Influence of Cooking Pollutant Diffusion Regularity by High-Rise Residential Inner-Courtyard Forms in Wuhan

Abstract

In China’s typical high-density cities, in order to meet the residential needs, a Chinese characteristic and typical high-rise residence with multiple flats sharing one staircase has been created. Due to the Chinese cooking methods, such as frying and stir-frying, the middle flats’ kitchens of these high-rise residences are easily exposed to cooking pollutants, which endanger people’s health. As the outdoor transition space directly adjacent to the kitchens of the middle flats, the inner-courtyards in high-rise residences make the cooking pollutants easier to be diffused. Therefore, the inner-courtyard form has a significant impact on the ventilation and diffusion of cooking pollutants. In this study, with the method of measurement and CFD simulation, the relationship between cooking pollutants diffusion in the kitchens of the middle flats and the flow field in inner-courtyards was analyzed, and the impact of different inner-courtyard forms on cooking pollutants diffusion distribution in high-rise residential under natural ventilation was discussed. The results show that different inner-courtyard forms have different effects on the diffusion of cooking pollutants: the enclosed courtyards will greatly increase the cross-contamination between the kitchen and the adjacent space; increasing the openness of the courtyard will not enhance the diffusion level of pollutants, but has a negative effect; compared with centralized courtyards, symmetrical courtyards have a better echo with the kitchen in the layout, which is more conducive to the diffusion of cooking pollutants.

1. Introduction

For residential buildings, it is commonly agreed that the kitchen fume is the main source of indoor air pollution, affecting people’s health after long-term inhalation [1,2]. Reducing kitchen cooking pollutants is an important way to achieve a healthy indoor air environment [3]. Cooking pollutants contain large amounts of fine particulate matter and toxic and harmful gaseous substances [4,5,6]. Data from studies in developing countries show that unventilated indoor cooking causes millions of deaths per year, mainly among women and children [7]. Due to the Chinese cooking methods, such as frying and stir-frying, they are prone to cause high concentrations of fumes, strong exposure to pollution and long residence times in the kitchen [4]. Although most households have installed smoke extraction facilities, such as range hoods in their kitchens, the fumes cannot be completely expelled and can still cause harm to people [6]. It has been showed that the removal efficiency of range hoods under the infiltration ventilation mode is 45.3%, while with the assistance of natural ventilation modes, the removal efficiency can rise to 55.6% [8]. Therefore, it is of great significance to study the diffusion and optimization of kitchen cooking pollutants driven by natural ventilation for improving the indoor air environment.

Many studies have been taken to address the impact of design factors on the optimization of kitchen cooking pollutants. Wang et al. [9] studied the effect of different sill heights on the diffusion of cooking pollutants in kitchens. Zhang et al. [8] conducted a study on the diffusion characteristics of kitchen fume under different opening and closing states of kitchen doors and windows. Cao et al. [10] clarified the effect of the capture efficiency of range hoods on smoke emission. In addition, other scholars have also studied the influence of kitchen layout on the diffusion of cooking pollutants from the perspective of architectural design [11]. For example, Ling et al. [12] established a typical kitchen model for residential buildings in China, explored the effects of the spatial proportions of the kitchens, the layout of doors, windows and cookers on the diffusion distribution of cooking pollutants with the use of ANSYS Fluent CFD Software and proposed optimization strategies for space design of kitchens. These studies taking the kitchen as a single space revealed the influence of kitchen design factors on the diffusion of cooking pollutants and proposed the optimization method. The kitchen is not an individual space that exists independently. Although these internal influencing factors have been well-addressed previously, the synergistic impacts from adjacent spaces (such as the inner-courtyard) related to the diffusion of kitchen cooking pollutants are still unknown.

Among high-density cities in China, a special high-rise residential layout system has gradually developed [13]. The inner-courtyard (non-enclosed space, with three walls and one side connected by a corridor) gradually appears in high-rise residences with multiple flats sharing one staircase, becoming a typical layout type in high-density cities in southern China, as shown in Figure 1a. The inner-courtyard (Figure 1b) of high-rise residences addresses the problems of direct ventilation of the middle flats’ kitchen, making it easier for cooking pollutants to be diffused [14] (Figure 1c). Studies about the inner-courtyard have also been carried out. Shi et al. [15] regarded four flats with inner-courtyards as research variables to explore the effect of inner-courtyard on the ventilation environment of the middle flats in different flats of high-rise residences. It was also shown that there is an optimal range of influence of inner-courtyard forms on the indoor air environment in high-rise residences. Hu et al. [14] used different design variables of inner-courtyards as research variables and reported that the indoor air environment can be optimal when the inner-courtyard is arranged as scattered as possible under the action of horizontal airflow and the depth of the inner-courtyard is about 4 m. The above studies show the influence of inner-courtyard forms on the indoor air environment of middle flats and reveal the conclusion that there is an optimal depth range of inner-courtyard in specific climatic regions. No common design specification standards about the inner-courtyard have been developed in China so far. Due to the complexity of the inner-courtyard forms, there are many factors that affect its ability to improve the diffusion of kitchen fume in kitchens of the middle flats, such as the different sizes of the inner-courtyard forms, the different opening forms of the inner-courtyard, etc. The diffusion level of cooking pollutants in kitchens also varies from designs.

Therefore, this study aims to address the impacts of the inner-courtyard form on the diffusion of kitchen cooking pollutants in high-rise residences. This study adopts the research ideas and methods of the HVAC discipline on kitchen cooking pollutants to analyze the correlation between cooking pollutant diffusion in kitchens of middle flats and the transition flow field in the inner-courtyard. Based on CFD simulation, this paper studied the influence and characteristics of different inner-courtyard forms on the distribution of cooking pollutant diffusion in high-rise residences under natural ventilation and then, proposed the optimized design method of inner-courtyard forms for high-rise residences to enhance kitchen cooking pollutant diffusion.

2. Methodology

In this study, models and methods for the diffusion of kitchen cooking pollutants based on CFD indoor and outdoor coupled simulations were established and validated based on site measurement in Wuhan, which can be considered representative of the climatic conditions of central China [16,17]. The site measurement revealed the pollution status of the middle flat kitchens and provided verification data for CFD simulation. In order to find out the associated impact between kitchen cooking pollutants diffusion and inner-courtyard form variables, high-rise residential buildings’ layouts were investigated in Wuhan, a typical high-density city in China. Different inner-courtyard forms were identified and then simplified into variable models. The above-verified CFD numerical simulation method was adopted in this study; a variables analysis was conducted to evaluate the simulation results of wind and particle concentration distribution in kitchens in order to explore the influence of different inner-courtyard forms on the distribution of cooking pollutants in kitchens of high-rise residential buildings (Figure 2).

2.1. Measurement Description

As shown in Figure 3a, a high-rise residential kitchen of middle flats in Wuhan was selected as the object of measurement with the inner-courtyard of 4.45 × 3.00 m and the corridor of 4.00 × 1.50 m. The kitchen of this flat, L-shaped layout is near the entrance with the space size of 3.00 × 1.80 × 2.80 m, the window size 1.20 × 1.50 m and the door size 0.90 × 2.10 m. A stove top is on the north side of the short side. The range hood is a top-suction type with high-speed gear and low-speed gear, and the size of the air inlet is 0.50 × 0.33 m. Through the average air velocity test at point 4′, the average air velocity of the range hood is 0.75 m/s in low-speed gear with doors and windows closed, and the actual operating air exhaust volume is 445.5 m³/h.

The measurement time is 20 July 2021; the dominant wind direction is SE. The measurement is divided into two groups of simultaneous fixed-point sampling. (1) Outdoor monitoring points: a measurement point is set for background air velocity and wind direction on the roof (Figure 3b). Continuous monitoring from 9:30 to 15:30 in summer is needed in order to obtain the outdoor environment air velocity and wind direction. Point P, located at the connecting corridor of the inner-courtyard, measures inlet flow velocity of outdoor inner-courtyard and particulate concentration level at the connecting corridor; (2) Indoor monitoring points: points 1~5 are arranged (Figure 3c,d) to monitor the changes in air velocity and PM2.5 concentration in the kitchen; point 6 is arranged in the living room to monitor the background concentration with the aim of obtaining a baseline value of PM2.5 concentration in the environment before measurement. Before the start of the measurement, all instruments were adjusted for uniform parameter configuration, range calibration, measurement interval, etc. The instruments used in the measurement are shown in

Table 1. Test apparatus and parameters.

Measured Parameter	Test Apparatus	Type	Range	Precision
Air velocity and wind direction in the environment	Environmental monitor	PC-8 Series Sensor	0~70 m/s 0~360°	±0.5 m/s ±3°
Indoor air velocity	Hot-line anemometer	SENTRY ST-730	0~20 m/s	0.01 m/s
PM2.5 concentration	BOHU portable air quality recorder [18]	B1, BOHU CO	0~1999 μg/m3	±1 μg/m3

.

In order to study the effect of the change in the wind field in the inner-courtyard on the distribution of cooking pollutants diffusion in the kitchen, 4 cases (

Table 2. Measurement condition settings.

Case	Cooking Method	Range Hood	Doors	Windows	Measurement Time
Case 1	Frying an egg	Low speed	Open	Open	12:00–12:05, October 24th
Case 2	Frying an egg	Low speed	Open	Closed	12:10–12:15, October 24th
Case 3	Frying an egg	Low speed	Closed	Open	12:20–12:25, October 24th
Case 4	Frying an egg	Low speed	Closed	Closed	12:30–12:35, October 24th

) with different opening and closing methods of kitchen doors and windows were set up to measure the air velocity and PM2.5 concentration around the breathing zone at 1.5 m height [19]. Among them, the kitchen and inner-courtyard can form a ventilation convection in case 1 (doors: open, windows: open); in case 3 (doors: closed, windows: open), the kitchen and inner-courtyard can only form a unilateral ventilation. As control groups, case 2 and case 4 have no connection with the ventilation of inner-courtyard due to the closed windows. To ensure that a relatively single and stable source of PM2.5 emission can be obtained for each measurement case, nearly 50 g of eggs and 6 g of cooking oil were selected during the cooking in this study; the instruments, cooking ingredients and cooking time were also kept the same; the range hoods were run in low-speed gear [20,21,22]. The interval time between the anemometer and the PM2.5 monitor at each point was set to 10 s, and each cooking lasted 5 min, i.e., 300 s, for a total of 30 times of measurement data [23,24].

2.2. CFD Modeling and Simulation

2.2.1. Build Physical Models

ANSYS Fluent CFD Software was adopted to simulate the diffusion of cooking pollutants in the kitchen; this study set up an 18-story building model with the floors set to 18, the floor height set to 3.00 m and the windows in flats fully open by default. Considering the variability of airflow at different heights and avoiding the complex influence of open airflow on the diffusion of cooking pollutants at the top floor, 3, 9 and 17 floors (Figure 4a) were chosen to cover the different trends of airflow and the diffusion of cooking pollutants at different heights as a whole. In order to make the simulation results closer to the reality, the outdoor and indoor wind environments were jointly simulated in the same model, and a model of 3 × 3 residences was established considering the influence of the surrounding buildings of the residential area on the simulation object (Figure 4b).

In order to compare and verify the simulation and measurement results, the dimension and layout of the kitchen model are the same as the measured environment, and the simplified human model is 0.40 m × 0.10 m × 1.65 m (Figure 4c). The stove is set to the left of the window, the height of the stove top is 0.90 m and the stove form is set as a square, which is the source of PM2.5 emission in this simulation. Since the background of this study is natural ventilation, the range hood, as an auxiliary tool of mechanical ventilation, is not the focus of the simulation in this study, so the range hood form is simplified and its auxiliary role of exhausting air is retained.

2.2.2. Model Meshing

ICEM is used to mesh grid of computational fluid domain and building geometry model: through the Boolean operation, the intersection of the building physical model established in Rhino, and the computational domain is carried out to form a continuous multiple surface, which is then exported into 3dm format, then imported into ICEM for grid meshing. Due to the complex contour of the building and the huge volume of the model, to speed up the computational efficiency, unstructured tetrahedral mesh is used for division (Figure 5). For important parts, such as the kitchen stove and the inlet and outlet boundary, the mesh quality is locally encrypted to improve the calculation accuracy.

After grid independence test, in this case, the total number of calculation grids 3,913,607 is adopted, in which the number of stove surface mesh is 124, the range hood mesh is 433 and the kitchen internal wall mesh is 53,262.

2.2.3. Boundary Condition Setting

After the physical model is determined and meshing performed, it is imported into Fluent software to set up the turbulence model and the boundary conditions. The kitchen fume airflow and smoke exhaust from range hoods both belong to continuous phase turbulence. In view of the presence of air thermal buoyant flow and heat source, which has a significant impact on the movement of particles, the revised RNG K-ε turbulence model, including buoyancy effect and standard wall function, is more suitable for solving kitchen flow field than other models [25]. Therefore, RNG K-ε turbulence model was selected to simulate the diffusion of cooking pollutants.

The boundary condition parameters of the outdoor calculation domain include the atmospheric air velocity, wind direction and wind pressure of the outdoor calculation domain, top and side boundaries, the roughness of the wall and ground [26], etc. The boundary conditions of the outdoor simulation domain are shown in

Table 3. Summary of boundary conditions and parameter settings for outdoor calculation domain.

Boundary Name	Boundary Condition	DPM Boundary	Setting Content
INLET	Velocity-inlet	Escape	(1) Velocity-inlet: $\mathrm{V}={\mathrm{V}}_0{(\frac{\mathrm{Z}}{{\mathrm{Z}}_0})}^{\mathsf{\alpha }}$, ${\mathrm{Z}}_0=$ 10 m, ${\mathrm{V}}_0$ = 2.02 m/s (summer), $\mathsf{\alpha }$ = 0.22; (2) Turbulent kinetic energy and turbulent dissipation rate: $\mathrm{K}=1.5{\left(\frac{\mathrm{I}}{{\mathrm{V}}_0}\right)}^2$, $\mathsf{\epsilon }=\frac{{\mathrm{C}}_{\mathsf{\mu }}{\mathrm{K}}^{\frac{3}{2}}}{\mathrm{I}}$, $\mathrm{I}=4{\left({\mathrm{C}}_{\mathsf{\mu }}\mathrm{K}\right)}^{\frac{1}{2}}{\mathrm{Z}}_0{\mathrm{Z}}^{\frac{3}{4}}{\mathrm{V}}_0$, $\mathrm{K}$ is Turbulent kinetic energy, $\mathsf{\epsilon }$ is turbulent dissipation rate.
OUTLET	Pressure-outlet	Escape	Pressure-outlet
GROUND	No-Slip	Reflect	No-Slip
WALL-SIDE	Symmetry	—	Symmetry
WALL-UP	Symmetry	—	Symmetry
WALL-INNER	No-Slip	Reflect	No-Slip

.

The entrance boundary is defined as Velocity-Inlet. According to the climate data of Wuhan, the dominant wind direction in summer is SE and the average air velocity (${\mathrm{V}}_0$) is 2.02 m/s (data source: Building Energy Efficiency Meteorological Parameters Standard- JGJ/T346-2014). The cooking pollutants can escape to the inner-courtyard under the condition that all kitchen doors and windows are open and the connection with the inner-courtyard can be closer, so the summer meteorological condition is selected.

Due to the unstable atmospheric state by the ground, building friction and terrain roughness, air velocity shows curve changes. Different air velocity at different heights forms gradient winds, and the gradient wind formula is introduced at the inflow surface:

$$\frac{\mathrm{V}}{{\mathrm{V}}_0}={\left(\frac{\mathrm{Z}}{{\mathrm{Z}}_0}\right)}^{\mathsf{\alpha }}$$

(1)

where V is the air velocity at height $\mathrm{Z}$, m/s; V₀ is the air velocity at the reference height ${\mathrm{Z}}_0$ (height ${\mathrm{Z}}_0$ is set to 10 m); α is the ground roughness index; the urban environment in this study is a large urban area with dense buildings, which belongs to ground type C. $\mathsf{\alpha }$ is taken as 0.22.

The boundary conditions of the kitchen space calculation domain include the emission source, import and export and wall surface, for which the following settings are made (

Table 4. Boundary condition settings of kitchen.

Boundary Name	Boundary Condition	DPM Boundary	Temperature (K)	Setting Value
Stove top	Velocity-inlet	Wall-jet	423.15 K	0.60 m/s
Exhaust vent of cook hook	Exhaust	Escape	313.15 K	−150 Pascal
Doors and windows	Interior	—	293.15 K	—
Wall and ground/operating tables/human model, etc.	Wall	Reflect	288.15 K	—

).

• Emission source: the kitchen stove surface is defined as the source of PM2.5 emission and heat source for the velocity-inlet boundary, and the velocity is set to 0.6 m/s [25]. The average temperature of the stove is taken as 150 °C for calculation in combination with relevant studies.
• Import and export: the doors and windows are all fully open, and the airflow flows into the room from outdoors through the doors and windows.
• Exhaust vent: use low-speed gear to exhaust, set exhaust negative pressure to 150 Pa [27].
• Wall surface: indoor and outdoor walls, operating tables, ground, etc., are adiabatic boundaries set as constant temperature wall boundaries.

2.2.4. Boundary Condition Setting

Because the PM2.5 in the kitchen environment is relatively concentrated and sparsely diffused, the solid phase solution method based on the Lagrangian method is more suitable for the study of the trajectory motion distribution of indoor particulate matter, so the Lagrangian method is chosen for the simulation of PM2.5 in the kitchen, and the Discrete Phase Model (DPM) is used for the physical model. The PM2.5 emission source (Injection) is the stove top, so it can be simplified as a surface source, which the emission direction is normal to boundary, i.e., the z-axis direction. PM2.5 contains mostly particles less than 2.5 × 10⁻⁶ m, where particles with the diameter of 2.5 × 10⁻⁶ m contribute 75% of the indoor particulate matter concentration [28]. Therefore, the diameter of PM2.5 is set to 2.5 × 10⁻⁶ m. In order to actually reflect the diffusion of cooking pollutants when frying eggs in the measurement, the PM2.5 emission volume is set to 3 × 10⁻⁸ kg/s and the density is set to 950 kg/m³ for the simulation [27,29,30].

2.2.5. Model Validation and Correction

To validate the simulation results on this study, a comparative analysis is performed by combining the measured data of case 1 in Section 2.2. In order to obtain more accurate simulation results, CFD simulation method is modified by numerical and parametric models to obtain better fitting results. The experimentally measured particulates concentration (C_test) may still deviate from the simulation results of C_CFD with a fixed emitted amount. Therefore, the relative magnitude of the air velocity V and the dimensionless concentration f (taking the emission source measuring point 4 as the base value) was set as the index for comparing the measured and simulated results in order to reduce the influence of the fixed emission setting on the simulation results. The measured values and simulation results of each measurement point are detailed in

Table 5. Measured values and simulation results of each measurement point.

Indicators		Point P	Point 1	Point 2	Point 3	Point 4	Point 5
Air velocity (m/s)	Vtest	0.75	1.26	1.63	1.45	1.25	0.35
	VCFD	0.58	1.55	1.82	1.54	1.52	0.42
PM2.5 Concentration (μg/m3)	Ctest	11.0	35.1	81.8	128.3	308.7	145.5
	ftest	0.036	0.114	0.265	0.416	1	0.471
	CCFD	6.86	24.4	57.2	87.9	254.0	98.3
	fCFD	0.027	0.096	0.225	0.346	1	0.387

.

$$\mathrm{f}=\frac{{\mathrm{C}}_{\mathrm{tpn}}}{{\mathrm{C}}_{\mathrm{tp}4}}$$

(2)

where C_tpn is the concentration value of PM2.5 at point n; C_tp4 is the base value concentration at point 4 of the release source, μg/m³.

Compared with the simulated results of V_CFD and f_CFD and the experimental data of V_test and f_test (Figure 6), it was found that the simulated results were generally consistent with the experimental data, and the errors at each point were within the range of 10–25%. In addition, the peak of the change curve is the same.

Comparing with the measured air velocity and PM2.5 concentration trend in the kitchen, the simulation results reveal that: on the one hand, the influence of the airflow organization in the inner-courtyard on the diffusion of cooking pollutants is recognized; on the other hand, the numerical simulation shows good conformity with the measurement. To sum up, the CFD simulation method based on indoor–outdoor coupling is validated in this study.

2.3. Inner-Courtyard Form Model

The inner-courtyard form of high-rise residences is an important design variable that reflects the difference in the diffusion of cooking pollutants. In order to enable the variables actually reflect the current situation of existing inner-courtyard flats in Wuhan, a typical high-density city in China, this study identified 5 typical layouts of high-rise residences with inner-courtyards in a survey of 35 high-rise residential communities in Wuhan through field research (

Table 6. Integration of the results of the study of high-rise residences with inner-courtyards.

Case	Actual Flat Plan	Simplified Flat Plan
A-1(Control group)
A-2
A-3
A-4
A-5

The blue area indicates the inner-courtyard, the red area indicates the kitchen of middle flats and the black area indicates the side flats.

). The flats of high-rise residences were reasonably extracted and simplified in order to focus study and improve simulation efficiency, and the total inner-courtyard width was kept consistent. The variables of the inner-courtyard forms were simplified and modeled based on architectural morphology (Table 6). The simplification principles are as follows.

• Protruding parts of the building unrelated to the research object were simplified to the most basic form on the basis of not affecting the simulation results.
• For rooms not related to the kitchen, such as bedrooms, living rooms and bathrooms, their internal walls, windows and other layout structures were ignored and they were simplified into the entity spaces to reduce the influence of other factors on the research object.
• The kitchen size and form were kept the same. The north corridors were uniformly set to 1.5 m wide and the length depended on the type of flats. The area of the traffic space and the side household were set at the same size.
• In order to ensure the natural flow of wind field in the kitchen and the household during the simulation, ventilation windows were set on the south wall as the outlet of pressure flow, and only the kitchen windows were set on the north side. The doors and windows were all fully open by default to realize the natural wind flow.
• The side flats were simplified as non-ventilated entity spaces to reduce interference.

These simplified inner-courtyard form settings are allowed for the control of three main variables: (1) inner-courtyard openness; (2) inner-courtyard blocking degree; (3) inner-courtyard layout, where A-1 is a flat with a closed inner-courtyard on the corridor side, which is used as a control group to recognize the effect of ventilation with and without inner-courtyards on the diffusion of cooking pollutants. The specific research design factor and corresponding cases of this study are shown in

Table 7. Research design factor and corresponding cases.

	Design Factor	Comparative Case
1	Inner-Courtyard Effectiveness	Case A-1	Case A-2
2	Inner-Courtyard Openness	Case A-2	Case A-3
3	Inner-Courtyard Blocking Degree	Case A-3	Case A-4
4	Inner-Courtyard Layout	Case A-3	Case A-5

.

3. Results and Discussion

3.1. Measurement Results

The PM2.5 concentration in the breathing zone of the kitchen personnel (i.e., point four) over time for the four measured cases is shown in Figure 7 (the effect of background concentration on the results has been removed from the calculation). The measurement results show that regardless of the airflow organization of the ventilation method, the PM2.5 concentration in the kitchen increases significantly after cooking activities, but there is a large difference between the magnitude of the increase and the instantaneous peak concentration. In Case One, the PM2.5 concentration increases more slowly and falls back more quickly with the lowest instantaneous peak value when the window is kept open in the kitchen. Case Four, as the control group of Case One, shows the worst and most unfavorable results because the closed kitchen environment prevents the diffusion and dilution of cooking pollutants. Compared with Case Two and Case Three, it is obvious that opening the external window of the kitchen makes indoor and outdoor air circulation, which is more conducive to the rapid reduction in PM2.5 concentration back down after cooking.

The above data show that, despite the state of range hoods on, the average concentration of PM2.5 in cooking pollutants during cooking is still greater than the daily average concentration limit standard in the above-mentioned standard, and the kitchen is in a serious pollution state for a long time. Specifically, the inner-courtyard can provide an airflow buffer space, which can greatly promote the natural ventilation of the kitchen and the external diffusion of cooking pollutants. However, further research is needed to strengthen and optimize the ventilation between the inner-courtyard form and the kitchen.

3.2. Simulation Results

The distribution of PM2.5 was observed by intercepting the cross-section when the diffusion of cooking pollutants reached a steady state. In this study, the horizontal cross-section around the breathing zone is at 1.5 m height, where the pollutant concentration has a greater impact on personnel and at which it is selected as the height of focus. The simulation results of air velocity and PM2.5 distribution under the dominant southeast wind in summer are shown in

Table 8. Air velocity simulation results for five inner-courtyard variables.

Case	3F	9F	17F
A-1
A-2
A-3
A-4
A-5

and

Table 9. Simulation results of PM2.5 distribution for five inner-courtyard variables.

Case	3F	9F	17F
A-1
A-2
A-3
A-4
A-5

, and the average air velocity and PM2.5 concentration magnitude in the kitchen at low and middle heights for different inner-courtyard forms are shown in Figure 8.

In order to specifically evaluate the internal airflow changes in the kitchen, this study uses the ratio of indoor air velocity to the initial outdoor air velocity to measure the level of indoor wind environment, e. l. The air velocity ratio R is the ratio of the absolute value of air velocity vs. at the measurement point to the absolute value of initial air velocity V0. At the same time, the air velocity around the breathing zone at 1.5 m height is located as the analysis standard, calculated as follows:

R = V_S/V₀

(3)

where V_S. denotes the air velocity at a measurement point in the kitchen, V₀ denotes the initial incoming air velocity and R denotes the air velocity ratio. Malaysian scholar Kubota T. [11] showed that when the air velocity ratio R < 0.5 in a certain area, the air velocity in the area is not conducive to airflow due to excessive losses; when the air velocity ratio R > 2.0, the air velocity increases too fast and will make pedestrians feel the air velocity is too high. In this study, the air velocity ratio is divided into five levels, and the larger the area of the air velocity ratio in the area of 0.5 ≤ R ≤ 2.0 is, the better the ventilation effect of the indoor environment will be.

In order to specifically evaluate the diffusion level of indoor kitchen fumes to the inner-courtyard, the K value was used to express the PM2.5 concentration. Referring to the Ambient Air Quality Standard (GB3095-2012) and the Ambient Air Quality Index (AQI) Technical Provisions HJ633-2012 grading and calculation standards: the PM2.5 concentration and IAQI level are divided into the following: air quality is excellent with 0 to 35 μg/m³ of PM2.5 concentration, air quality is good with 35 to 75 μg/m³ of PM2.5 concentration, air quality is in light pollution with 75 to 115 μg/m³ of PM2.5 concentration, air quality is in moderate pollution with 115 to 150 μg/m³ of PM2.5 concentration, air quality is in heavy pollution with 150 to 250 μg/m³ of PM2.5 concentration and air quality is in serious pollution with more than 250 μg/m³ of PM2.5 concentration. In this study, the particle concentration K > 75 μg/m³ is taken as the high concentration interval, and the higher the percentage of its area indicates, the more serious pollution of kitchen fumes and the weaker the external diffusion level will be; the higher the value in the concentration interval of 0 ≤ K < 75 μg/m³ is, the larger the percentage of low concentration particles in the kitchen and the better the air quality will be.

For the following four groups of Comparative Case, about 1000 data points were extracted for the left and right kitchens of 3F, 9F and 17F in Cases A-1 to A-5, and the average in the space was obtained. Each point was assigned to the corresponding R interval and K interval by calculating, and the average air velocity area ratio and PM2.5 concentration area ratio in the kitchen of middle flats were illustrated by column analysis chart.

3.2.1. Influence of Inner-Courtyard on Cooking Pollutants Diffusion

Compared to Case A-2, the control group Case A-1 is a closed inner-courtyard. Combined with the simulated cloud plots of A-2 and A-3 in Table 8 and Table 9, it can be seen that there is almost no airflow movement path in the closed inner-courtyard at the middle and low levels and the cooking pollutants accumulate in the kitchen and inner-courtyard. In the 17F, due to the influence of airflow from the top floor, it is obvious for the airflow movement path that the cooking pollutants in the kitchen are more likely to diffuse to the top.

Analysis of air velocity: Figure 9a shows that under the summer southeast wind, 0 ≤ R < 0.125 air velocity ratio in the kitchen reaches about 80.99%, and the 0.5 ≤ R < 2.0 high air velocity interval is 0%, which means that the kitchen interior is almost at the static wind level, while 0.5 ≤ R < 2.0 high air velocity ratio of Case A-2 reaches 16.05%. The 17F scenario was better ventilated due to the influence of airflow across the top floor and the airflow inside the inner-courtyard and kitchen affected by wind pressure changes. The air velocity in the kitchen of the control group A-1 with closed inner-courtyard is significantly lower than that of the non-closed Case A-2, which indicates that adding an inner-courtyard can significantly improve the indoor ventilation environment in the kitchen of high-rise residences with multiple flats sharing one staircase.

Analysis of particle concentration: Table 9 shows that with the closed inner-courtyard, cooking pollutants are formed inside the kitchen and the inner-courtyard to accumulate, and when the steady state is reached, the low and middle level cooking pollutants are uniformly distributed throughout the space, while the area contaminated with a high concentration of K ≥ 75 μg/m³ in the kitchen accounts for 15.70%; the diffusion trend of PM2.5 along the vertical direction of the inner-courtyard is enhanced in the 17F due to the change in cross-level airflow at the top, which there is a vertical diffusion advantage compared with the low and middle levels. The low concentration area (0 ≤ K < 35 μg/m³) of Case A-2 reaches 87.89%, which is 23.3% higher than that of Case A-1. The high concentration area (K ≥ 75 μg/m³) of Case A-2 decreases to 4.24%, and the high concentration area changes significantly for the open inner-courtyard (Figure 9b).

In summary, the average PM2.5 concentration of the control group A-1 enclosed inner-courtyard is significantly higher than that in the non-enclosed inner-courtyard, which is a greater hazard to the population, indicating the significant effect of increasing the non-enclosed inner-courtyard on cooking pollutants diffusion.

3.2.2. Influence of Inner-Courtyard Openness on Cooking Pollutants Diffusion

Compared to Case A-2, Case A-3 enlarges the opening size of the inner-courtyard. Combined with the simulated cloud plots of A-2 and A-3 in Table 8 and Table 9, it can be seen that they have a relatively consistent ventilation trajectory. However, the change in the size of the opening shifts the outflow path of PM2.5 in the inner-courtyard and creates a tendency of dispersion. The distribution level of PM2.5 concentration in the kitchen is reduced.

Analysis of air velocity: the change in airflow in the inner-courtyard did not significantly affect the average air velocity in the kitchen, and the average air velocity in Case A-3 was slightly lower than Case A-2 in the ground floor 3F and the middle floor 9F (Figure 8a). As shown in Figure 10a, Case A-2 and Case A-3 accounted for a larger percentage in the 0.125 ≤ R < 0.250 and 0.250 ≤ R < 0.375 air velocity ratio intervals with a small difference in size. In the 0.5 ≤ R < 2.0 air velocity ratio interval, Case A-2 accounted for 16.05% and Case A-3 was slightly lower at 13.13%. In summary, the average air velocity of Case A-3 with doubled inner-courtyard opening is slightly lower than Case A-2, indicating that increasing the size of the inner-courtyard opening has a negative effect on the average air velocity of the kitchen.

Analysis of particle concentration: the increase in the size of the inner-courtyard opening reduces the average PM2.5 concentration in the lower kitchen in Case A-3 by 32.7% compared to Case A-2 (Figure 8b). Combined with the analysis of PM2.5 concentration area between A-2 and A-3 house types in Figure 10b, it can be seen that: (i) after the increase in the inner-courtyard opening, the motion trajectory of PM2.5 in the inner-courtyard for external diffusion in Case A-3 is significantly weakened compared to Case A-2, especially in the middle and top floors, and the tendency of PM2.5 accumulation in the inner-courtyard is obvious. (ii) The low concentration area (0 ≤ K < 35 μg/m³) of Case A-2 (87.89%) is better than Case A-3 (79.62%); the high concentration area (K ≥ 75 μg/m³) is 4.24% for Case A-2 and 9.03% for Case A-3. With the increase in the inner-courtyard opening, the area of high concentration in the kitchen accounted for nearly double, and there were large differences in the distribution of concentrations in the left and right kitchens, a phenomenon related to the dominant wind direction of the city.

In summary, increasing the size of the inner-courtyard opening does not significantly improve the ability of cooking pollutants to diffuse to the outside, but makes it easier for pollutants to accumulate in the inner-courtyard and cause cross-contamination, and reinforces the difference in the distribution of fumes concentration between the left and right kitchens.

3.2.3. Influence of Inner-Courtyard Blocking Degree on Cooking Pollutants Diffusion

Compared to Case A-3, Case A-4 adds a traffic nucleus at the inner-courtyard opening, creating an obstruction to airflow. Combining A-3 and A-4 in Table 8 and Table 9, it can be seen that Case A-4 is obstructed by the middle traffic nucleus, and the airflow in the inner-courtyard forms a left–right bypass. The level of PM2.5 accumulation in the inner-courtyard is reduced compared to Case A-3.

Analysis of air velocity: the average air velocity did not change significantly after adding the traffic nucleus at the inner-courtyard opening (Figure 8a). As shown in Figure 11a, Case A-3 and Case A-4 accounted for a larger percentage in the 0.125 ≤ R < 0.250 and 0.250 ≤ R < 0.375 air velocity ratio intervals, accounting for more than 1/3 of the kitchen area. In the 0.5 ≤ R < 2.0 air velocity ratio interval, Case A-4 accounted for 16.63%, an increase of 26.7% compared to Case A-3. It indicates that the increase in the traffic nucleus at the inner-courtyard opening outflow, which cut the size of the outflow opening, has a certain positive effect on the airflow field of the kitchen.

Analysis of particle concentration: with the increase in the size of the inner-courtyard opening, the average particle concentration in the kitchen of the middle floor 9F of Case A-4 decreased by 26.6% compared to A-3, while the top floor 17F increased by 25.3% (Figure 8b). Combined with the analysis of the area ratio of PM2.5 concentration between Case A-3 and Case A-4 in Figure 11b, it can be seen that: (i) combined with the PM2.5 diffusion trajectory, the increased traffic nucleus part of Case A-4 did not have an obvious blocking effect on the PM2.5 diffusion path, and the PM2.5 diffused outward from the openings on both sides and accumulated to a lesser extent in the inner-courtyard than Case A-3. (ii) The low concentration area (0 ≤ K < 35 μg/m³) of Case A-4 is higher than Case A-3; the high concentration area (K ≥ 75 μg/m³) of Case A-4 (8.09%) is slightly lower than Case A-3 (9.03%), but the trend of enhancing the diffusion of grease is not obvious.

In summary, the additional traffic nucleus on the basis of the same inner-courtyard opening does not have a large impact on the level of diffusion of kitchen fume particles, but rather the movement of particles within the inner-courtyard for external diffusion is enhanced by reducing the size of the inner-courtyard opening to the outside.

3.2.4. Influence of Inner-Courtyard Layout on Cooking Pollutants Diffusion

Under the condition that the total width of inner-courtyard openings is the same, compared to Case A-3, Case A-5 is divided into two symmetrical inner-courtyards. Combining the simulated cloud diagrams of Case A-3 and Case A-5 in Table 8 and Table 9, it can be seen that in the southeast wind downward Case A-5 the wind field of the left and right two kitchens is more fully and uniformly distributed and it is not easy to have a dead corner of ventilation; the grease particles in the kitchen are mostly concentrated in the diagonal area of the stove.

Analysis of air velocity: by adjusting the centralized inner-courtyard to a symmetrical layout, the average air velocity in the kitchen of each floor of the high-rise residence was significantly increased (Figure 8a). Specifically, the high air velocity area (0.5 ≤ R < 2.0) of Case A-5 reaches 41.41%, which is more than 20% of the kitchen area; that of Case A-3 is only 13.13%, and the former is nearly three times the latter (Figure 12a), indicating that the kitchen wind environment in the inner-courtyard of this decentralized layout is better than that in the inner-courtyard of the centralized layout.

Analysis of particle concentration: the change in the layout of the inner-courtyard has a positive effect on the reduction in the average particle concentration in the kitchens of the middle and upper floors and a negative effect on the kitchens of the lower floors instead (Figure 8b). Combined with the analysis in Figure 12b, it can be seen that the low concentration area (0 ≤ K < 35 μg/m³) of Case A-5 (87.91%) is higher than Case A-3 (79.62%); the high concentration area (K ≥ 75 μg/m³) of Case A-5 (5.59%) is lower than CaseA-3 (9.03%). The distribution area of Case A-5 is concentrated, and the impact on the main activity area of humans is lower than that of Case A-3.

In summary, the symmetrical inner-courtyard, as a transfer space for the diffusion of grease particles, can be dispersed to better correspond with the two sides of the middle flats’ kitchen windows. Through the inner-courtyard, the indoor space can be better connected with the outdoors to form the airflow through the hall and the airflow circulation can be strengthened in the middle flats. Compared to other internal inner-courtyards, the symmetrical layout of the inner-courtyard form is the least harmful to the population. Based on the unique living environment and cooking methods in China, the study on the inner-courtyard form of high-rise residences in the field of architecture design is important for optimizing the level of ventilation and diffusion of cooking pollutants in the kitchen and can provide new ideas for the design of high-rise residences.

4. Conclusions

In China’s high-density cities, high-rise residences with multiple flats sharing one staircase are created to meet the population’s living needs. The combination of the inner-courtyards adjacent to the middle flats and kitchens composes the ventilation flow line for the outdoor diffusion of cooking particles, and the typical design of a building space plays an important role in promoting the natural ventilation of the middle flats.

By refining the commonalities and differences in inner-courtyards in high-rise residences with four flats sharing one staircase, corresponding building models are established and the effects of different inner-courtyard forms on the diffusion distribution of cooking particles in adjacent kitchens are compared by simulating several different inner-courtyard variables. The conclusions can be summarized as follows:

In the situation of southeast-facing ventilation, adding an open inner-courtyard can effectively improve the indoor ventilation of the middle flats and promote the diffusion of cooking pollutants; there are some differences in the air velocity between the kitchens of the left and right flats, but the change pattern is basically the same; closed inner-courtyard not only does not improve the indoor ventilation, but also reduces the indoor wind environment quality of the ground floor households.

In the case of southeast-facing ventilation, appropriately reducing the size of the inner-courtyard opening is conducive to strengthening the wind pressure difference, which makes the movement path of kitchen pollutants diffusing to the outside strengthen; a too large inner-courtyard opening tends to make particles easily accumulate in the inner-courtyard, which is easy to cause cross-contamination, and the difference in the distribution of PM2.5 concentration between the left and right kitchens is more obvious.

In the case of southeast-facing ventilation, for individual layout, on the basis of the same total width of the inner-courtyard opening, the additional traffic nucleus blocking does not have a large impact on the level of diffusion of kitchen grease particles; instead, the wind pressure difference increases due to the reduced size of the inner-courtyard opening to the outside, which makes the movement of particles in the inner-courtyard to the outside diffusion enhanced.

In the case of southeast-facing ventilation, the symmetrical and decentralized arrangement of the inner-courtyard can better correspond to the position of the kitchen windows of the middle house on both sides. Through the inner-courtyard, the indoor space can be better connected with the outdoor area to form a pass-through breeze and strengthen the airflow circulation in the middle flats, so the decentralized arrangement of the inner-courtyard is better than the centralized arrangement; in the future design of multi-family high-rise residential units, the design method of a decentralized arrangement of the inner-courtyard can be preferred to promote the diffusion of kitchen fumes.