Effects of Radiant Floor Heating Integrated with Natural Ventilation on Flow and Dispersion in a Newly Decorated Residence

To date, few studies have been conducted on the characteristics of flow and dispersion caused by indoor radiant floor heating integrated with natural ventilation. In this study, we employed reduced−scale numerical models validated by wind−tunnel experiments to investigate the influence of radiant floor heating integrated with natural ventilation on airflow, heat transfer, and pollutant dispersion within an isolated building. The Richardson number (Ri) was specified to characterize the interaction between the inflow inertia force and the buoyancy force caused by radiant floor heating. Several Ri cases from 0 to 26.65, coupled with cross− or single−sided ventilation, were considered. Model validation showed that the numerical model coupled with the RNG k-ε model was able to better predict the indoor buoyant flow and pollutant dispersion. The results showed that the similarity criterion of Ri equality should be first satisfied in order to study indoor mixed convection using the reduced−scale model, followed by Re−independence. For cross−ventilation, when Ri < 5.31, the incoming flow inertia force mainly dominates the indoor flow structure so that the ACH, indoor temperature, and pollutant distributions remain almost constant. When Ri > 5.31, the thermal buoyancy force becomes increasingly important, causing significant changes in indoor flow structures. However, for single−sided ventilation, when Ri > 5.31 and continues to increase, the buoyancy force mainly dominates the indoor flow structure, causing a significant increase in ACH, thus reducing the indoor average temperature and pollutant accumulation.


Introduction
In recent decades, economic conditions have continued to improve, and the demands for comfortable and healthy living environments have increased. However, with the increasing demand for building decorations, a large number of new decoration materials, chemicals for daily use, and household appliances have been introduced into residential and public buildings, causing a relative increase in the sources and types of indoor air pollutants, posing a great threat to indoor environmental quality [1].
The main sources of indoor air pollution include interior decoration materials, human metabolism, daily household waste, and outdoor air pollutants [2]. For a newly renovated house, the chemical, physical, biological, and radioactive pollutants emitted by decoration materials have the greatest impact on human health. Good ventilation is the main measure used to improve indoor air quality, especially natural ventilation, which is an economical, effective, and energy-saving green ventilation method [3,4]. of non-isothermal mixing ventilation in an enclosure with a heated floor were evaluated by Kosutova et al. [31]. Moreover, according to the locations of radiant surfaces and air distribution principles, integrated radiant heating/cooling systems that are typically used together with different ventilation modes were reviewed by Zhang et al. [32] to evaluate thermal comfort and indoor air quality for design recommendations. During the last two decades, the increasing use of radiant floor heating applications has gradually replaced the use of traditional radiators and air conditioners, and these have become the main modes of indoor heating for new residential buildings [33,34].
Usually, in a newly decorated and unoccupied residence, heating process can promote the release of toxic and harmful substances such as formaldehyde from building materials, and natural ventilation can effectively and quickly discharge these indoor pollutants. Even when the occupied residences are heated in winter, a fresh air system or reasonable window ventilation is needed to deliver fresh air indoors. Zhou et al. [35] conducted experimental and numerical studies to investigate the effects of ventilation and flow heating systems on the dispersion and deposition of fine particles in an enclosed environment. Their study could be helpful for the design of ventilation and heating systems to remove PM pollution from rooms. To the best knowledge of the authors, studies on the effects of radiant floor heating integrated with natural ventilation on flow and dispersion in a newly decorated room have not been reported to date. One objective of this study was to establish a coupled CFD numerical model for natural ventilation and radiant floor heating effects, validated by means of wind-tunnel experiments. Secondly, the numerical model was used to study the characteristics of flow and pollutant dispersion in a newly decorated room under the coupled effect of radiant floor heating and window ventilation. The results of this study may be helpful in promoting the rapid release and removal of pollutants from building materials in newly decorated rooms through ventilation and heating systems.

Physical Model
The physical model and its dimensions are shown in Figure 1, where the reduced scale ratio is 1:10. Two windows of the same size (W × W) were included on the windward and leeward walls of a cubic ventilated building (H × H × H). Two natural ventilation patterns were simulated, with cross−ventilation (both windows opening) and single−sided ventilation (window 1 opening, window 2 closed). Moreover, the indoor ground was heated at a constant temperature, T f , to mimic the radiant floor heating. T m represented the mean air temperature in the room, and T a represented the ambient temperature outside. New furniture (0.2 m × 0.2 m × 0.1 m, full scale) was placed in the indoor ground center, which released pollution gas in the form of VOCs at a constant rate under the heating conditions. To accurately reproduce the outdoor and indoor flow structures and the heat transfe and pollutant dispersion in the above−described physical model at a reduced scale, it wa necessary to follow some similarity criteria. First, the building-height Reynolds numbe (ReH) should be satisfied for the outdoor flow and dispersion around the building block [36], which can be specified as follows: number (Re H ) should be satisfied for the outdoor flow and dispersion around the building blocks [36], which can be specified as follows: Meanwhile, the window Reynolds number (Re w ) of the room can be defined to characterize the indoor flow structure and pollutant dispersion, defined by: In addition, to mimic the interaction of the buoyancy force caused by the radiation heating floor and the freestream inertial force from the natural ventilation, the Richardson number (Ri, the ratio of Grashof number (Gr) to the square of Re w ) is adopted and defined as follows: where U H is the freestream wind speed at the building height H (m/s); U w is the mean wind velocity through the open window (m/s); ν is the kinematic viscosity of air; a v is the thermal expansion coefficient; and g is the gravitational acceleration. In this study, seven Ri values (from 0 to 26.65) for reduced-scale physical models were investigated, as shown in Table 1, with U H changing from 0.1 to 6 m/s, and the relative parameters Re H , U w, Re w , and Gr are also listed. The governing equations used to describe the indoor airflow, heat transfer, and pollutant dispersion, considering the thermal effect from the radiation floor, are shown as follows, including the continuity equation in incompressible form, as well as the RANS (Reynolds-averaged Navier-Stokes) equation, the energy equation, and the species transport equation for passive advection-diffusion, where u i is the time-averaged velocity to be solved (m/s); u j is the air velocity vector (m/s); ρ is the air density (kg/m 3 ); p is the pressure (Pa); µ and µ t are the molecular viscosity and turbulent viscosity, respectively (Pa·s); T is the temperature (K); Pr is the Prandtl number; σ t is the turbulent Prandtl number (also written as Pr t = 0.85); S T is the heat source term (W/(m 3 ·s)); c i is the mass concentration of pollutants (kg/m 3 ); D i,m is the molecular diffusion coefficient for pollutants (m 2 /s); S c denotes the pollution source term (kg/(m 3 ·s)); and Sc t is the turbulent Schmidt number (=0.7) [37]. The discrete ordinates (DO) radiation model was employed to consider the radiation heat transfer between the heated radiant floor (aluminum) and the building's inner walls (wood). The DO model solves the radiative transfer equation (RTE) for a finite number of discrete solid angles, each associated with a vector direction → s which is fixed in the global Cartesian system (x, y, z). Herein, the air in the ventilated room model is treated as a non-participating medium due to its optical thickness being almost zero. The solid surfaces were assumed to be diffusive and gray, and the values of their internal emissivity were selected as follows: 0.9 and 0.89 for radiator and walls (wood), respectively [38].
The model validation, as described in Section 4.1, proved that the RNG k-ε model was able to better predict the characteristics of the indoor airflow, heat transfer, and pollutant diffusion. The RNG k-ε turbulence model includes the k (turbulent kinetic energy) and ε (the dissipation rate of k) equations proposed by Yakhot and Orszag [39]. Figure 2 shows the computational domain and boundary conditions. According to Tomanaga et al. [40], the independence of the computational domain was implemented, indicating that the appropriate computation domain was finally determined as Lx × Ly × Lz = 25H × 13H × 7H. Here, the inlet, top, right, and left planes were all 6H away from the corresponding building model surfaces. Furthermore, the outlet plane was 18H away from the leeward surface of the building model to ensure the occurrence of fully developed flow there. The computational domain was discretized using ANSYS ICEM 18.0 by means of structured grids with variable sizes: the finest grid resolution with a cell magnitude of 0.02-0.05H inside the indoor scale; a coarser resolution close to the building and ground surfaces with a magnitude of 0.05-0.1H; and a gradually coarse mesh from the building and ground surfaces to the domain boundaries, using an increasing ratio of 1.12-1. 16  Three grid resolution cases are shown in Figure 3a-c, where the coarse, fine, and fine grid numbers are 1.80 million, 5.80 million, and 8.80 million, respectively. Figure 3d ind cates that the total independent grid number was 5.8 million. Table 2 summarizes th boundary conditions for the numerical models. Three grid resolution cases are shown in Figure 3a-c, where the coarse, fine, and finer grid numbers are 1.80 million, 5.80 million, and 8.80 million, respectively. Figure 3d indicates that the total independent grid number was 5.8 million. Table 2 summarizes the boundary conditions for the numerical models.

Wind-Tunnel Experimental Setup
The wind-tunnel experiments for numerical validation were carried out in the Environmental Wind Tunnel Laboratory at University of Shanghai for Science and Technology (EWT Lab at USST), which is an open-circle atmospheric boundary layer wind tunnel with test section dimensions of 2.5 m in width, 1.8 m in height, and 25 m in length. The wind speeds on the inlet plane can be adjusted continuously from 0.1 to 20 m/s, and the scaled profiles of the atmospheric boundary layer (ABL) flow can be generated by means of six Irwin-type spires and roughness elements of different sizes, arranged regularly within the 15 m long development section (Figure 4). The building model, made of wood, with a reduced scale ratio of 1:10 was placed at the center of a circular turntable with a diameter of 2 m in the test section.

Wind-Tunnel Experimental Setup
The wind-tunnel experiments for numerical validation were carried out in the Environmental Wind Tunnel Laboratory at University of Shanghai for Science and Technology (EWT Lab at USST), which is an open-circle atmospheric boundary layer wind tunnel with test section dimensions of 2.5 m in width, 1.8 m in height, and 25 m in length. The wind speeds on the inlet plane can be adjusted continuously from 0.1 to 20 m/s, and the scaled profiles of the atmospheric boundary layer (ABL) flow can be generated by means of six Irwin-type spires and roughness elements of different sizes, arranged regularly within the 15 m long development section (Figure 4). The building model, made of wood, with a reduced scale ratio of 1:10 was placed at the center of a circular turntable with a diameter of 2 m in the test section.
During the wind-tunnel tests, the mean velocity and turbulence intensity were measured using a TSI IFA 300 3D constant-temperature hot-film anemometer with a high accuracy of ±0.1%. Aluminum heating panels with adjustable temperatures from ambient temperature to 400 • C were placed on the indoor ground to simulate the thermal convection caused by radiant floor heating. The pollution source was placed on the indoor ground center and was connected to the tracer gas release system through the bottom pipes. After releasing the gas, the sampling pumps (with a sampling rate of 150 mL/min) could collect the tracer gas into sampling bags by connecting the sampling tubes (D = 2 mm) at different heights ( Figure 4b). The tracer gas concentrations in the sampling bags were measured using a DB−600T SF 6 quantitative detector with a measurement accuracy of ±1 ppm. The normalized concentration K is specified as follows: where C r and C e are the volume fractions of the measured SF 6 (ppm) and the pollution source (=2.5 × 10 5 ppm). T-type thermocouples were applied to measure the air temperature along the indoor vertical centerline when the indoor ground was heated. The dimensionless temperature θ is specified as: where T is the measured air temperature value (K). In addition, the laser sheet-CCD concentration testing system was also used to characterize the pollutant dispersion in the room under different Ri cases, which allowed the high-speed camera to capture the diffusion features of trace smoke displayed on a sheet laser.  During the wind-tunnel tests, the mean velocity and turbulence intensity were measured using a TSI IFA 300 3D constant-temperature hot-film anemometer with a high accuracy of ±0.1%. Aluminum heating panels with adjustable temperatures from ambient temperature to 400 °C were placed on the indoor ground to simulate the thermal convection caused by radiant floor heating. The pollution source was placed on the indoor ground center and was connected to the tracer gas release system through the bottom pipes. After releasing the gas, the sampling pumps (with a sampling rate of 150 mL/min) could collect the tracer gas into sampling bags by connecting the sampling tubes (D = 2 mm) at different heights ( Figure 4b). The tracer gas concentrations in the sampling bags were measured using a DB−600T SF6 quantitative detector with a measurement accuracy of ±1 ppm. The normalized concentration K is specified as follows: where Cr and Ce are the volume fractions of the measured SF6 (ppm) and the pollution source (=2.5 × 10 5 ppm). T-type thermocouples were applied to measure the air temperature along the indoor vertical centerline when the indoor ground was heated. The dimensionless temperature θ is specified as: where T is the measured air temperature value (K). In addition, the laser sheet-CCD concentration testing system was also used to characterize the pollutant dispersion in the room under different Ri cases, which allowed the high-speed camera to capture the diffusion features of trace smoke displayed on a sheet laser.

Validation of Numerical Models
The numerical model validations were conducted by comparing the wind-tunnel experimental data (WT data) for cross-ventilation under Ri = 0.27 with the established numerical models by adopting three high-Re turbulence models, namely, standard, RNG, and realizable k-ε (SKE, RNG, RLKE) turbulence models. First, Figure 5a shows a comparison of normalized velocity (U/U 0 ) distributions observed along the indoor vertical centerline. It can be noted that the RNG model performed better when predicting the indoor flow structure than the other two turbulence models, although the results from the three turbulence models showed similar trends. Wind speed tended to be higher in the middle and lower at both ends. A comparison of the dimensionless concentrations (K) along the indoor vertical centerline is depicted in Figure 5b, with the pollutant concentration decreasing sharply with increasing height. The same trends can also be observed in Figure 5c, where the dimensionless temperature (θ) distributions between WT tests and numerical models are depicted. Based on the above comparisons, we found that the distributions of U/U 0 , K, and θ in the room obtained using the RNG model agreed better with the WT data (with mean deviations of approximately less than 6%), followed by the RLKE model, and the SKE model performed the worst.
For further confirmation of the model validation, the characteristics of flow and dispersion, measured using a laser sheet-CCD concentration testing system under different Ri cross-ventilation conditions, have been depicted in Figure 6a-f. Here, the red lines drawn from the visualization of smoke plumes represent the streamlines, and the smoke diffusion can be used to characterize the pollutant dispersion under different Ri conditions. By comparing these results with the following streamlines and concentration distributions under the same Ri conditions (Ri values ranging from 0 to 11.11), we can further confirm that the RNG model showed high numerical accuracy in predicting the indoor flow and dispersion under the joint action of different inertia forces and thermal buoyancy forces.
ison of normalized velocity (U/U0) distributions observed along the indoor vertical cen-terline. It can be noted that the RNG model performed better when predicting the indoor flow structure than the other two turbulence models, although the results from the three turbulence models showed similar trends. Wind speed tended to be higher in the middle and lower at both ends. A comparison of the dimensionless concentrations (K) along the indoor vertical centerline is depicted in Figure 5b, with the pollutant concentration decreasing sharply with increasing height. The same trends can also be observed in Figure  5c, where the dimensionless temperature (θ) distributions between WT tests and numerical models are depicted. Based on the above comparisons, we found that the distributions of U/U0, K, and θ in the room obtained using the RNG model agreed better with the WT data (with mean deviations of approximately less than 6%), followed by the RLKE model, and the SKE model performed the worst.   It is worth noting that their flow patterns and pollutant distributions can be regarded as almost the same from the point of view of the numerical simulation. That is because, considering forced convection by cross-ventilation, the flow structures in the room entered the region of Re-independence (three values of Rew greater than 15,000, Cui et al. [41]), which means that the flow structures will change little with increasing Re. In such situations, the Ri value becomes the only influencing factor. Therefore, the concept of Re-independence is not only valid for pure forced convection flow but is also applicable to mixed convection involving thermal buoyancy flow. However, Figure 5b shows the distributions of K against the indoor vertical centerline under the above three cases, which indicates that the relative deviation became much smaller with increasing Re values, although this deviation among the three cases was already less than 5%. Based on the above analysis, we can conclude that the similarity criterion of Ri equality should be first satisfied by using the reduced−scale model to study the indoor mixed convection and should then be followed by Re-independence.  It is worth noting that their flow patterns and pollutant distributions can be regarded as almost the same from the point of view of the numerical simulation. That is because, considering forced convection by cross-ventilation, the flow structures in the room entered the region of Re-independence (three values of Re w greater than 15,000, Cui et al. [41]), which means that the flow structures will change little with increasing Re. In such situations, the Ri value becomes the only influencing factor. Therefore, the concept of Re-independence is not only valid for pure forced convection flow but is also applicable to mixed convection involving thermal buoyancy flow. However, Figure 5b shows the distributions of K against the indoor vertical centerline under the above three cases, which indicates that the relative deviation became much smaller with increasing Re values, although this deviation among the three cases was already less than 5%. Based on the above analysis, we can conclude that the similarity criterion of Ri equality should be first satisfied by using the reduced−scale model to study the indoor mixed convection and should then be followed by Re-independence.

Contours of U/U0 against Increasing Ri
Figure 8a-g show the contours of dimensionless velocity (U/U0) plotted against increasing Ri numbers for cross−ventilation cases. With increasing Ri values, ranging from 0 (pure natural ventilation) to 26.65, several features can be observed. Firstly, when Ri < 5.31, with the increasing Ri, the indoor flow distribution changed little (similar flow structure), which shows that the air entered the room from the windward side window and flowed out from the leeward side window horizontally, forming a clockwise vortex at the lower part of the room. This is because when Ri is small (less than 5.31), the inertial force of the incoming flow plays a leading role in dominating the structures of the indoor flow field; meanwhile, the thermal buoyancy force caused by the radiant floor heating is small and can be ignored. Secondly, when Ri is greater than 5.31, we can observe that the indoor flow fields changed significantly, showing that the airflow horizontally entered the room from the leeward window and was deflected downward, squeezing the vortex in the lower part into the left corner of the room. As the Ri continued to increase, the downward deflection of the airflow entering the room became more obvious, and the vortex was gradually squeezed to become smaller and smaller. This is because when the Ri value was greater than 5.31, the buoyance force caused by the radiant heating floor could no longer be ignored, and it played an increasingly important role in changing the indoor flow structure under the combined action of the inflow inertial force and the increase in Ri. In addition, with the increase in Ri, the gradually enhanced thermal buoyant force caused more and more thermal airflow to gather in the top of the room, thus pushing down the airflow entering the room from the windward window in an increasingly obvious manner. Then, the two streams are mixed together and flow out of the room through the leeward window. The characteristics of the flow field discussed above are highly consistent with the  , which shows that the air entered the room from the windward side window and flowed out from the leeward side window horizontally, forming a clockwise vortex at the lower part of the room. This is because when Ri is small (less than 5.31), the inertial force of the incoming flow plays a leading role in dominating the structures of the indoor flow field; meanwhile, the thermal buoyancy force caused by the radiant floor heating is small and can be ignored. Secondly, when Ri is greater than 5.31, we can observe that the indoor flow fields changed significantly, showing that the airflow horizontally entered the room from the leeward window and was deflected downward, squeezing the vortex in the lower part into the left corner of the room. As the Ri continued to increase, the downward deflection of the airflow entering the room became more obvious, and the vortex was gradually squeezed to become smaller and smaller. This is because when the Ri value was greater than 5.31, the buoyance force caused by the radiant heating floor could no longer be ignored, and it played an increasingly important role in changing the indoor flow structure under the combined action of the inflow inertial force and the increase in Ri. In addition, with the increase in Ri, the gradually enhanced thermal buoyant force caused more and more thermal airflow to gather in the top of the room, thus pushing down the airflow entering the room from the windward window in an increasingly obvious manner. Then, the two streams are mixed together and flow out of the room through the leeward window. The characteristics of the flow field discussed above are highly consistent with the flow field visualization results (the red streamlines) obtained from the WT test, shown in Figure 6, which again verifies the reliability of the numerical model adopted in this study. flow field visualization results (the red streamlines) obtained from the WT test, shown in Figure 6, which again verifies the reliability of the numerical model adopted in this study. The contour plots of dimensionless velocity (U/U0) on the vertical center plane against increasing Ri values for single-sided ventilation cases are depicted in Figure 9. The biggest difference from the cross-ventilation results was the fact that there was less airflow entering the room in the single-sided ventilation cases. However, with the increase in Ri, the following characteristics of indoor flow structures can be obtained. Firstly, when Ri = 0, the incoming flow was blocked by the indoor positive air pressure and was then deflected downward and entered the room vertically along the lower edge of the window. Then, two vortices were formed in the right part of the room: a clockwise one at the bottom, and another counterclockwise one at the top. However, these flow structures were very unstable, because when the indoor floor started to heat up (with Ri equal to 0.04, as shown in Figure 9b), the two small vortices merged to form a large counterclockwise vortex. Secondly, when the Ri value was less than 5.31, as the Ri increased, we were able to note that the large vortex maintained a relatively stable structure; however, the mean velocities in the room increased gradually. When the incoming flow decreased, the mean indoor velocity increased, indicating that the thermal buoyancy force caused by radiant floor heating gradually dominated the indoor flow structures. Thirdly, as the Ri continued to increase (Figure 9f,g), the large indoor counterclockwise vortex was gradually compressed by the thermal airflow at the top to right−bottom of the room. Furthermore, the windward window was obviously divided between the upper and lower parts, with the external airflow entering the room from the lower part of the window and forming the main vortex, combined with the indoor thermal airflow. The contour plots of dimensionless velocity (U/U 0 ) on the vertical center plane against increasing Ri values for single-sided ventilation cases are depicted in Figure 9. The biggest difference from the cross-ventilation results was the fact that there was less airflow entering the room in the single-sided ventilation cases. However, with the increase in Ri, the following characteristics of indoor flow structures can be obtained. Firstly, when Ri = 0, the incoming flow was blocked by the indoor positive air pressure and was then deflected downward and entered the room vertically along the lower edge of the window. Then, two vortices were formed in the right part of the room: a clockwise one at the bottom, and another counterclockwise one at the top. However, these flow structures were very unstable, because when the indoor floor started to heat up (with Ri equal to 0.04, as shown in Figure 9b), the two small vortices merged to form a large counterclockwise vortex. Secondly, when the Ri value was less than 5.31, as the Ri increased, we were able to note that the large vortex maintained a relatively stable structure; however, the mean velocities in the room increased gradually. When the incoming flow decreased, the mean indoor velocity increased, indicating that the thermal buoyancy force caused by radiant floor heating gradually dominated the indoor flow structures. Thirdly, as the Ri continued to increase (Figure 9f,g), the large indoor counterclockwise vortex was gradually compressed by the thermal airflow at the top to right−bottom of the room. Furthermore, the windward window was obviously divided between the upper and lower parts, with the external airflow entering the room from the lower part of the window and forming the main vortex, combined with the indoor thermal airflow.

Mean ACH Plotted against the Square Ri
To quantitatively evaluate the ventilation capacity as the Ri value increased, we made use of the air exchange rate (ACH) across the open window plane, i.e., a method which has been adopted in several studies [16,42], consisting of the mean (ACH) and turbulence (ACH ′ ) components as follows: where ACH is induced by the exchange of the mean velocity and ACH ′ is induced by the fluctuation velocity. According to the approach proposed by Li et al. [42], the ACH′ across the open window plane can be determined based on the turbulent kinetic energy k as follows: where

Mean ACH Plotted against the Square Ri
To quantitatively evaluate the ventilation capacity as the Ri value increased, we made use of the air exchange rate (ACH) across the open window plane, i.e., a method which has been adopted in several studies [16,42], consisting of the mean (ACH) and turbulence (ACH ) components as follows: where ACH is induced by the exchange of the mean velocity and ACH is induced by the fluctuation velocity. According to the approach proposed by Li et al. [42], the ACH across the open window plane can be determined based on the turbulent kinetic energy k as follows: where     In Table 3, we can first note that with the increase in Ri, the dimensionless ACH− becomes larger and larger, compared to the dimensionless ACH+, with the maximum deviation reaching 20% when Ri = 26.65. This is because with the increase in Ri, indoor air is heated by the radiation floor and the degree of thermal expansion increases, causing the average momentum of the airflow to flow out from the leeward window, increasing more and more significantly than that entering the room from the windward window. Second, although the dimensionless ACH across W 1 and W 2 changes with the increase in Ri, the dimensionless ACH on these two window planes is almost identical (ACH' W1 + = ACH' W2 −). Therefore, the dimensionless ACH+ also differs from the dimensionless ACH− (ACH− > ACH+) more and more significantly with the increase in Ri, which is different from the numerical results obtained for ACH+ = ACH− under the isothermal cases reported in some previous studies [16,42,43]. Third, when Ri is less than 5.31, the proportion of the dimensional ACH is about 70%, which is about 30% of the value of ACH . However, as the Ri value continues to increase, the proportion of the dimensional ACH gradually decreases slightly, which is because, under the studied cross-ventilation cases, the rate of the contribution of the dimensional ACH is always larger than that of ACH , and the increase in Ri leads to an insignificant increase in the dimensional ACH across W 2 (ACH−). In Table 4, for the single-sided ventilation cases, we can observe that the largest difference was the fact that as the Ri value increased, the proportion of the dimension ACH increased significantly from 75 to 90% (with Ri values from 0 to 1.86), then decreased from 90% to about 26% (with Ri values from 1.86 to 26.65). This indicates that the air exchange efficiency between indoor and outdoor air was mainly dominated by turbulence velocity when Ri was less than 5.31; when Ri = 26.65, it was mainly dominated by mean velocity; and when Ri = 11.11, it was dominated by both turbulence and mean velocities.

Ri ACH+/(V/T) ACH ' +/(V/T) ACH−/(V/T) ACH ' −/(V/T) ACH+/(V/T) ACH−/(V/T) ACH+/ACH+ ACH ' +/ACH+
To further confirm the effects of wind and thermal buoyancy on the indoor and outdoor air exchange, Figure 10 depicts the mean dimension ACH (the average value of ACH+ and ACH−) against the square Ri value for cross-and single-sided ventilation cases. Based on the variation trend shown in Figure 10, several features can be noted. Firstly, the dimensionless ACH values for cross-ventilation were about five times greater than those for single-sided ventilation under the same Ri cases, indicating that cross-ventilation was more conducive to indoor ventilation capacity. Secondly, for cross-ventilation, when Ri was no more than 5.31, it seems that the dimensional ACH (about 0.15) was independent of the Ri numbers, which indicates that under these cases, the air exchange between indoors and outdoors was mainly dominated and driven by the wind, whereas thermal buoyancy caused by the radiation floor heating could be ignored. However, when Ri was greater than 5.31, as the Ri value increased, the dimensionless ACH decreased slightly, indicating that the effect of thermal buoyancy could not be ignored, and the indoor flow structures and ventilation capacity were dominated by the combined action of wind and thermal buoyancy. Thirdly, for the single-sided ventilation, when Ri was no more than 0.27, the dimensionless ACH was independent of the Ri value and the thermal buoyancy could be ignored; when Ri was between 0.27 and 5.31, as the Ri increased, the dimensionless ACH decreased slightly, with wind and buoyancy working together to reduce the indoor ventilation capacity. However, as Ri continued to increase, although the incoming wind speed (U w ) also continued to decrease, the dimensionless ACH increased significantly, which indicates that the thermal buoyancy mainly dominated the indoor flow structures and air exchange capacity with the outdoors. Through the above analysis, we can conclude that the thermal buoyancy effects caused by radiant floor heating will dominate the indoor flow more quickly in the case of single-sided ventilation with increasing Ri values. greater than 5.31, as the Ri value increased, the dimensionless ACH indicating that the effect of thermal buoyancy could not be ignored, structures and ventilation capacity were dominated by the combined thermal buoyancy. Thirdly, for the single-sided ventilation, when R 0.27, the dimensionless ACH was independent of the Ri value and th could be ignored; when Ri was between 0.27 and 5.31, as the Ri increa less ACH decreased slightly, with wind and buoyancy working tog indoor ventilation capacity. However, as Ri continued to increase, alt wind speed (Uw) also continued to decrease, the dimensionless AC cantly, which indicates that the thermal buoyancy mainly domina structures and air exchange capacity with the outdoors. Through the can conclude that the thermal buoyancy effects caused by radiant floo inate the indoor flow more quickly in the case of single-sided ventila Ri values.   Figure 11, it can be noted that when Ri < 5.3 indoor temperature distributions could be divided into three parts ba wind: the upper part, the middle part, and the lower part. Here, the hottest since it was closest to the heat source, followed by the upper p ature of the middle part was the lowest due to the incoming flow o increase in Ri, the indoor mean temperature increased, with an area  Figure 11 depicts the contours of dimensionless temperature (θ) against increasing Ri values in the vertical center planes for cross-ventilation cases. The following features can be observed. First, in Figure 11, it can be noted that when Ri < 5.31 (Figure 11a-d), the indoor temperature distributions could be divided into three parts based on the incoming wind: the upper part, the middle part, and the lower part. Here, the lower part was the hottest since it was closest to the heat source, followed by the upper part, and the temperature of the middle part was the lowest due to the incoming flow of fresh air. With the increase in Ri, the indoor mean temperature increased, with an area of high temperature in the bottom left corner of the lower part increasing significantly, and an area of low temperature in the middle part also greatly decreasing. This is because when Ri was less than 5.31, the incoming wind still dominated the indoor flow and dispersion. With the increase in Ri, although the indoor ventilation capacity remained basically unchanged (ACH remained unchanged in Figure 10), the increasing heat release from the radiation floor mainly caused the indoor temperature to rise gradually. Second, when Ri was greater than 5.31, as Ri increased, the incoming wind and thermal buoyancy together dominated the indoor flow structure, causing the temperature of the upper part and the right-middle part to rise significantly. This indicates that as the Ri continued to increase, the incoming wind was bent downward to the right corner (Figure 8f,g) to carry more heat to the upper part. Moreover, as the Ri value increased, the decreasing ACH coupled with the increasing heat release from the radiation floor together led to a significant increase in temperature, especially in the upper part of the room. In Figure 12, for the investigation of single-sided ventilation, we can note that the high temperature occupied the greatest part of the room, and only a small part near and below the window, where the airflow entered the room, showed relatively lower temperature distributions. When Ri was less than 5.31, the mean temperature in the room increased significantly with the increase in Ri. However, when Ri was greater than 5.31 with a continuous increase, the indoor mean temperature decreased, and there was a greater heat flow out of the room from the upper window, climbing along the windward wall to the roof. This is because when Ri was less than 5.31, although the indoor ventilation capacity (ACH) remained almost unchanged with the increase in Ri, the release of heat from the radiation floor continued to increase, causing the indoor temperature to rise gradually. However, when Ri was greater than 5.31 for the single−sided ventilation model, the indoor ventilation capacity increased significantly with the continuous increase in Ri, and although the heat release rate also increased, it was always smaller than the amount carried out by the airflow. Therefore, based on this analysis, we can conclude that the indoor temperature distributions depended on the ventilation mode and the Ri value. For the studied Ri numbers, the mean temperature in the room increased with increasing Ri in the cross−ventilation cases; however, in the single−sided ventilation model, as the Ri increased, the mean indoor temperature increased first and then decreased. In Figure 12, for the investigation of single-sided ventilation, we can note that the high temperature occupied the greatest part of the room, and only a small part near and below the window, where the airflow entered the room, showed relatively lower temperature distributions. When Ri was less than 5.31, the mean temperature in the room increased significantly with the increase in Ri. However, when Ri was greater than 5.31 with a continuous increase, the indoor mean temperature decreased, and there was a greater heat flow out of the room from the upper window, climbing along the windward wall to the roof. This is because when Ri was less than 5.31, although the indoor ventilation capacity (ACH) remained almost unchanged with the increase in Ri, the release of heat from the radiation floor continued to increase, causing the indoor temperature to rise gradually. However, when Ri was greater than 5.31 for the single−sided ventilation model, the indoor ventilation capacity increased significantly with the continuous increase in Ri, and although the heat release rate also increased, it was always smaller than the amount carried out by the airflow. Therefore, based on this analysis, we can conclude that the indoor temperature distributions depended on the ventilation mode and the Ri value. For the studied Ri numbers, the mean temperature in the room increased with increasing Ri in the cross−ventilation cases; however, in the single−sided ventilation model, as the Ri increased, the mean indoor temperature increased first and then decreased.

Mean h against the Square Ri
To further evaluate the effect of ventilation capacity and the Ri value on the indoor temperature distributions, Figure 13 depicts the mean indoor surface convective heat transfer coefficient h against the square Ri for cross-and single−sided ventilation cases.
Here, h is specified as follows: where q is surface heat flux (W/m 2 ), and Tm is the mean temperature in the room (K). In Figure 13, it can first be noted that for the cross-ventilation cases, when Ri was less than 5.31, h decreased sharply from 35 to 20 W/(m 2 ·K) with increasing Ri, indicating that the mean indoor h depended strongly on Ri. This is because when Ri < 5.31, the inertial force of incoming wind dominated the indoor flow structure, and as the Ri increased, the weakened ventilation capacity led to the accumulation of heat and an increase in the mean temperature in the room. Together with the increase in the temperature difference between the heating floor and indoor air, this resulted in a significant decrease in the mean h. However, when Ri was greater than 5.31, the h curve was quite mild, meaning that h had almost nothing to do with Ri, which was because, although the temperature difference between the heating floor and the indoor ambient air increased with the continuous increase in Ri, the ventilation capacity also increased due to the effect of enhanced thermal buoyancy. Second, for the single-sided ventilation cases, with the increase in Ri, the mean values of h first decreased sharply (when Ri was no more than 1.86), and then increased mildly when Ri was between 1.86 and 11.11 and increased greatly when Ri was greater than 11.11. Unlike the cross-ventilation case, the main reason for the increase in the mean h with the continuous increase in Ri for the single-sided ventilation cases is that when Ri was greater than 1.86, the thermal buoyancy force caused by the heating floor could no longer be ignored, especially for Ri values greater than 11.11, the indoor flow structure was mainly dominated by thermal buoyancy, and the ventilation capacity increased sharply. Third, based on the above analysis, we can conclude that the mean h in the room was mainly dependent on the relative strength of the incoming inertial wind force and the thermal buoyancy force. When the incoming wind dominated the indoor flow structure,

Mean h against the Square Ri
To further evaluate the effect of ventilation capacity and the Ri value on the indoor temperature distributions, Figure 13 depicts the mean indoor surface convective heat transfer coefficient h against the square Ri for cross-and single−sided ventilation cases.
Here, h is specified as follows: where q is surface heat flux (W/m 2 ), and T m is the mean temperature in the room (K). In Figure 13, it can first be noted that for the cross-ventilation cases, when Ri was less than 5.31, h decreased sharply from 35 to 20 W/(m 2 ·K) with increasing Ri, indicating that the mean indoor h depended strongly on Ri. This is because when Ri < 5.31, the inertial force of incoming wind dominated the indoor flow structure, and as the Ri increased, the weakened ventilation capacity led to the accumulation of heat and an increase in the mean temperature in the room. Together with the increase in the temperature difference between the heating floor and indoor air, this resulted in a significant decrease in the mean h. However, when Ri was greater than 5.31, the h curve was quite mild, meaning that h had almost nothing to do with Ri, which was because, although the temperature difference between the heating floor and the indoor ambient air increased with the continuous increase in Ri, the ventilation capacity also increased due to the effect of enhanced thermal buoyancy. Second, for the single-sided ventilation cases, with the increase in Ri, the mean values of h first decreased sharply (when Ri was no more than 1.86), and then increased mildly when Ri was between 1.86 and 11.11 and increased greatly when Ri was greater than 11.11. Unlike the cross-ventilation case, the main reason for the increase in the mean h with the continuous increase in Ri for the single-sided ventilation cases is that when Ri was greater than 1.86, the thermal buoyancy force caused by the heating floor could no longer be ignored, especially for Ri values greater than 11.11, the indoor flow structure was mainly dominated by thermal buoyancy, and the ventilation capacity increased sharply. Third, based on the above analysis, we can conclude that the mean h in the room was mainly dependent on the relative strength of the incoming inertial wind force and the thermal buoyancy force. When the incoming wind dominated the indoor flow structure, h decreased significantly with the increase in the Ri value, and when the indoor flow structure was dominated by both incoming wind and thermal buoyancy, h depended little on the Ri value (which was unchanged with the increase in the Ri value); however, when the thermal buoyancy force dominated the indoor flow structure, h increased significantly with the increase in Ri.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW h decreased significantly with the increase in the Ri value, and when the indoor flo ture was dominated by both incoming wind and thermal buoyancy, h depended the Ri value (which was unchanged with the increase in the Ri value); however, w thermal buoyancy force dominated the indoor flow structure, h increased sign with the increase in Ri.

Contours of K against Increasing Ri
To reveal the effects of different Ri values and ventilation modes on the ind lutant distribution, Figure 14 shows the contours of the dimensionless concentr in the indoor vertical center plane, plotted against varying Ri values for cross ve cases. We can observe that the distribution of K against the increasing Ri values ar to the dimensionless temperature distributions shown in Figure 11. Firstly, whe less than 5.31, the indoor pollutant distributions could also be divided into th based on the incoming wind: the upper part, middle part, and lower part. Here, t part was more seriously polluted due to the proximity of the pollutant source, by the upper part, and then the concentration in the middle part was the lowest d incoming flow of fresh air. Secondly, it can be noted that when Ri < 5.31, the ind lutant distributions in the three parts changed little with the increase in Ri, with pollutant concentration in the lower part moving from the bottom center to the left corner and the pollutant concentration in the middle part increasing slightly increase in Ri. This is because when Ri was less than 5.31, the inertial force of the tal incoming wind still dominated the indoor flow and the pollutant dispersion buoyancy force could be ignored, resulting in the formation of the above three par ever, as shown in Figure 8, as the buoyancy force (Ri) increased, the clockwise v the lower part moved gradually from the bottom right (Ri = 0) to the bottom cen 0.04, 0.27, and 1.86), causing the distribution to show a high pollutant conce Thirdly, when Ri was greater than 5.31, the thermal buoyancy force caused by th tion floor could no longer be ignored, but rather acted together with the inertia the incoming flow to cause the incoming flow to be deflected from the horizontal to the downward-right area. Therefore, as the Ri value increased, the high−conce  Figure 14 shows the contours of the dimensionless concentration (K) in the indoor vertical center plane, plotted against varying Ri values for cross ventilation cases. We can observe that the distribution of K against the increasing Ri values are similar to the dimensionless temperature distributions shown in Figure 11. Firstly, when Ri was less than 5.31, the indoor pollutant distributions could also be divided into three parts based on the incoming wind: the upper part, middle part, and lower part. Here, the lower part was more seriously polluted due to the proximity of the pollutant source, followed by the upper part, and then the concentration in the middle part was the lowest due to the incoming flow of fresh air. Secondly, it can be noted that when Ri < 5.31, the indoor pollutant distributions in the three parts changed little with the increase in Ri, with the high pollutant concentration in the lower part moving from the bottom center to the bottom left corner and the pollutant concentration in the middle part increasing slightly with the increase in Ri. This is because when Ri was less than 5.31, the inertial force of the horizontal incoming wind still dominated the indoor flow and the pollutant dispersion and the buoyancy force could be ignored, resulting in the formation of the above three parts. However, as shown in Figure 8, as the buoyancy force (Ri) increased, the clockwise vortex in the lower part moved gradually from the bottom right (Ri = 0) to the bottom center (Ri = 0.04, 0.27, and 1.86), causing the distribution to show a high pollutant concentration. Thirdly, when Ri was greater than 5.31, the thermal buoyancy force caused by the radiation floor could no longer be ignored, but rather acted together with the inertial force of the incoming flow to cause the incoming flow to be deflected from the horizontal direction to the downward-right area. Therefore, as the Ri value increased, the high−concentration area of pollutants in the lower part was gradually deflected from the left corner to the right corner and diffused out through the leeward window.   Figure 14, the indoor pollutant distributions for single−sided ventilation changed greatly with increasing Ri values. First, when Ri = 0 (no thermal effect), because it was difficult for the fresh airflow from the outside to enter the room, there was no stable flow field structure formed by the thermal convection in the room, so the pollutants were evenly distributed in the room. Second, when Ri > 0, a stable counterclockwise main vortex was formed in the room under the influence of the thermal buoyancy caused by the heating floor coupled with the incoming wind ( Figure 9). Therefore, under the action of this counterclockwise vortex, the indoor high−concentration pollutants mainly gathered in the right and top areas of the room. With an increase in the Ri value from 0.04 to 5.31, the values of the dimensionless ACH of the single−sided ventilation cases remained almost constant or even decreased slightly ( Figure 10). However, the K distributions in the room seemed to decrease gradually, particularly in the area of high concentration at the right and top of the room, which decreased significantly. This is because with the increase in Ri, the mean dimensionless velocities in the room increased gradually (see Figure 9) due to the increasingly important role of the thermal buoyancy caused by the heating ground. Therefore, in the single-sided ventilated room, the effect of thermal buoyancy on indoor air flow and pollutant dispersion was more obvious than that in the cross−ventilated room, because the inertial force of outdoor flow had less of an influence on the flow structure in the single−side ventilated rooms. Third, as the Ri continued to increase (Ri from 11.11 to 26.65), the average values of K in the room continued to decrease and the characteristics of the K distribution also changed slightly, showing that the high concentration gradually moved from the top to the center of the room. This is mainly because when Ri value was greater than 11.11, the thermal buoyancy force dominated the indoor flow structures, and more and more thermal airflows gathered at the top of the room, squeezing the interior counterclockwise vortex down to the lower part (Figure 9f,g). Furthermore, there were obvious thermal airflows out of the room through the upper part of the window, taking away more indoor   Figure 14, the indoor pollutant distributions for single−sided ventilation changed greatly with increasing Ri values. First, when Ri = 0 (no thermal effect), because it was difficult for the fresh airflow from the outside to enter the room, there was no stable flow field structure formed by the thermal convection in the room, so the pollutants were evenly distributed in the room. Second, when Ri > 0, a stable counterclockwise main vortex was formed in the room under the influence of the thermal buoyancy caused by the heating floor coupled with the incoming wind ( Figure 9). Therefore, under the action of this counterclockwise vortex, the indoor high−concentration pollutants mainly gathered in the right and top areas of the room. With an increase in the Ri value from 0.04 to 5.31, the values of the dimensionless ACH of the single−sided ventilation cases remained almost constant or even decreased slightly ( Figure 10). However, the K distributions in the room seemed to decrease gradually, particularly in the area of high concentration at the right and top of the room, which decreased significantly. This is because with the increase in Ri, the mean dimensionless velocities in the room increased gradually (see Figure 9) due to the increasingly important role of the thermal buoyancy caused by the heating ground. Therefore, in the single-sided ventilated room, the effect of thermal buoyancy on indoor air flow and pollutant dispersion was more obvious than that in the cross−ventilated room, because the inertial force of outdoor flow had less of an influence on the flow structure in the single−side ventilated rooms. Third, as the Ri continued to increase (Ri from 11.11 to 26.65), the average values of K in the room continued to decrease and the characteristics of the K distribution also changed slightly, showing that the high concentration gradually moved from the top to the center of the room. This is mainly because when Ri value was greater than 11.11, the thermal buoyancy force dominated the indoor flow structures, and more and more thermal airflows gathered at the top of the room, squeezing the interior counterclockwise vortex down to the lower part (Figure 9f,g). Furthermore, there were obvious thermal airflows out of the room through the upper part of the window, taking away more indoor air pollutants. In addition, unlike the cases of Ri values lower than 11.11, due to the strong thermal buoyancy, the air pollutants flowing out of the window climbed up along the vertical façade of the building, then skipped over the roof and traveled down to the wind. air pollutants. In addition, unlike the cases of Ri values lower than 11.11, due to the strong thermal buoyancy, the air pollutants flowing out of the window climbed up along the vertical façade of the building, then skipped over the roof and traveled down to the wind.

Mean K in the Room against the Square Ri
To further analyze the indoor concentrations quantitatively, Figure 16 depicts the mean K in the room against the square Ri for cross− and single−sided ventilation cases. Based on the curves, we can first note that the mean concentrations in the room for crossventilation cases were much smaller than those observed for the single-sided ventilation cases; however, this difference decreased with the increase in the Ri value. Second, we can observe that with the increasing Ri, the mean concentrations in the room for the cross−ventilation cases remained almost unchanged (less than 25) against the increasing Ri; however, the mean values of K for the single−sided ventilation cases sharply decreased from 230 to about 50, which indicates that the indoor pollutant dispersion for the single−sided ventilation cases depended strongly on the Ri value. This is because it was difficult for external airflows to enter the single−sided ventilation room, and the thermal buoyancy force caused by the radiation heating floor rapidly dominated the indoor flow structure and pollutant dispersion. In addition, by comparing Figures 10 and 16, we can note that the dimensionless ACH did not seem to correlate well with the mean concentration in the room, which is because the diffusion of indoor pollutants to the outdoors was also determined by the indoor flow structure and location of the pollution source. For instance, in the cross-ventilation cases, when Ri was less than 5.31, the inertial force dominated the indoor flow field, and the indoor flow structures and the dimensionless ACH remained almost the same (Figures 8a-d and 10); therefore, the mean K in the room also remained constant. However, as the Ri continued to increase, although the dimensionless ACH de- To further analyze the indoor concentrations quantitatively, Figure 16 depicts the mean K in the room against the square Ri for cross− and single−sided ventilation cases. Based on the curves, we can first note that the mean concentrations in the room for cross-ventilation cases were much smaller than those observed for the single-sided ventilation cases; however, this difference decreased with the increase in the Ri value. Second, we can observe that with the increasing Ri, the mean concentrations in the room for the cross−ventilation cases remained almost unchanged (less than 25) against the increasing Ri; however, the mean values of K for the single−sided ventilation cases sharply decreased from 230 to about 50, which indicates that the indoor pollutant dispersion for the single−sided ventilation cases depended strongly on the Ri value. This is because it was difficult for external airflows to enter the single−sided ventilation room, and the thermal buoyancy force caused by the radiation heating floor rapidly dominated the indoor flow structure and pollutant dispersion. In addition, by comparing Figures 10 and 16, we can note that the dimensionless ACH did not seem to correlate well with the mean concentration in the room, which is because the diffusion of indoor pollutants to the outdoors was also determined by the indoor flow structure and location of the pollution source. For instance, in the crossventilation cases, when Ri was less than 5.31, the inertial force dominated the indoor flow field, and the indoor flow structures and the dimensionless ACH remained almost the same (Figures 8a-d and 10); therefore, the mean K in the room also remained constant. However, as the Ri continued to increase, although the dimensionless ACH decreased from 0.15 to 0.13 (Figure 10), the mean K in the room also decreased slightly ( Figure 16). This is because when Ri exceeded 5.31, although the ACH decreased, the indoor flow structure changed greatly (with the airflow blowing directly towards the pollution source), resulting in an increase in the effective ventilation rate that could carry more pollutants to the outside. To sum up, it can be noted that the mean indoor pollutant concentration was not only related to the dimensionless ACH but was also closely related to the indoor flow structure, i.e., the effective ventilation rate must be increased to reduce the indoor pollutant accumulation.
Int. J. Environ. Res. Public Health 2022, 19, x FOR PEER REVIEW creased from 0.15 to 0.13 (Figure 10), the mean K in the room also decreased slight ure 16). This is because when Ri exceeded 5.31, although the ACH decreased, the flow structure changed greatly (with the airflow blowing directly towards the po source), resulting in an increase in the effective ventilation rate that could carry mo lutants to the outside. To sum up, it can be noted that the mean indoor pollutant c tration was not only related to the dimensionless ACH but was also closely relate indoor flow structure, i.e., the effective ventilation rate must be increased to red indoor pollutant accumulation.

Conclusions
In this study, reduced-scale numerical models were used to investigate the in of radiant floor heating integrated with natural ventilation on indoor flow and disp The numerical model was validated by means of wind−tunnel tests. Seven Ri value ing from 0 to 26.65, coupled with cross-or single−sided ventilation, were consider conclusions are as follows: (1) It can be noted that the similarity criterion of Ri equality should be satisfied using a reduced−scale model to study the indoor mixed convection, follow Re−independence, and the Re value should be as large as possible in order to the deviation caused by the reduced scale. (2) Indoor flow structures: For cross-ventilation, when Ri was less than 5.31, the indoor flow structures re almost the same, and the inertial force dominated the indoor flow field. When greater than 5.31, the dimensionless ACH vs. Ri 1/2 results confirmed that the indo field was dominated by the wind and buoyancy force together. However, for singl ventilation cases, when Ri was greater than 5.31, the buoyancy force dominated the flow structure, and the incoming inertial force could be ignored. Meanwhile, the sionless ACH increased significantly. Therefore, we found that the thermal buoya fects caused by radiant floor heating dominated the indoor flow structure more e single-sided ventilation with increasing Ri.
(1) Indoor temperature distributions: In the case of cross−ventilation, the indoor temperature distributions could vided into three parts according to the incoming wind, and the high temperatur mainly concentrated in the lower part. With increasing Ri, the indoor mean h de sharply first, then remained almost unchanged (equal to about 20) when Ri was

Conclusions
In this study, reduced-scale numerical models were used to investigate the influence of radiant floor heating integrated with natural ventilation on indoor flow and dispersion. The numerical model was validated by means of wind−tunnel tests. Seven Ri values ranging from 0 to 26.65, coupled with cross-or single−sided ventilation, were considered. Our conclusions are as follows: (1) It can be noted that the similarity criterion of Ri equality should be satisfied first by using a reduced−scale model to study the indoor mixed convection, followed by Re−independence, and the Re value should be as large as possible in order to reduce the deviation caused by the reduced scale. (2) Indoor flow structures: For cross-ventilation, when Ri was less than 5.31, the indoor flow structures remained almost the same, and the inertial force dominated the indoor flow field. When Ri was greater than 5.31, the dimensionless ACH vs. Ri 1/2 results confirmed that the indoor flow field was dominated by the wind and buoyancy force together. However, for single−sided ventilation cases, when Ri was greater than 5.31, the buoyancy force dominated the indoor flow structure, and the incoming inertial force could be ignored. Meanwhile, the dimensionless ACH increased significantly. Therefore, we found that the thermal buoyancy effects caused by radiant floor heating dominated the indoor flow structure more easily in single-sided ventilation with increasing Ri.
(1) Indoor temperature distributions: In the case of cross−ventilation, the indoor temperature distributions could be divided into three parts according to the incoming wind, and the high temperatures were mainly concentrated in the lower part. With increasing Ri, the indoor mean h decreased sharply first, then remained almost unchanged (equal to about 20) when Ri was greater than 5.31. For single−sided ventilation, high temperatures occupied most of the room. Moreover, as the Ri value increased, the indoor mean h for the single-sided ventilation scenario first decreased sharply, then increased mildly, and finally increased significantly when Ri was greater than 11.11.
(2) Indoor pollutant dispersion: In the case of cross−ventilation, when Ri was less than 5.31, the indoor pollutant distribution in the three parts changed little with the increase in Ri, and the lower part was seriously polluted due to the proximity of the pollutant source, followed by the upper part. When Ri was greater than 5.31, as Ri continued to increase, the high concentration of pollutants in the lower part was gradually deflected from the left corner to the right corner. However, for the single-sided ventilation scenario, the high concentration of pollutants was mainly concentrated in the bottom right corner and along the right wall, and the mean K in the room was greatly reduced with the increase in Ri.
In addition, we found that the indoor pollutant concentration was not only related to the dimensionless ACH but was also closely related to the indoor flow structure, i.e., the effective ventilation rate must be increased to reduce the indoor pollutant concentration and accumulation.
Limitations: The scenario simulated in this study was that in a newly decorated and unoccupied residence, in which the heating system could promote the release of VOCs such as formaldehyde from the building materials, natural ventilation from windows could quickly remove the pollutants from the room, so there was no discussion of thermal comfort. In future works, we will continue to investigate the coupled effects of indoor heating and fresh air systems on indoor pollutant removal and thermal comfort in occupied residences.