Effects of the Design Parameters of Ridge Vents on Induced Buoyancy-Driven Ventilation

: With ridge vents that are commonly used in building ventilation applications as the research object, this study analyzed how design parameters affect the efﬁciency of thermal buoyancy-driven ventilation induced by ridge vents through computational ﬂuid dynamics (CFD). The design parameters of ridge vents include the width S, height H, and eave overhang E. In consideration of engineering practices, the parameter ranges were set as follows: S = 1.2, 1.8, 2.4, and 3 m; H = 0.3, 0.6, 0.9, and 1.2 m; and E = 0, 0.3, and 0.6 m. The results show that when a ridge vent is under buoyancy-driven ventilation, the height H serves as the dominant design parameter. Correlation equations of the induced ventilation rates with the relevant ridge vent design parameters are provided. for natural ventilation. the of all roof after are assumed to be isothermal, T H . In the external ﬂow ﬁeld, after the pitched roof receives solar heat, a buoyancy-driven ﬂow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the ﬂow of outdoor air, as indicated by the


Introduction
Natural ventilation is the process of introducing fresh air into an indoor space by means of natural forces, such as wind and/or thermal buoyancy, instead of the use of mechanical energy. These natural forces, which usually affect the efficiency of natural ventilation, can be isolated, opposed, or mutually reinforced and sometimes work in synergy. The design methods and research results related to natural building ventilation have been fruitful. Further information can be found in review papers [1][2][3][4].
Ridge vents (or roof-mounted monitors), which are a common natural ventilation approach, encourage airflow by means of thermal buoyancy or wind. Designing and building a sloped roof with an opening at the soffits and ridges to promote airflow through the attic roof and/or the entire building are common practices. In cold or mild climates, ridge vents are mainly used to control moisture in attic spaces; in warm climates, they are used to remove the solar heat gain from roofs [5]. There are many studies on ridge vents, most of which focus on attic ventilation, whole building ventilation, and greenhouse environment control.
For the application of ridge vents in attic ventilation, Tariku and Iffa [5] applied transient boundary conditions to investigate the thermal dynamic responses of a typical attic roof with a ridge vent. Their results show that in terms of energy, an attic roof with a high ventilation rate could increase energy consumption in winter and reduce the cooling load in summer. Wang and Shen [6] used a transient computational fluid dynamics (CFD) model to analyze the effect of the ventilation ratio and vent balance on the cooling load and airflow in naturally ventilated attics. The results show that changes in the ventilation ratio and vent configuration had little impact on the streamline pattern. Iffa and Tariku [7] discussed how changes in roof sheathing, ceiling insulation (baffle size) and locations of the vent area affect the air and temperature distributions in the attic space in summer and winter. Their results show that when the airflow was driven by wind, increasing the baffle size significantly influenced the air distribution.
Regarding the application of ridge vents in whole building ventilation, Wen et al. [8] designed and developed a ventilated building-integrated photovoltaic (BIPV) system with a double-skin roof structure to enable environmental control and indoor ventilation induction. The influence of the locations of the covered ridges with sidewall openings (CRSOs) and BIPV openings (toward the outdoors and indoors) with different outdoor wind velocities on the flow structures was analyzed numerically. The results show that in calm wind situations, when the opening faced outward (i.e., soffits), the outdoor mode had a better ventilation effect than the indoor mode when the opening faced inward. In contrast, at a high wind velocity (2 m/s), the ventilation rate of the indoor mode was higher than that of the outdoor mode. Kang and Lee [9] conducted a wind tunnel test to explore the natural ventilation of entrained air (by outdoor wind blowing) in large factories. Three different types of louver ventilators were installed in the upper one-third of an open windward wall in a factory model. The results show that a ventilator with outer and inner louvers with appropriate inclination angles could effectively improve the overall ventilation efficiency of factories. A wind exchanger (or windcatcher), a structural form on the roof of a building, could increase wind-driven ventilation. Cruz-Salas et al. [10] experimentally evaluated six wind exchanger configurations with different wind orientations in a room with a window on the windward side. The results show that the performance of the wind exchanger depended on the relative relation between its opening and the wind direction.
Van Overbeke et al. [11] used a natural ventilation test facility to develop technology to measure sidewall and ridge vent ventilation rates with a 3D ultrasonic anemometer and a static 2D ultrasonic anemometer. The results show that the ridge vents had a relatively constant ventilation rate, while the side vents could change from outlet to inlet depending on the incidence angle of the wind. Wang et al. [12] conducted numerical simulations of pollutant diffusion between two workshops. One of the workshops had an open roof vent skylight with an opening width of 3 m. The results show that outdoor wind clearly interacted with the thermal buoyancy produced by the heat source of the downstream workshop. When the ventilation flow was driven by outdoor wind, the concentration of air pollutants in the pedestrian respiratory zone was low; when it was driven by thermal buoyancy, air pollutants migrated to the pedestrian respiratory zone.
Regarding the application of ridge vents in greenhouse environment control, Espinoza et al. [13] analyzed the impact of the ventilator configuration on the internal airflow pattern in a three-span Mediterranean greenhouse. The results show that the airflow pattern in the greenhouse depended on the ventilation surface distribution and how the ventilation flow was obstructed. The case with two roof vents and two side vents could improve the airflow at the height of the plants, although the overall volumetric flow rate was lower than that of the case with three roof vents and two side vents. Chu and Lan [14] investigated the wind-driven ventilation of monoslope greenhouses with ridge vents via a large eddy simulation (LES) model and wind tunnel experiments. The results show that the multispan greenhouses with open ridge vents had much higher ventilation rates than those with closed ridge vents. Villagran and Bojacá [15] conducted numerical simulations to assess how inflatable air ducts affect thermal behavior when the roofs of naturally ventilated multi-tunnel greenhouses were closed at night. The results show that an inflatable air duct could decrease the negative thermal gradient between the inside and outside of the greenhouse.
Taiwan is situated in a tropical area; on the ridges of buildings, various ridge vents (as illustrated in the red dotted zone in Figure 1) related to the aforementioned "whole building ventilation" purpose can be easily seen. However, people have different evaluations of their ability to induce natural ventilation. What is the ventilation rate? Are there any appropriate design parameters? To date, these details have not been unveiled in the literature. Therefore, in this study, CFD numerical simulations were conducted to investigate the influence of ridge vent design parameters on the efficiency of indoor buoyancy-driven ventilation.
Ridge vents are applicable to various spaces, such as factories, stadiums, exhibition halls, greenhouses etc. For the convenience of explanation, an industrial workshop was used as the application scenario in this study.
Buildings 2022, 12, x FOR PEER REVIEW 3 of 13 literature. Therefore, in this study, CFD numerical simulations were conducted to investigate the influence of ridge vent design parameters on the efficiency of indoor buoyancydriven ventilation. Ridge vents are applicable to various spaces, such as factories, stadiums, exhibition halls, greenhouses etc. For the convenience of explanation, an industrial workshop was used as the application scenario in this study.

Research Object
As shown in Figure 2a, after the pitched roof  of the industrial workshop receives solar heat, the air temperature around the roof panel increases. Because the roof panel is inclined, the indoor side below the panel experiences a buoyancy-driven boundary layer airflow that moves obliquely upward and then drives the flow of air inside the workshop below the roof panel. The two flows (buoyancy-driven airflow and induced indoor airflow) move outward through the ridge vent (), contributing to natural ventilation, as shown by the blue lines  in the figure.

Research Object
As shown in Figure 2a, after the pitched roof Buildings 2022, 12, x FOR PEER REVIEW Alternatively, the local negative pressure caused by the external wind pass the ridge vent can exhaust the indoor air, creating another natural ventilation mec Although this issue is not what we are exploring in this study, but worthy of fur sideration. When high temperatures and low wind velocities are present for a lon of time, the thermal buoyancy mentioned above becomes an important driving natural ventilation. In this study, the temperatures of all roof surfaces after solar are assumed to be isothermal, TH. In the external flow field, after the pitched roof solar heat, a buoyancy-driven flow that moves obliquely upward also forms on door side above the roof panel, which then drives the flow of outdoor air, as indi the green lines .
Because the types of spaces below the roof and the openings are diverse and of this study is to assess the thermal buoyancy-driven ventilation induced by rid in the process of physical modeling, the space below the ridge vent (i.e., the blac zone shown in Figure 2a) is ignored based on reasonable boundary condition Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are sym To save computational time, half of the representative roof is adopted as the model by means of the symmetry axis , as shown in Figure 2b. During the p CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and heigh black dotted zone in Figure 2a is determined first, and then the roof structure and roof ventilation design are determined. Therefore, the representative roof discusse paper has the same length (X + direction) and width (Y + direction) as those of the w space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2 Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effec ventilation performance of the ridge vent in the X-axis direction on both sides of the length of the physical model in the X-axis direction was determined by ta entire representative roof into consideration (X = X + = 0-18 m). For the relevant g data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. (2) The lower boundary of the computational domain below the roof is given Neumann conditions (blue line , Y = 0-6.7 m; Z = 0 m) so that the fluid can flow freely into or out of the computational domain. This represents that air can flow into and out of the roof space from and to the workshop space. (3) For the external flow field, the lower boundary of the computational domain is also given Neumann conditions (blue line , Y > 6.7 m; Z = 0 m) to represent the free flow of outdoor air (symbol  in Figure 2a).
In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. is not what we are exploring in this study, but worthy of further conigh temperatures and low wind velocities are present for a long period l buoyancy mentioned above becomes an important driving force for . In this study, the temperatures of all roof surfaces after solar heating sothermal, TH. In the external flow field, after the pitched roof receives ncy-driven flow that moves obliquely upward also forms on the oute roof panel, which then drives the flow of outdoor air, as indicated by pes of spaces below the roof and the openings are diverse and the aim ssess the thermal buoyancy-driven ventilation induced by ridge vents, ysical modeling, the space below the ridge vent (i.e., the black dotted ure 2a) is ignored based on reasonable boundary condition settings. tive roof is obtained.
configurations (, ) and heat flow patterns (TH , ) are symmetric. onal time, half of the representative roof is adopted as the physical f the symmetry axis , as shown in Figure 2b. During the process of following assumptions are made: 0 ( in Figure 2b) is set at the boundary of the computational domain no-slip conditions to realize symmetry of the flow fields. ndary of the computational domain below the roof is given Neumann ue line , Y = 0-6.7 m; Z = 0 m) so that the fluid can flow freely into or putational domain. This represents that air can flow into and out of the m and to the workshop space. al flow field, the lower boundary of the computational domain is also n conditions (blue line , Y > 6.7 m; Z = 0 m) to represent the free flow (symbol  in Figure 2a).
of architectural design, the workshop space (area and height) in the n Figure 2a is determined first, and then the roof structure and possible ign are determined. Therefore, the representative roof discussed in this length (X + direction) and width (Y + direction) as those of the workshop 8 m and 13.4 m, respectively. To simplify the CFD calculation, during cess, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the igure 2a) was analyzed. To understand the possible edge effects on the ance of the ridge vent in the X-axis direction on both sides of the roof, hysical model in the X-axis direction was determined by taking the e roof into consideration (X = X + = 0-18 m). For the relevant geometric in the figure.
Buildings 2022, 12, x FOR PEER REVIEW 3 of 13 literature. Therefore, in this study, CFD numerical simulations were conducted to investigate the influence of ridge vent design parameters on the efficiency of indoor buoyancydriven ventilation. Ridge vents are applicable to various spaces, such as factories, stadiums, exhibition halls, greenhouses etc. For the convenience of explanation, an industrial workshop was used as the application scenario in this study.

Research Object
As shown in Figure 2a, after the pitched roof  of the industrial workshop receives solar heat, the air temperature around the roof panel increases. Because the roof panel is inclined, the indoor side below the panel experiences a buoyancy-driven boundary layer airflow that moves obliquely upward and then drives the flow of air inside the workshop below the roof panel. The two flows (buoyancy-driven airflow and induced indoor airflow) move outward through the ridge vent (), contributing to natural ventilation, as shown by the blue lines  in the figure.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, T H . In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines t what we are exploring in this study, but worthy of further conmperatures and low wind velocities are present for a long period yancy mentioned above becomes an important driving force for is study, the temperatures of all roof surfaces after solar heating rmal, TH. In the external flow field, after the pitched roof receives riven flow that moves obliquely upward also forms on the outpanel, which then drives the flow of outdoor air, as indicated by f spaces below the roof and the openings are diverse and the aim the thermal buoyancy-driven ventilation induced by ridge vents, l modeling, the space below the ridge vent (i.e., the black dotted a) is ignored based on reasonable boundary condition settings. of is obtained. igurations (, ) and heat flow patterns (TH , ) are symmetric. time, half of the representative roof is adopted as the physical symmetry axis , as shown in Figure 2b. During the process of wing assumptions are made: in Figure 2b) is set at the boundary of the computational domain ip conditions to realize symmetry of the flow fields. y of the computational domain below the roof is given Neumann e , Y = 0-6.7 m; Z = 0 m) so that the fluid can flow freely into or ional domain. This represents that air can flow into and out of the to the workshop space. w field, the lower boundary of the computational domain is also nditions (blue line , Y > 6.7 m; Z = 0 m) to represent the free flow bol  in Figure 2a).
chitectural design, the workshop space (area and height) in the re 2a is determined first, and then the roof structure and possible re determined. Therefore, the representative roof discussed in this th (X + direction) and width (Y + direction) as those of the workshop nd 13.4 m, respectively. To simplify the CFD calculation, during nly half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b . Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations ( Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines . Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH.
In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction ( Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH.
In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.  ernatively, the local negative pressure caused by the external wind passing over e vent can exhaust the indoor air, creating another natural ventilation mechanism. h this issue is not what we are exploring in this study, but worthy of further conon. When high temperatures and low wind velocities are present for a long period the thermal buoyancy mentioned above becomes an important driving force for ventilation. In this study, the temperatures of all roof surfaces after solar heating med to be isothermal, TH.
In the external flow field, after the pitched roof receives at, a buoyancy-driven flow that moves obliquely upward also forms on the oute above the roof panel, which then drives the flow of outdoor air, as indicated by n lines . ause the types of spaces below the roof and the openings are diverse and the aim tudy is to assess the thermal buoyancy-driven ventilation induced by ridge vents, rocess of physical modeling, the space below the ridge vent (i.e., the black dotted own in Figure 2a) is ignored based on reasonable boundary condition settings. representative roof is obtained. e geometric configurations (, ) and heat flow patterns (TH , ) are symmetric.
computational time, half of the representative roof is adopted as the physical y means of the symmetry axis , as shown in Figure 2b. During the process of deling, the following assumptions are made: e plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain wall with no-slip conditions to realize symmetry of the flow fields. e lower boundary of the computational domain below the roof is given Neumann ditions (blue line , Y = 0-6.7 m; Z = 0 m) so that the fluid can flow freely into or of the computational domain. This represents that air can flow into and out of the f space from and to the workshop space. the external flow field, the lower boundary of the computational domain is also en Neumann conditions (blue line , Y > 6.7 m; Z = 0 m) to represent the free flow utdoor air (symbol  in Figure 2a). the process of architectural design, the workshop space (area and height) in the tted zone in Figure 2a is determined first, and then the roof structure and possible tilation design are determined. Therefore, the representative roof discussed in this as the same length (X + direction) and width (Y + direction) as those of the workshop low, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during lation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the irection (Figure 2a) was analyzed. To understand the possible edge effects on the ion performance of the ridge vent in the X-axis direction on both sides of the roof, th of the physical model in the X-axis direction was determined by taking the presentative roof into consideration (X = X + = 0-18 m). For the relevant geometric e Table 1. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. Table 1. Geometric data.

Parts of the Model Geometric Data
Coordinates (X + , Y + , Z + ) For illustration of the factory case and representative roof (Figures 1 and 2a) Coordinates (X, Y, Z) For illustration of the physical model ( The computational domain set is shown in Figure 3a. In the X'-, Y'-and Z'-axis directions, the distances between the physical model and the computational domain are Lx, Ly and 2 Lz, respectively. These distances, obtained through multiple tests, can properly indicate that the representative roof is in an open space. Lx, Ly and Lz represent the size of the physical model in the X'-, Y'-and Z'-axis directions, respectively. The plane of symmetry (Y' = 0 m) is set to a wall with no-slip conditions, and the other boundaries are set to Neumann conditions. For the grid point system, to increase the simulation correctness, the number of grids close to the model boundary and inside the model must be increased. When the grid independence of the mesh domain is tested, the air velocity along the Y'-axis (direction of the design parameter S) based on different grid points is used to calculate the deviation percentages and to determine a suitable grid point system for our calculations, as shown in Figure   The heat source (driving force) of buoyant ventilation is the solar-heated roof panels. The aforementioned geometric configurations cause the areas of roof panels to vary with the design parameters. That is, when the design parameters are different, the heat sources may differ in size. For the upper roof panel, when E = 0.6 m, there is a larger deck area (i.e., a larger heat source); for the lower roof panel, when S = 3 m, there is a smaller deck area. For the conditions of controlling the heat source, this may not be an ideal heat-transfer study design, but the results can be applied in engineering practice.
The ventilation rate . Q vent (m 3 /s) of a ridge vent design case is calculated by: The heat source (driving force) of buoyant ventilation is the solar-heated roof panels. The aforementioned geometric configurations cause the areas of roof panels to vary with the design parameters. That is, when the design parameters are different, the heat sources may differ in size. For the upper roof panel, when E = 0.6 m, there is a larger deck area (i.e., a larger heat source); for the lower roof panel, when S = 3 m, there is a smaller deck area. For the conditions of controlling the heat source, this may not be an ideal heat-transfer study design, but the results can be applied in engineering practice.
The ventilation rate vent Q  (m 3 /s) of a ridge vent design case is calculated by: in which

Numerical Methods
The commercial CFD code PHOENICS is used to perform the numerical simulations of the problem investigated on a laptop with an Intel ® i7-1165G7. The governing equations, including a 3D incompressible Navier-Stokes equation, a time-independent convec-

Numerical Methods
The commercial CFD code PHOENICS is used to perform the numerical simulations of the problem investigated on a laptop with an Intel ® i7-1165G7. The governing equations, including a 3D incompressible Navier-Stokes equation, a time-independent convection diffusion equation and the LVEL turbulence model, with boundary conditions and parameters (shown in Table 2) are solved using the finite volume method. The formulations for these equations can be found in the PHOENICS handbook [16]; therefore, they are not available here. To connect the steep gradients of the dependent variables near a solid surface, a general wall function is used. The iterative computation continues until all field variables of the problem satisfy the specified 10 −3 relative convergence. Table 2. Parameters specified in the numerical calculations. (Figure 3a). For the grid point system, to increase the simulation correctness, the number of grids close to the model boundary and inside the model must be increased. When the grid independence of the mesh domain is tested, the air velocity along the Y'-axis (direction of the design parameter S) based on different grid points is used to calculate the deviation percentages and to determine a suitable grid point system for our calculations, as shown in Figure 3b  The heat source (driving force) of buoyant ventilation is the solar-heated roof panels. The aforementioned geometric configurations cause the areas of roof panels to vary with the design parameters. That is, when the design parameters are different, the heat sources may differ in size. For the upper roof panel, when E = 0.6 m, there is a larger deck area (i.e., a larger heat source); for the lower roof panel, when S = 3 m, there is a smaller deck area. For the conditions of controlling the heat source, this may not be an ideal heat-transfer study design, but the results can be applied in engineering practice.
The ventilation rate vent Q  (m 3 /s) of a ridge vent design case is calculated by: in which

Numerical Methods
The commercial CFD code PHOENICS is used to perform the numerical simulations of the problem investigated on a laptop with an Intel ® i7-1165G7. The governing equations, including a 3D incompressible Navier-Stokes equation, a time-independent convection diffusion equation and the LVEL turbulence model, with boundary conditions and parameters (shown in Table 2) are solved using the finite volume method. The formulations for these equations can be found in the PHOENICS handbook [16]; therefore, they are not available here. To connect the steep gradients of the dependent variables near a solid surface, a general wall function is used. The iterative computation continues until all field variables of the problem satisfy the specified 10 −3 relative convergence. Table 2. Parameters specified in the numerical calculations. (Figure 3a).
Distance between the physical model and in Figure 2b. The numerical simulation accuracy depends on the resolution of the computational mesh, and a finer grid leads to solutions that are more accurate. An increase in the number of cells provides better information; however, this is accompanied by a significant increase in computational resources. A grid system with approximately 90 × 201 × 154 (2,785,860) cells is used for the numerical simulations in this study.
To validate the present modeling works, simulations were performed for the selected case of the similar configuration and parameters for comparison with the experimental results. The experimental model (shown in Figure 3c), made of acrylic, is a 1/50 scale of the practical case shown in Figure 1c. To show the internal conditions, the heaters were removed from the roofs during image acquisition. Since it is difficult to place heaters over the two small upper roof panels and they have little impact on the temperature distribution inside the model, only 600 W/m 2 heaters are laid over the two large lower roof panels. To get an obvious vertical temperature change, a 1000 W/m 2 10 cm × 10 cm heater was placed in the middle of the model bottom. Type-T thermocouples with ± 0.1 • C uncertainties in the measured quantities are installed upward from the center of the heater at the model bottom, with 1 measuring point per centimeter and 20 points in total. Both the simulation and experimental environments have the same temperature, i.e., 28.1 • C.
The dimensions of the model and the computational domain are 0.36 m (X + ) × 0.268 m (Y + ) × 0.189 m (Z + ) and 1.08 m × 1.07 m × 0.567 m, respectively. In simulations, the floor is an adiabatic plate with no-slip condition, and the other boundary conditions of the computational domain are Neumann conditions. Although the geometry of the experimental model (Figure 3c; 1/50 scale of Figure 1c) and that of the physical model in the present study (Figure 2b) are not identical, there is a sufficient amount of similarity to consider this validation approach: both models are isolated, same pitched roof configurations, both have similar boundary conditions and both are subjected to thermally buoyant force. As a result, the essential thermal and airflow features in the validation works will also be present in the physical model.
The validation result (Figure 3d) shows a good agreement between predicted air temperature and experimental values with an average error of 8.8%, which indicates the reliability of the CFD modeling.

Flow Patterns and Temperature Distribution Observations
As shown in Figure 4a, sunshine on the roof panel leads to heat accumulation and a temperature rise. Then, the air around the roof panel is heated, increasing the temperature and decreasing the density, which, together with the inclined roof surface, results in two buoyancy-driven boundary layer flows ( Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines . Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. Table 1. Geometric data.

Parts of the Model Geometric Data
Coordinates (X + , Y + , Z + ) For illustration of the factory case and representative roof (Figures 1 and 2a Alternatively, the local negative pressure caused by the external wind passing ov the ridge vent can exhaust the indoor air, creating another natural ventilation mechanis Although this issue is not what we are exploring in this study, but worthy of further co sideration. When high temperatures and low wind velocities are present for a long peri of time, the thermal buoyancy mentioned above becomes an important driving force f natural ventilation. In this study, the temperatures of all roof surfaces after solar heati are assumed to be isothermal, TH. In the external flow field, after the pitched roof receiv solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the ou door side above the roof panel, which then drives the flow of outdoor air, as indicated the green lines . Because the types of spaces below the roof and the openings are diverse and the a of this study is to assess the thermal buoyancy-driven ventilation induced by ridge ven in the process of physical modeling, the space below the ridge vent (i.e., the black dott zone shown in Figure 2a) is ignored based on reasonable boundary condition settin Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetr To save computational time, half of the representative roof is adopted as the physi model by means of the symmetry axis , as shown in Figure 2b. During the process CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational doma to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in t black dotted zone in Figure 2a is determined first, and then the roof structure and possib roof ventilation design are determined. Therefore, the representative roof discussed in th paper has the same length (X + direction) and width (Y + direction) as those of the worksh space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, duri the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in t Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on t ventilation performance of the ridge vent in the X-axis direction on both sides of the ro the length of the physical model in the X-axis direction was determined by taking t entire representative roof into consideration (X = X + = 0-18 m). For the relevant geomet data, see Table 1. Table 1. Geometric data.

Parts of the Model Geometric Data
Coordinates (X + , Y + , Z + ) For illustration of the factory case and representative roof (Figures 1 and 2a Alternatively, the local negative pressure caused by th the ridge vent can exhaust the indoor air, creating another na Although this issue is not what we are exploring in this stud sideration. When high temperatures and low wind velocitie of time, the thermal buoyancy mentioned above becomes a natural ventilation. In this study, the temperatures of all ro are assumed to be isothermal, TH.
In the external flow field, solar heat, a buoyancy-driven flow that moves obliquely u door side above the roof panel, which then drives the flow o the green lines .
Because the types of spaces below the roof and the ope of this study is to assess the thermal buoyancy-driven ventil in the process of physical modeling, the space below the rid zone shown in Figure 2a) is ignored based on reasonable Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patt To save computational time, half of the representative roo model by means of the symmetry axis , as shown in Figu CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b Figure 2a).
In the process of architectural design, the workshop s black dotted zone in Figure 2a is determined first, and then t roof ventilation design are determined. Therefore, the repres paper has the same length (X + direction) and width (Y + direct space below, i.e., 18 m and 13.4 m, respectively. To simplify the simulation process, only half of the roof and ridge vent ( Y + axis direction (Figure 2a) was analyzed. To understand th ventilation performance of the ridge vent in the X-axis direc the length of the physical model in the X-axis direction w entire representative roof into consideration (X = X + = 0-18 m data, see Table 1. For illustration of the factory case and representative roof (Figures 1 and 2a)  ) For illustration of the physical model (Figure 2b Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH.
In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields.  Figure 2a).
In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. For illustration of the factory case and representative roof (Figures 1 and 2a) For illustration of the physical model (Figure 2b) Alternatively, the local negative pressure caused by the external wind passing over he ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. lthough this issue is not what we are exploring in this study, but worthy of further conideration. When high temperatures and low wind velocities are present for a long period f time, the thermal buoyancy mentioned above becomes an important driving force for atural ventilation. In this study, the temperatures of all roof surfaces after solar heating re assumed to be isothermal, TH. In the external flow field, after the pitched roof receives olar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outoor side above the roof panel, which then drives the flow of outdoor air, as indicated by he green lines .
Because the types of spaces below the roof and the openings are diverse and the aim f this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, n the process of physical modeling, the space below the ridge vent (i.e., the black dotted one shown in Figure 2a) is ignored based on reasonable boundary condition settings. hen, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. o save computational time, half of the representative roof is adopted as the physical odel by means of the symmetry axis , as shown in Figure 2b. During the process of FD modeling, the following assumptions are made: 1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields.  Figure 2a).
In the process of architectural design, the workshop space (area and height) in the lack dotted zone in Figure 2a is determined first, and then the roof structure and possible oof ventilation design are determined. Therefore, the representative roof discussed in this aper has the same length (X + direction) and width (Y + direction) as those of the workshop pace below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during he simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the entilation performance of the ridge vent in the X-axis direction on both sides of the roof, he length of the physical model in the X-axis direction was determined by taking the ntire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric ata, see Table 1.
Parts of the Model Geometric Data Coordinates (X + , Y + , Z + ) For illustration of the factory case and representative roof (Figures 1 and 2a) does not contact the upper roof panel. Instead, it flows vertically upward 2, 12, x FOR PEER REVIEW 4 of 13 Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields.  Figure 2a).
In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1. Coordinates (X + , Y + , Z + ) For illustration of the factory case and representative roof (Figures 1 and 2a) For illustration of the physical model (Figure 2b) under the influence of thermal buoyancy and a symmetric flow pattern.
Then, the space below the representative roof is assumed to be a workshop to show how the flow pattern of the representative roof affects the air pollutant discharge in such a space. The distance between the air particles Then, the space below the representative roof is assumed to be a workshop to show how the flow pattern of the representative roof affects the air pollutant discharge in such a space. The distance between the air particles  in the air trajectory and the central axis of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air particles on the left (such as  (1 m from the central axis of symmetry),  (2 m), and  (3 m)) can all smoothly flow upward from the workshop space below the representative roof and then out of the ridge vent with the buoyancy-driven flow. The air particles on the right side of  are restricted by the inner circulation at the ridge vent from flowing outside. Equipment with in the air trajectory and the central axis of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air particles on the left (such as   Then, the space below the representative roof is assumed to be a workshop to show how the flow pattern of the representative roof affects the air pollutant discharge in such a space. The distance between the air particles  in the air trajectory and the central axis of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air particles on the left (such as  (1 m from the central axis of symmetry),  (2 m), and  (3 m)) can all smoothly flow upward from the workshop space below the representative roof and then out of the ridge vent with the buoyancy-driven flow. The air particles on the right side of  are restricted by the inner circulation at the ridge vent from flowing outside. Equipment with (3 m)) can all smoothly flow upward from the workshop space below the representative roof and then out of the ridge vent with the buoyancy-driven flow. The air particles on the right side of Then, the space below the representative roof is assumed to be a w how the flow pattern of the representative roof affects the air pollutant a space. The distance between the air particles  in the air trajectory a of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air p (such as  (1 m from the central axis of symmetry),  (2 m), and  (3 m flow upward from the workshop space below the representative roof a ridge vent with the buoyancy-driven flow. The air particles on the r restricted by the inner circulation at the ridge vent from flowing outsid are restricted by the inner circulation at the ridge vent from flowing outside. Equipment with heat dissipation is usually installed or a process for discharging air pollutants usually occurs in the space below  Then, the space below the representative roof is assumed to be a workshop to show how the flow pattern of the representative roof affects the air pollutant discharge in such a space. The distance between the air particles  in the air trajectory and the central axis of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air particles on the left (such as  (1 m from the central axis of symmetry),  (2 m), and  (3 m)) can all smoothly flow upward from the workshop space below the representative roof and then out of the ridge vent with the buoyancy-driven flow. The air particles on the right side of  are restricted by the inner circulation at the ridge vent from flowing outside. Equipment with . Then, according to the air trajectory, the high-temperature or polluted air inside is easily drawn out by the airflow. In contrast, the space below the right side of Then, the space below the representative roof is assumed to be a workshop to show how the flow pattern of the representative roof affects the air pollutant discharge in such a space. The distance between the air particles  in the air trajectory and the central axis of symmetry, as shown in Figure 4a, is 0.6 m (i.e., S/2), and the air particles on the left (such as  (1 m from the central axis of symmetry),  (2 m), and  (3 m)) can all smoothly flow upward from the workshop space below the representative roof and then out of the ridge vent with the buoyancy-driven flow. The air particles on the right side of  are restricted by the inner circulation at the ridge vent from flowing outside. Equipment with is generally the central aisle of the workshop, which seldom experiences high temperature or air pollutants. Thus, ventilation is not necessary there. Therefore, even if inner circulation occurs at the ridge vent above the aisle, the flow pattern has little influence on the entire ventilation efficiency.   The eave overhang (E value) in Figure 4a is 0. However, to prevent rainwater from entering the room through the ridge vent, an appropriate eave overhang is often designed. If the eave overhang is 0.6 m (as shown in Figure 4b), the buoyancy-driven flow Buildings 2022, 12, x FOR PEER REVIEW Alternatively, the local negative pressure cause the ridge vent can exhaust the indoor air, creating an Although this issue is not what we are exploring in sideration. When high temperatures and low wind v of time, the thermal buoyancy mentioned above be natural ventilation. In this study, the temperatures are assumed to be isothermal, TH. In the external flow solar heat, a buoyancy-driven flow that moves obli door side above the roof panel, which then drives th the green lines .
Because the types of spaces below the roof and of this study is to assess the thermal buoyancy-drive in the process of physical modeling, the space below zone shown in Figure 2a) is ignored based on reas Then, a representative roof is obtained.
The geometric configurations (, ) and heat fl To save computational time, half of the representa model by means of the symmetry axis , as shown CFD modeling, the following assumptions are made  Alternatively, the local negative pressure caused by the external wind passing over dge vent can exhaust the indoor air, creating another natural ventilation mechanism. ugh this issue is not what we are exploring in this study, but worthy of further conation. When high temperatures and low wind velocities are present for a long period e, the thermal buoyancy mentioned above becomes an important driving force for al ventilation. In this study, the temperatures of all roof surfaces after solar heating ssumed to be isothermal, TH. In the external flow field, after the pitched roof receives heat, a buoyancy-driven flow that moves obliquely upward also forms on the outside above the roof panel, which then drives the flow of outdoor air, as indicated by reen lines .
Because the types of spaces below the roof and the openings are diverse and the aim s study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, e process of physical modeling, the space below the ridge vent (i.e., the black dotted shown in Figure 2a) is ignored based on reasonable boundary condition settings. , a representative roof is obtained. The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. ve computational time, half of the representative roof is adopted as the physical el by means of the symmetry axis , as shown in Figure 2b. During the process of modeling, the following assumptions are made: The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. The lower boundary of the computational domain below the roof is given Neumann conditions (blue line , Y = 0-6.7 m; Z = 0 m) so that the fluid can flow freely into or . Therefore, after combining with the buoyancy-driven flow 4 of 13 Alternatively, the local negative pressure caused by the external wind passing over ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. though this issue is not what we are exploring in this study, but worthy of further coneration. When high temperatures and low wind velocities are present for a long period time, the thermal buoyancy mentioned above becomes an important driving force for tural ventilation. In this study, the temperatures of all roof surfaces after solar heating assumed to be isothermal, TH. In the external flow field, after the pitched roof receives lar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outor side above the roof panel, which then drives the flow of outdoor air, as indicated by green lines . Because the types of spaces below the roof and the openings are diverse and the aim this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, the process of physical modeling, the space below the ridge vent (i.e., the black dotted ne shown in Figure 2a) is ignored based on reasonable boundary condition settings. en, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. save computational time, half of the representative roof is adopted as the physical del by means of the symmetry axis , as shown in Figure 2b. During the process of D modeling, the following assumptions are made: The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. The lower boundary of the computational domain below the roof is given Neumann Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. Alternatively, the local negative pressure caused by the external wind passing over the ridge vent can exhaust the indoor air, creating another natural ventilation mechanism. Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. sideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.   Figure 4d. In terms of the air temperature, the indoor side of the upper roof panel (symbol A) accumulates heat, as shown in the red zone in Figure 4c,d. The air in the red zone is restricted by the inner circulation Although this issue is not what we are exploring in this study, but worthy of further consideration. When high temperatures and low wind velocities are present for a long period of time, the thermal buoyancy mentioned above becomes an important driving force for natural ventilation. In this study, the temperatures of all roof surfaces after solar heating are assumed to be isothermal, TH. In the external flow field, after the pitched roof receives solar heat, a buoyancy-driven flow that moves obliquely upward also forms on the outdoor side above the roof panel, which then drives the flow of outdoor air, as indicated by the green lines .
Because the types of spaces below the roof and the openings are diverse and the aim of this study is to assess the thermal buoyancy-driven ventilation induced by ridge vents, in the process of physical modeling, the space below the ridge vent (i.e., the black dotted zone shown in Figure 2a) is ignored based on reasonable boundary condition settings. Then, a representative roof is obtained.
The geometric configurations (, ) and heat flow patterns (TH , ) are symmetric. To save computational time, half of the representative roof is adopted as the physical model by means of the symmetry axis , as shown in Figure 2b. During the process of CFD modeling, the following assumptions are made: (1) The plane Y = 0 ( in Figure 2b) is set at the boundary of the computational domain to a wall with no-slip conditions to realize symmetry of the flow fields. In the process of architectural design, the workshop space (area and height) in the black dotted zone in Figure 2a is determined first, and then the roof structure and possible roof ventilation design are determined. Therefore, the representative roof discussed in this paper has the same length (X + direction) and width (Y + direction) as those of the workshop space below, i.e., 18 m and 13.4 m, respectively. To simplify the CFD calculation, during the simulation process, only half of the roof and ridge vent (Y = 0-6.7 m, Figure 2b) in the Y + axis direction (Figure 2a) was analyzed. To understand the possible edge effects on the ventilation performance of the ridge vent in the X-axis direction on both sides of the roof, the length of the physical model in the X-axis direction was determined by taking the entire representative roof into consideration (X = X + = 0-18 m). For the relevant geometric data, see Table 1.   The parameters considered (i.e., variables discussed) in the design of the ridge vent include the width S, height H, and eave overhang E (Figure 2b). In consideration of engineering practices, the following ranges of design parameters S, H, and E are used: The heat source (driving force) of buoyant ventilation is the solar-heated roof panels. The aforementioned geometric configurations cause the areas of roof panels to vary with the design parameters. That is, when the design parameters are different, the heat sources may differ in size. For the upper roof panel, when E = 0.6 m, there is a larger deck area (i.e., a larger heat source); for the lower roof panel, when S = 3 m, there is a smaller deck area. For the conditions of controlling the heat source, this may not be an ideal heat-transfer study design, but the results can be applied in engineering practice.

Edge Effects
The ventilation rate vent Q  (m 3 /s) of a ridge vent design case is calculated by: in which

Numerical Methods
The commercial CFD code PHOENICS is used to perform the numerical simulations of the problem investigated on a laptop with an Intel ® i7-1165G7. The governing equations, including a 3D incompressible Navier-Stokes equation, a time-independent convection diffusion equation and the LVEL turbulence model, with boundary conditions and parameters (shown in Table 2) are solved using the finite volume method. The formulations for these equations can be found in the PHOENICS handbook [16]; therefore, they are not available here. To connect the steep gradients of the dependent variables near a solid surface, a general wall function is used. The iterative computation continues until all field variables of the problem satisfy the specified 10 −3 relative convergence. Table 2. Parameters specified in the numerical calculations. (Figure 3a).  Figure 5b,c, the influence range of the edge effect expands accordingly. When H increases to 1.2 m, the blue zone in Figure 5d shows that V z exhibits a more significant change along the X-axis. When S = 1.2 m (Figure 5a,b), the value of V z increases with increasing Y*; that is, V z increases toward the edge of the horizontal opening of the ridge vent (i.e., approaching the lower roof panel). However, when S = 3 m (Figure 5c,d), the value of V z does not increase with increasing Y*. According to Figure 5c, the overall value of Q v is 2.83 m 3 /s. The ventilation rates in the edge effect zones on both sides are both 0.98 m 3 /s, the sum of which accounts for approximately 70% of Q v . The ventilation rate in the unit length along the X-axis within the edge effect zone is 0.163 (m 3 /s)/m, while that within the nonedge effect zone is 0.144 (m 3 /s)/m; the differences between the two are not significant.

Design Parameter Effects
As shown in Figure 6a, when H and E are constants, as S increases, ventilation rate Q v first increases and then decreases. Despite the slight change in Q v , the difference between the values can still be observed. When S = 1.8 m, Q v has local maximum values. However, since the ridge vent is designed in consideration of aesthetics and roof construction, the designer cannot always make S approximately 1.8 m; moreover, due to the small change in Q v , the design results of S hardly affect the value of Q v under different parameters. The design can be based on the actual needs without considering whether S can reach the local maximum value.

Design Parameter Effects
As shown in Figure 6a, when H and E are constants, as S increases, ventilation rate v Q first increases and then decreases. Despite the slight change in v Q , the difference between the values can still be observed. When S = 1.8 m, v Q has local maximum values.
However, since the ridge vent is designed in consideration of aesthetics and roof construction, the designer cannot always make S approximately 1.8 m; moreover, due to the small change in v Q , the design results of S hardly affect the value of v Q under different parameters. The design can be based on the actual needs without considering whether S can reach the local maximum value. Figure 6b illustrates that when S and E are constants, v Q experiences a significant growth with increasing H. According to the line aggregations shown in the figure, S and E have far less of an impact on v Q than H does. When the ridge vent enables ventilation through thermal buoyancy, H becomes the dominant design parameter, which is beneficial for design work. When conditions of high temperature and low wind velocity occur most of the time, the designer may try to increase the height of the ridge vent (H) to improve the ventilation efficiency. However, considering the limitation of the vertical  Figure 6b illustrates that when S and E are constants, Q v experiences a significant growth with increasing H. According to the line aggregations shown in the figure, S and E have far less of an impact on Q v than H does. When the ridge vent enables ventilation through thermal buoyancy, H becomes the dominant design parameter, which is beneficial for design work. When conditions of high temperature and low wind velocity occur most of the time, the designer may try to increase the height of the ridge vent (H) to improve the ventilation efficiency. However, considering the limitation of the vertical support, impact of typhoons, and visual aesthetics, the value of H is not considerably increased to attain a high ventilation rate.
Buildings 2022, 12, x FOR PEER REVIEW 11 of 13 support, impact of typhoons, and visual aesthetics, the value of H is not considerably increased to attain a high ventilation rate. According to Figure 6c, compared to E = 0.3 m and E = 0.6 m, E = 0 m leads to a higher ventilation rate, although the roof panel of the ridge vent has no overhang when E = 0 m. In this case, rainwater enters the room through the ridge vent, which seriously affects the indoor environment. Therefore, designers include overhang, and the value of E is generally no more than 0. According to Figure 6c, compared to E = 0.3 m and E = 0.6 m, E = 0 m leads to a higher ventilation rate, although the roof panel of the ridge vent has no overhang when E = 0 m. In this case, rainwater enters the room through the ridge vent, which seriously affects the indoor environment. Therefore, designers include overhang, and the value of E is generally no more than 0.6 m. When E = 0.3 m and E = 0.6 m, the values of Q v show little difference. Thus, a designer can design the eave overhang (E value) as desired without affecting the efficiency of buoyant ventilation.
Since E = 0 m rarely occurs in design practice and the Q v values of E = 0.3 m and E = 0.6 m are almost the same, we do not consider the parameter E in the comprehensive analysis. As shown in Figure 6d, the ventilation rate Q v (m 3 /s) can be expressed as follows: Q v = 1.9 + 1.86H − (0.18H + 0.1)(S − 1.8) 2 (Error = 2.66%) The correlation equation deviates 2.66% from the simulation result. The applicable parameter ranges are S = 1.2-3.0 m, H = 0.3-1.2 m, and E = 0.3-0.6 m. For the convenience of prediction and clear description, H is the dominant design parameter, and the influence of S can be ignored. The ventilation rate Q v (m 3 /s) at this moment is simplified as follows (as shown in Figure 6d): Q v = 1.9 + 1.86H (Error = 5.36%)

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This correlation equation deviates just 5.36% from the simulation result, which is acceptable in engineering practice and helpful for quick estimation of the ventilation rate. For example, when the operating space in the workshop below the ridge vent is 6 m in height, 13.4 m in width, and 18 m in length (both the width and length are the same as those of our study model), then when H = 0.3-1.2 m, we can quickly obtain the ventilation rate per hour as (= 3600Q v Air volume (6×13.4×18) ) 0.75-3 air changes per hour (ACH) according to Equation (3).

Conclusions
Numerical simulations are used to investigate how the design parameters of ridge vents affect the efficiency of thermal buoyancy-driven natural ventilation. The length and width of the representative roof are 18 m and 13.4 m, respectively. The height depends on the design parameters of the ridge vent. The design parameters include the width S, height H, and eave overhang E. In consideration of engineering practices, their ranges are set as follows: S = 1. The current results are limited to the investigated object and selected typical weather conditions. To explore practical applications and ventilation rates in other conditions, tests should be performed again under specific weather conditions. Configurations of the object (e.g., building height, geometry, building openings, ridge vent design, etc.) and design and layout of indoor partitions would affect ventilation performance. Although the investigation of these subjects (wind conditions, object configurations and indoor partitioning) is not what we explored in this study but is worth discussing.