1. Introduction
In the residential spaces, the kitchen and the living room are interconnected in general. Thus, if the harmful substances generated in the kitchen are not properly discharged through the vents in the kitchen or other ventilation facilities, the quality of the indoor air will decrease, causing adverse effects on the human body. In the kitchen, which is a place that causes the generation of indoor air pollutants, oil mists generated in the cooking process can cause respiratory disease, asthma, respiratory disorder, etc.^{[1]}
The kitchen hood removes these harmful substances. Therefore, the hood has a significant effect on the kitchen and indoor environment, and research on the filter to effectively remove oil mists from the kitchen is important.^{[2]} The shape of the filters used in the kitchen has a significant effect on their pressure loss and efficiency. The typical ones are mesh and baffle types. The mesh type causes almost no pressure loss, but its disadvantage is low oil mist collection efficiency. The baffle type has an advantage in collection efficiency, but its disadvantage is high pressure loss, which increases the capacity and vibration of the fan while sucking air. Various shapes of filters have already been analyzed, but most of them focused on the shape of the main filter.^{[37]} The chevron type, which is a baffle type, showed a collection efficiency of 93% and a pressure loss of 6.35 mmAq in previous studies. Due to the high pressure loss, the fan requires high power and the workability of the shape is inefficient.
In this study, the workability of the chevrontype filter is improved by removing the protrusions that generate high pressure and simplifying the shape. In addition, the pressure loss is lowered and the collection efficiency is increased through computational fluid dynamics analysis. Variables are set according to the shape and location of the subfilter, and a simplified subfilter that can reduce the load on the fan by lowering the pressure loss is proposed.
2. Theoretical Background and Numerical Analysis Method
2.1 Turbulence Model
To calculate the collection efficiency and pressure loss of the filter, the kω SST (ShearStress Transport) of ANSYS FLUENT 15.0 was selected as the turbulence model for this analysis, considering the importance of the flow near the wall.
The kω SST model combines the advantages of two models: the k  є model, which can analyze the region of a low Reynolds number near the wall. Eq. (1) represents the kinetic energy k, and Eq. (2) represents the transport equation of the specific dissipation rate ω. D_{ω} in Eq. (2) is a crossdiffusion term. Near the wall, the kє model is used to predict the viscous effect properly, and inside the flow, the kє model is used for calculation.
In the above equation, the viscous terms Γ_{k} and Γ_{ω} are defined by the strain rate and specific dissipation rate, instead of the Reynolds number, to reflect the transport effect of the turbulent stress. Y_{k} and Y_{ω} are dissipation terms applying the regression analysis (piecewise) method. In Eq. (1), ${\tilde{G}}_{k}$, which is the generation term of k, represents a value corrected for the strain of the flow and the specific dissipation rate ω.^{[8]}
2.2 Particle Collection Theory
In this study, the Lagrangian method is used to calculate the position of each particle moving in a flow field. The particle kinetic equation of the Lagrangian method is expressed as Eq. (3):
Where the left term represents the inertia force generated when a velocity acts on a particle; on the right side, F_{D}(uu_{p}) is the drag applied to the particle, $\overrightarrow{{g}_{x}}\left({\rho}_{p}\rho \right)/{\rho}_{p}$ is the force of gravity and buoyancy, and $\overrightarrow{{F}_{x}}$ mainly represents the lift. In each equation, u is the fluid speed, u_{p} is the particle speed, μ is the viscosity coefficient, ρ is the fluid density, and, ρ_{p} is the particle density.
The drag F_{D}(uu_{p}) can be determined by Eq. (4), and $\overrightarrow{{F}_{x}}$ can be determined by Eq. (5).^{[9]}
When particles move along the streamline, they are captured by a filter due to the inertia of the particles. This is called inertial collision and can be expressed by the Stokes number as the ratio of the particle’s stopping distance and the filter’s diameter, as in Eq. (6) ^{[10]}:
where τ is the relaxation time after the particle moves out of the streamline and returns to the streamline again, which can be calculated by Eq. (7):
where U_{0} is the initial speed of the particle and τU_{0} is the shortest distance the particle moved for the relaxation time. A large S_{tk} means that there are many colliding particles, and the larger this value is, the greater the collection efficiency of the filter becomes. ^{[911]}
2.3 Analysis of Boundary Conditions and Basic Filter
One of the chevrontype filters was analyzed by simulation. Table 1 lists the basic properties of the air and oil mist for the flow analysis, and Table 2 lists the detailed boundary conditions for the filter analysis. Fig. 1 shows a simplified filter (Sfilter) to which the existing chevron filter shape and the subfilter have not been applied.
For this analysis, it was assumed that the droplet had a spherical shape and that droplets were uniformly sprayed in the inlet condition.
Fig. 2 shows the pressure distribution of the chevron filter and Sfilter. The pressure loss of the chevron filter was relatively high at 6.35 mmAq, and the pressure loss of the Sfilter was calculated as 0.94 mmAq.
Fig. 3 shows the efficiencies of the chevron filter and Sfilter. The chevron filter showed very high efficiency at 92.4%, but its pressure loss was large. The pressure loss of the Sfilter was low, but its efficiency was 36.8%. The filters used in kitchens are generally designed with a pressure loss goal of 3 mmAq. or lower; thus, this study used a subfilter to increase the efficiency.
2.4 Design of Subfilter Shape
The boundary conditions applied to the numerical analysis to analyze the efficiency and pressure loss of the filter are shown in Fig. 4, and the three shapes selected for the subfilter are shown in Fig. 5. The subfilter was expected to play the role of a turbulence generator that generates turbulence in the incoming flow as the main filter.
A multiphase flow analysis was performed to examine oil mist and air simultaneously. The incoming mist was sprayed from the inlet and passed through the filter, and the mist that was not trapped was discharged through the outlet. The collection efficiency of the filter is expressed as Eq. (8).
To analyze the subfilter according to its position, the filter was mounted at 1 mm in the –y direction from the main filter, and the efficiency was analyzed while moving it by 0, 0.25 mm, and 0.5 mm in the +x direction. Furthermore, each shape was drawn with the moved point as the center of a triangle.
3. Numerical Analysis Results
3.1 Analysis Result by Shape
Table 3 shows the total collection efficiency and pressure loss of the filter after applying the subfilter and the speed of entering the bottom of the main filter. Fig. 6 shows the efficiency of each particle size for the three types of proposed filters. The analysis results confirmed that applying the subfilter increased the collection efficiency. The circle showed the highest collection efficiency, followed by the droplet and the cone.
The pressure loss was 0.94 mmAq for N/A for no subfilter and 1.26 mmAq for the circle. Thus, applying the subfilter did not have a significant effect on pressure loss.
Fig. 7 shows the pressure distribution and vector components. The direction of the vortex in the wake of the subfilter suggests that the subfilter plays the role of a turbulence generator at the inlet of the main filter.
The efficiency increased as the speed increased because the Stokes number increased in proportion to the speed. When the Stokes number increases, the particles of inertial collision increase, which in turn increases the collection efficiency.^{[911]}
3.2 Analysis Results by Position
The position of the subfilter became a variable that controlled the turbulence component of the fluid entering the main filter. The basic position of the subfilter was in the middle of the inlet of the main filter. Table 4 lists the collection efficiency, pressure loss, and the speed of the filter bottom when the fluid moved 0.25 mm in the +x direction. Fig. 8 shows the collection efficiency by particle size in a graph. When the subfilter was moved 0.25 mm in the +x direction, the filter inlet speed decreased. The total collection efficiency decreased by 2.89%, 8.78%, and 4.72% for the circle, droplet, and cone types, respectively, and the pressure loss also decreased.
Fig. 9 shows the pressure distribution of the filter on the right and the vector component on the left.
The circle type showed the best efficiency when the fluid moved 0.25 mm as well. As the pressure interval changed, the speed and efficiency also decreased. Finally, regarding the collection efficiency and pressure when the fluid was moved 0.5 mm in the +x direction, since the gap of the main filter was 1 mm, when it moved 0.5 mm,it was located at the bottom of the main filter.
Table 5 shows the collection efficiency, pressure loss, and speed when the fluid moved 0.5 mm. Fig. 10 shows the total collection efficiency in a graph, and Fig. 11 shows the pressure and vector.
The subfilter appears to have had almost no effect on controlling the flow into the bottom of the main filter because the subfilter did not play its role as a turbulence generator. Furthermore, the subfilter showed a lower collection efficiency of 3μ m or smaller ultrafine oil mist than the chevron filter. This is considered a problem in the inertial collection filter, and more variables are needed for a subfilter or main filter shape to collect ultrafine dust.
Fig. 12 shows the total collection efficiency of each filter by distance. A tendency of lowering the collection efficiency with a longer distance can be seen. When the subfilter was the circle type, the highest efficiency was obtained when it was located at the bottom center of the inlet of the main filter.
4. Conclusions
A numerical analysis was conducted according to different subfilter shapes to increase the efficiency of the main filter. The results confirmed that the filter efficiency was increased just by mounting a subfilter to play the role of a turbulence generator.

(1) The collection efficiency increased as the turbulence component of the subfilter wake was changed. The efficiency was increased by the increased speed because the collection efficiency was increased as the dimensionless variable called the Stokes number was increased by the inertial collision in the particle collection efficiency.

(2) The streamlined circle shape of the subfilter was effective at increasing the collection efficiency. It increased the collection efficiency by 27.8% compared with the Sfilter, and the pressure loss increased by 0.32 mmAq.

(3) The best position of the subfilter for efficient particle collection was at the bottom center of the inlet of the main filter. The circle type increased the collection efficiency by 15.7% at the 0 mm position compared with the 0.5 mm position.

(4) The filter with a subfilter had lower collection efficiency for ultrafine oil mist smaller than 3μm. To address this problem, more variables are required for the existing main filter and subfilter shapes.