impact of student activities on experimental accuracy. Thermometers were positioned at the sampling points depicted in Figure 3d for air temperature measurements. Upon opening the window, the air temperature at a height of 0.2 m in the room rapidly decreased and stabilized after 5 min, with an average temperature of 11.9 °C. Meanwhile, at a height of 1.5 m, the air temperature stabilized after approximately 10 min, maintaining an average temperature of 13.2 °C. The results obtained after the convergence of simulation computations are illustrated in Figure 3c, indicating an average air temperature of 11.0 °C at a height of 0.2 m and 12.3 °C at a height of 1.5 m. Upon comparing experimental and simulated results, it is evident that at 0.2 m from the floor inside the room, there is an absolute error of 0.9 °C between experimental and simulated outcomes. Similarly, at a height of 1.5 m, the absolute error in the obtained results is also 0.9 °C. There are two possible reasons for the error. On the one hand, it is because of unstable outdoor wind force, which leads to differences in air flow inside the dormitory compared to simulation results. On the other hand, students act as heat sources, and their body heat output is also influenced by objective factors such as clothing.

Although variations exist between simulated outcomes and actual measurements, these differences are considered acceptable. Therefore, these simulation settings will be applied in future research endeavors.

2.6. Applicability

The main objective of this article is to establish the correlation between ventilation efficiency in line-type dormitory buildings and outdoor environmental factors (wind direction, wind speed, and air temperature difference). Therefore, the conclusion will be further substantiated by real-time monitoring of indoor pollutant concentrations in this type of dormitory building.

The instruments utilized in these experiments included an air quality monitor (Brand AirNow; Carbon dioxide concentration accurate ±40 ppm; PM2.5 accurate ±10 μg/m³) Thermometer (Brand: Sensirion-sensor; Temperature accuracy: ±0.2 °C) and Anemometer (Brand: Aicevoos; Accuracy ±0.1 m/s). The instrument is positioned at the center of the room [2,15], and its results will be presented in the Section 4.

3. Results and Discussion

Under varying wind directions, the primary factors that facilitate the movement of indoor air particles will also change. The simulated cloud maps and the numerical values were combined to summarize and analyze all cases.

3.1. Phenomena

The cloud maps were created to show air age distribution based on different wind directions to help readers visually understand the air age distribution in the room. The selected section is the Z-Y plane, with positions at X = 0.5 m, 3.5 m, and 6.5 m. The impact of buildings on environmental airflow is not the focus of this study; therefore, the flow field cloud map of the entire environment will not be displayed. This part of the work calculated a total of 48 cases and fitted the VOA change curve of each case using the polynomial fitting method.

• Case 1 S Wind Direction

The impact of wind force on the indoor airflow field involves two primary aspects. Firstly, as the ambient wind speed increases, a pressure gradient is created, leading to a decrease in air pressure outside the window, resulting in an outward flow of indoor air. Secondly, although the environmental wind direction is parallel to the window surface, the outdoor airflow is influenced by the dormitory building, generating a component of airflow that tends toward the X-axis direction. The airflow entering the room can promote the movement of indoor air particles, thereby enhancing turbulence intensity inside the room. As shown in Figure 4, when the temperature difference between indoor and outdoor air is constant, the increase in wind speed leads to a gradual increase in the gradient difference in indoor air age on the horizontal plane. The air age value shows a positive correlation with the vertical distance between the air particle and the window surface. Additionally, from Figure 4, it is evident that when wind speeds reach 5.4 m/s and 7.9 m/s, the longitudinal gradient difference of air age gradually decreases. This phenomenon indicates that the indoor flow field’s enhanced intensity under the influence of wind and the airflow toward the X-axis direction plays a significantly dominant role in the indoor flow field.

In this wind direction, the air temperature difference between indoors and outdoors is another crucial factor influencing dormitory ventilation. Firstly, due to the influence of temperature, the indoor air pressure exceeds the outdoor air pressure, causing indoor air to gradually flow toward the outside under the effect of pressure. Secondly, there are temperature differences at different heights within the room. As cold air with higher density enters the dormitory from outside, it flows toward the positions closer to the floor upon entering the room. Additionally, with the influx of cold air, the indoor hot air gradually rises due to density effects. Therefore, the indoor temperature is positively correlated with the height above the room floor. Additionally, under the influence of the temperature field, the pressure increases at higher positions within the room. The airflow inside is hindered by the pressure gradient, resulting in a positive correlation between air age and the height above the room floor.

From the three surfaces depicted in Figure 4, it is evident that at wind speeds of 1.5 m/s and 3.3 m/s, there is a significant increase in air age at an indoor height of approximately 2 m or above. The reason is that, due to the longitudinal air pressure gradient indoors, the air at the height above the window stays indoors for a long time. The distribution of outdoor air age under the same air temperature in Figure 4 suggests that when the wind speed reaches 5.4 m/s or above, the longitudinal pressure gradient inside the room gradually weakens due to wind speed influence. In addition, air age is higher in locations further away from the window when the outdoor temperature is 20 °C. This phenomenon can be attributed to a smaller temperature difference between indoor and outdoor air, resulting in a less pronounced settling of airflow and a decrease in the temperature gradient difference of indoor air. Under the influence of wind, it is beneficial for indoor air particles to leave the indoor flow field.

Table 2. T_VOA=70%, S (0°) wind direction.

Wind Speed	Outdoor Temperature
	−10 °C	0 °C	10 °C	20 °C
1.5 m/s	1181 s	1290 s	1434 s	1706 s
3.3 m/s	1028 s	1203 s	1317 s	1519 s
5.4 m/s	897 s	949 s	1111 s	1290 s
7.9 m/s	716 s	839 s	977 s	1055 s

shows the time required for indoor natural ventilation with VOA = 70% under different wind speeds and outdoor temperature when the wind direction is S. Through a comprehensive analysis of the impact of wind speed and air temperature difference on natural ventilation in the room; it can be found that an increase in wind speed and air temperature difference has different promotion effects on indoor ventilation efficiency. Based on the calculation results, when the wind speed is 1.5 m/s or 3.3 m/s, the relationship between outdoor temperature and T_VOA=70% can be described as a concave function. While the outdoor wind speed is equal to or greater than 5.4 m/s, The relationship between outdoor temperature and T_VOA=70% is a convex function. Therefore, it can be inferred that under this wind direction, when the wind speed is below 3.3 m/s, the influence of air pressure gradient due to indoor-outdoor temperature difference on indoor ventilation is more significant. While the wind speed increases, the enhancing effect of air temperature difference on indoor ventilation will diminish. Under the same outdoor temperature, an increase in wind speed results in a gradual decrease in T_VOA=70%; however, the rate of T_VOA=70% decrease gradually slows down.

Figure 5 depicts the VOA curve and its fitting equation. In order to facilitate the description of the variation pattern of the VOA curve, the rapidly growing part of the curve is defined as the growth area, the steadily rising part of the curve is approximated as a linear area, and the slowing-down part of the curve is defined as the decline area (as shown in Figure 2). By comparing the variation patterns of VOA curves at identical outdoor temperatures, it can be observed that as the wind speed increases, the slope of the linear area of the curve also increases. This suggests that with an increase in wind speed, there is a corresponding improvement in indoor ventilation efficiency. Additionally, when comparing VOA curves at the same wind speed, it is evident that the growth rate of the linear area of the curve remains almost consistent. An increase in outdoor temperature leads to a delayed onset of the growth area within the curve. This phenomenon suggests that the greater the temperature differential between indoor and outdoor air, the more rapid the increase in indoor ventilation efficiency following ventilation initiation. The timing of the growth area occurrence is solely related to the air temperature difference between indoors and outdoors. When the wind speed reaches 7.9 m/s, the growth area of the curve remains close to time = 600 s. Furthermore, the decreasing area of the curve indicates a decrease in indoor ventilation efficiency, and the proportion of this area to the overall curve can reflect the volume ratio of the room with low removal efficiency of indoor air pollutants. In this wind direction, the proportion of the decline area of the curve in all cases is almost consistent.

• Case 2 SW Wind Direction

Figure 6 illustrates the distribution of air age for three indoor cross-sections under a wind direction at a 45° angle to the window surface. From this figure, it can be observed that the indoor air age distribution is relatively uniform in all cases. The impact of wind force on indoor airflow is highly significant in this wind direction. Upon comparing the effects of changes in wind speed on ventilation efficiency under the same air temperature, it becomes evident that an increase in wind speed significantly reduces the value of indoor air age. The airflow enters the room through windows near the Y-axis and is influenced by the room walls, resulting in counterclockwise circulation within the room and being discharged through another window. The reason for the indoor circulation is that the airflow entering the room from the window near the Y-axis changes direction under the influence of the wall, resulting in the flow velocity of the airflow not decreasing rapidly. Therefore, the air pressure gradually increases in the positive direction of the Z-axis, resulting in a flow of indoor air out of the window near the X-axis. As a result, a significant gradient in air age near the X-axis window is evident, with higher air ages observed in most areas of the section close to the window.

Table 3. T_VOA=70%, SW (45°) wind direction.

Wind Speed	Outdoor Temperature
	−10 °C	0 °C	10 °C	20 °C
1.5 m/s	759 s	821 s	876 s	925 s
3.3 m/s	656 s	701 s	725 s	752 s
5.4 m/s	379 s	381 s	396 s	384 s
7.9 m/s	280 s	272 s	273 s	275 s

presents the time required for indoor natural ventilation to achieve a VOA value of 70% under different wind speeds and outdoor temperatures, with a wind direction of SW. It is observed that when the ambient wind speed reaches 5.4 m/s, the T_VOA=70% values for different temperatures are nearly identical under the same wind speed. The impact of indoor and outdoor temperature differences on ventilation efficiency is noticeable only when the wind speed is below 3.3 m/s. Thus, under this wind direction, as outdoor wind speeds increase, the influence of indoor and outdoor temperature differences on room ventilation efficiency diminishes. Furthermore, at a wind speed of 1.5 m/s, elevated areas in rooms of Case B1 and Case B2 exhibit higher air ages. This is attributed to the influence of air temperature, causing increased air pressure at higher positions, hindering longitudinal airflow movement. As the wind speed increases to 3.3 m/s or above, indoor air circulation accelerates, and the vertical distribution of indoor air age gradually becomes more uniform.

The VOA curves are depicted in Figure 7. Analyzing the trend of changes in the linear area of the curve reveals that as wind speed increases, the growth amplitude of the linear area gradually intensifies. This suggests a positive correlation between indoor ventilation efficiency and wind speed. In this wind direction, the proportion of the decline area of the curve is higher than that observed in the other two investigated wind directions. It can be inferred that an increase in indoor airflow velocity can generate vortices near certain corners, potentially leading to the entrapment of air particles within this area for an extended period.

• Case 3 W Wind Direction

Figure 8 illustrates the distribution of air age across three sections within a room under a perpendicular wind direction relative to the window surface. The influence of temperature on indoor air age is analogous to that of the south (S) wind direction. Outdoor cold air, with higher density than indoor air, flows toward lower positions inside the room upon entering. Consequently, air particles near the ground in the room move faster and exhibit a shorter air age. The air pressure generated by the temperature field increases with height, while the intensity of the flow field gradually decreases under the influence of the longitudinal pressure gradient. Therefore, it can be observed from Figure 8 that there is a positive correlation between air age and indoor height.

The impact of wind on the indoor flow field is manifested in several aspects. Firstly, when students open the windows, outdoor air enters the dormitory under the force of the wind. Due to the symmetrical structure of the XY plane of the dormitory, even in strong outdoor wind conditions, the indoor airflow field can remain relatively stable. Secondly, the dormitory building influences the direction and velocity of outdoor airflow, resulting in an increase in air pressure around its windward side. This air pressure impedes the airflow to the room.

The time values corresponding to VOA = 70% are presented in

Table 4. T_VOA=70%, W (90°) wind direction.

Wind Speed	Outdoor Temperature
	−10 °C	0 °C	10 °C	20 °C
1.5 m/s	945 s	1087 s	1205 s	1418 s
3.3 m/s	862 s	1045 s	1113 s	1267 s
5.4 m/s	801 s	953 s	1074 s	1098 s
7.9 m/s	768 s	796 s	825 s	851 s

. There is a significant positive correlation between indoor ventilation efficiency and both wind speed and temperature difference. The analysis of wind force indicates that the increase in air pressure inside the dormitory will hinder the movement of indoor air particles toward the outside. However, under the influence of the temperature field, the interaction between cold and hot air in the room during natural ventilation will promote the air particles to be driven by thermal pressure. Therefore, even though indoor air is obstructed by outdoor high-pressure zones during flow, it can still effectively interact with outdoor air. While ensuring indoor air quality, the rate of change in the time required for achieving optimal ventilation at different temperatures gradually decreases with the increase in wind speed. This suggests that the impact of thermal pressure on air inflow is gradually diminishing, while the driving effect of wind force on airflow will gradually play a dominant role in indoor air exchange.

The VOA curves for all cases in this wind direction are illustrated in Figure 9. When the outdoor wind speed remains constant, an increase in the air temperature difference between the indoor and outdoor environments leads to a positive shift of the growth area of the curve along the X-axis. However, when the outdoor wind speed exceeds 5.4 m/s, the influence of the temperature difference on the growth area curve becomes negligible. This indicates that wind speed plays a primary role in determining indoor ventilation efficiency when it reaches or surpasses 5.4 m/s. Additionally, with a constant temperature differential between indoor and outdoor environments, an increase in outdoor wind speed results in a higher slope of the linear segment of the curve. This suggests that indoor ventilation efficiency improves with higher wind speeds. Furthermore, as the wind speed reaches 7.9 m/s, there is a greater proportion of decline area in the curves. This indicates that while an increase in wind speed can decrease the time required for indoor pollutant removal, it can also have adverse impacts on overall decontamination due to the influence of indoor airflow.

3.2. Equations

This study on natural ventilation in dormitories incorporates wind speed and temperature as independent variables in the outdoor environment, with the T_VOA=70% as the dependent variable. The obtained conclusion of ventilation time under three different wind directions can be utilized to construct a respective three-dimensional surface equation. The X-axis represents the temperature value, the Y-axis represents the wind speed value, and the Z-axis represents the minimum time that ventilation should be maintained.

When the wind direction is S, the fitting plane formed by the data is similar to a Gaussian surface. Equation (19) can be derived by simplifying the surface equation. The final fitted surface obtained is shown in Figure 10a.

$$Z={a+e}^{b\times x\times y}+c\times x+d\times y+f\times x\times y$$

(19)

The value of ‘a’ is 1428.88 ± 23.20, ‘b’ is 1476.82 ± 1.49, ‘c’ is 18.62 ± 1.89, ‘d’ is −76.11 ± 4.54 and ‘f’ is −0.91 ± 0.37. The R² of the fitted surface is 0.98.

When the wind direction is SW, there is a small difference in the temperature axis, while the difference in the wind speed axis follows an exponential relationship. Therefore, sampling using the fitting surface method should follow the exponential distribution. The corresponding fitting surface can be seen in Figure 10b.

$$Z=a+b\times e^{-x/c}\times e^{-y/d}$$

(20)

The value of ‘a’ is −211.59 ± 357.93, ‘b’ is 1289.77 ± 306.62, ‘c’ is −291.11 ± 182.41, and ‘d’ is 7.71 ± 3.77. The R² of the fitted surface is 0.95.

When the wind direction is W, the data distribution method is more appropriate for fitting the rational 2D equation. The surface of data fitting can be observed in Figure 10c.

$$Z=\frac{a+a_1\times x+b_1\times y+b_2\times y^2+b_3\times y^3}{1+a_2\times x+a_3\times x^2+{+a_4\times y^3+b}_4\times y+b_5\times y^2}$$

(21)

The fitting results indicate that ‘a’ is 1221.966 ± 79.48, ‘a₁’ is −16.21 ± 8.85, ‘b₁’ is −223.50 ± 215.03, ‘b₂’ is 43.95 ± 46.88, and ‘b₃’ is −2.30 ± 2.14; the value of ‘a₂’ and ‘a₃’ less than 1 × 10⁻⁴ can be omitted; ‘b₄’ is −0.10 ± 0.14 and ‘b₅’ is 0.02 ± 0.02. The R² of the fitted surface is 0.97.

By employing 3D surface equations, the assessment of indoor ventilation efficiency can be conducted across diverse ambient conditions, enabling accurate prediction of the minimum duration necessary for achieving optimal indoor air exchange.

The VOA curve represents the process of reducing the volume of areas with indoor air pollution, while indoor carbon dioxide concentration, serving as an indicator of air quality, often reflects the overall level of indoor air pollution. Although these two methods of evaluating indoor air quality have different emphases, based on the definition of air age, it can be inferred that the removal rate of indoor carbon dioxide should be approximately equal to the numerical values of VOA. According to the actual situation, the growth rate of indoor pollutants is related to the number of students in the dormitory and the movement behavior of students in the dormitory. Therefore, it is imperative to adjust the function in the conclusion when utilizing carbon dioxide concentration as a metric for assessing indoor air pollution.

$$f\left(t\right)=\frac{Z\times (C_{initial}+n\times {\int }_0^t\frac{0.02\times 1.964\times {10}^6}{V_{dorm}\times 3600}dt\times \eta )}{C_{initial}}$$

(22)

Among them, ‘$C_{initial}$’ represents the initial indoor carbon dioxide concentration. ‘$n$’ represents the number of personnel in the dormitory. ‘$\eta$’ denotes the correction coefficient for the respiratory intensity of personnel (generally assumed to be $\eta$ = 1); 0.02 refers to the average hourly exhalation rate of carbon dioxide per individual during steady breathing (m³); 1.964 is the mass of one cubic meter of carbon dioxide (kg). ‘$t$’ represents the duration of time for indoor carbon dioxide concentration to reach stability. The calculated result ‘$f\left(t\right)$’ of the equation indicates the minimum duration required for ensuring adequate indoor ventilation. This equation takes into account the real-time generation of carbon dioxide and ensures that the conclusion is more applicable to real-life scenarios.

4. Tests and Discussion

Based on the formula obtained from the conclusion, we conducted an applicability experiment to validate our research findings. The experimental scenario is shown in Figure 11.

During the experiment, the outdoor carbon dioxide concentration in the area was approximately 370 ppm and particle pollutant concentration was <3 μg/m³. The indoor space has a volume of approximately 85 m³.

Table 5. Experimental condition.

Wind Direction	Outside Air Temperature	Wind Speed	Data Graph	The Value of ‘t’ (Equation (22))	The Ratio of Carbon Dioxide Concentration Change
S	6 °C	2.2 m/s	Figure 12a	30 min	72.0%
S	10 °C	1.7 m/s	Figure 12b	35 min	79.9%
SW	14 °C	3.8 m/s	Figure 12c	15 min	77.1%
SW	8 °C	1.7 m/s	Figure 12d	19 min	81.1%
W	4 °C	1.9 m/s	Figure 12e	25 min	71.1%
W	12 °C	1.8 m/s	Figure 12f	31 min	74.8%

shows the prerequisite conditions for the outdoor environment and the experimental results.

In theory, the average indoor carbon dioxide concentration should reach the value ($C_{ppm}\times 70\%$). Where $C_{initial}$ represents the concentration of carbon dioxide in the room before ventilation. $C_{steady}$ represents the value at which the carbon dioxide concentration stabilizes after indoor ventilation.

$$C_{ppm}=C_{initial}-C_{steady}$$

(23)

However, discrepancies exist between experimental results and theoretical predictions. The underlying causes of these differences are as follows. Firstly, the intermittency of the wind may lead to variations in the indoor and outdoor airflow fields. While in this study, simulated wind speeds are considered constant, in reality, wind speeds often fluctuate. Combining with the findings of Mott et al. [48] on the impact of intermittent winds on natural ventilation in rooms, we identify wind speed fluctuations as a major factor causing differences between calculations and actual observations. Secondly, the amount of carbon dioxide exhaled by the human body depends on metabolism, and individual differences may result in variations in carbon dioxide emission rates [49]. Since the carbon dioxide generation rate used in the study is an average value, it may contribute to differences between calculated and measured results.

We monitored the concentration of inhalable particulate matter indoors and observed a fluctuating downward trend in the concentration of indoor particulate pollutants in groups (a), (b), (d), and (f), while the concentration of particulate pollutants in the other three groups remained relatively constant. The concentration of indoor particulate matter is influenced by the deposition of indoor dust and the level of students’ indoor activities. The reduction in inhalable particulate matter concentration can serve as evidence for the efficacy of natural ventilation in enhancing indoor air quality. The variables involved in this experiment are relatively complex, resulting in significant errors in some of the data obtained from the experimental conclusions. Although there were discrepancies between the experimental and simulation results, it is noteworthy that group (d) exhibited the highest deviation of 11.1%, while the absolute error between the conclusions of other experimental groups and theoretical calculations was less than 10%. The overall trend of the experimental results is consistent with relevant conclusions drawn in our current work. Therefore, the conclusions drawn from this study can be considered reliable.

This study presents a systematic analysis of indoor natural ventilation of the room in “line” type dormitory buildings under varying environmental conditions, utilizing the CFD method. This work improves the way Liu [39] and Yang [40] use air age as an indicator to analyze indoor environmental quality and utilizes the widely adopted Rosin-Rammler distribution method in data statistics to fit the proportion curve of indoor air age more conveniently. Moreover, this study facilitates a comparative analysis of indoor air quality under diverse environmental conditions by utilizing the VOA curve proposed in this article.

Currently, airborne diseases continue to pose a significant threat to public health safety [50]. In densely populated areas such as university dormitories, proper ventilation is crucial for maintaining safe indoor pollutant levels. Therefore, this study formulated pollutant removal rate equations for three wind directions, which were subsequently adjusted based on real-world conditions. Consequently, these equations are beneficial for providing recommendations to students when formulating ventilation strategies.

Despite this study combining the analysis of wind environment and building shape to assess the ventilation of dormitories in Northeastern universities and proposing a corresponding relationship equation for “T_VOA=70%—outdoor temperature—wind speed”, the research only used four-student rooms as models, excluding the more common six-student rooms in the region. Therefore, whether the conclusions of this study can be applied to the ventilation of six-student dormitories awaits further experimental investigation. Additionally, both the experimental and simulated aspects of this work assumed that windows in nearby rooms of the studied room were closed. The impact of nearby rooms opening windows on the generated airflow field is not clearly defined. Furthermore, as mentioned earlier, environmental wind speed conforms to the power-law equation, meaning that wind speed is positively correlated with environmental height. This paper primarily investigates the natural ventilation of rooms located in the middle of dormitory buildings under various environmental conditions. The relationship between the ventilation efficiency of the room and the height of the room is a topic worthy of future research.

5. Conclusions

This study focuses on dormitories in the Northeast region and conducts a multifactor analysis of variables such as air temperature, wind speed, and wind direction to explore the efficiency of natural ventilation in dormitories. Additionally, functions describing the change in indoor air quality over time are established for different ventilation scenarios. Simulation results reveal that, although wind speed and indoor-outdoor temperature difference are crucial factors in improving indoor ventilation efficiency, wind direction significantly influences the degree to which these factors promote indoor ventilation. Specifically, under a wind direction of 45°, the T_VOA=70% for dormitories at different outdoor temperatures stabilizes around 380 s at a wind speed of 5.4 m/s. However, at a wind direction of 0°, even with a wind speed of 7.9 m/s, there is still a noticeable difference in T_VOA=70% between rooms at −10 °C and 20 °C, with a difference of 339 s. Therefore, there is a substantial difference in the relationship between outdoor wind speed, temperature, and T_VOA=70% under different wind directions. When the wind direction is 0°, the relationship exhibits characteristics of a Gaussian function (Equation (19)). In this case, both wind speed and air temperature difference are considered the main factors promoting indoor ventilation when the wind speed is below 7.9 m/s. When the wind direction forms a 45° angle with the windows, the relationship between wind speed and T_VOA=70% follows an exponential pattern (Equation (20)), with the impact of indoor-outdoor temperature difference on natural ventilation being relatively small. For a wind direction angle of 90°, wind-induced airflow causes an increase in air pressure on the windward side of the dormitory building, hindering ventilation to some extent. Therefore, the fitting method for the function is the rational 2D (Equation (21)). Moreover, to ensure the practicality of the conclusions, physical quantities were incorporated into the numerical equation, constructing the equation f(t) (Equation (22)), and validation was performed by monitoring the carbon dioxide concentration in dormitories. The research findings assist students in scientifically formulating ventilation plans and provide valuable insights into the relationship between local architectural design and prevailing winds.