1. Introduction
Machinery and equipment can effectively filter large amounts of floating matter and foreign matter flowing into waterintake pumping stations, drainage pumping stations, relay pumping stations, and coolant inlets in power plants when large volumes of foreign matter is generated in rivers or the water flow is increased rapidly by rain. If foreign matter flows into the channels, it can flow into the drai nage pumping stations and power plant coolant inlets. This foreign matter will be sucked into motors or pumps and enter pumps’ impellers and impeller casings, causing the pumps to overload, which may even burn out the pumps. Moreover, if foreign matter enters the drainage pumping station and relay pumping station and proper drainage is not performed, it can cause floods, resulting in enormous property damage.^{[1]} To prevent these problems, particulate separators are used to filter foreign matter from rivers and facilitate smooth drainage. Since particulate separators were first introduced, technical developments have been made to improve their problems and performance. However, the performance of particulate separators has not changed significantly. ^{[2]}
Recently, localized torrential rainfalls have developed with South Korea’s changing climate patterns, and the amount of foreign matter has greatly increased due to the large amount of flow over a short period. Therefore, we need to develop particulate separators that can quickly drain a large amount of flow while effectively filtering foreign matter.
A particulate separator is divided into a screen unit and rake unit. The screen filters the incoming foreign matter, but if foreign matter accumulates in the screen, it hinders and can halt the water flow. To prevent the foreign matter accumulating, a rake is installed that removes foreign matter from the screen.^{[1,3]}
Existing studies had problems because if the spacing between the screens was reduced to effectively filter foreign matter, it lowered the drain performance and if the spacing were widened to improve drainage, it lowered the particulate separation performance.
This study reduces the screen spacing by introducing the Coanda effect to optimize the shape of the particulate separator screen, thereby achieving excellent drain performance while improving the particulate separation performance.
2. Theoretical Background and Numerical Analysis Method
2.1 Coanda effect
The Coanda effect refers to the phenomenon of a fluid flowing along a curved surface. The surface pressure along the curved wall gradually increases to the surrounding pressure, and the curved wall and flow jet are separated in this condition.
Bradshaw described the Coanda effect from the perspective of nonviscous, nonrotating flow through a theoretical hypothesis. Assuming that the flow is initially nonviscous, the formula for the flow’s pressure behavior is derived from the Bernoulli equation as follows^{[4–5]}:
where ρ is the density of the ejected fluid, U is the mean flow rate, and a is the radius of the curvature. Under the condition of Eq. (2), the pressure of the nonviscous fluid is lower than the surrounding pressure.
Here, bis the spacing of the ejected slots.^{[4–6]}
The mean speed decreases while the surface pressure along the wall increases and equals the atmospheric pressure. When the condition of the surface pressure p_{s} is ${p}_{s}={p}_{\infty}$ , flow separation from the curved surface occurs.^{[4]}
The Coanda effect can be explained with a few physical parameters. Through a Coanda flow analysis at a high Reynolds number by Newman in Eq. (3), the flow along a cylinder is described as the following proposed equation^{[4]}:
where, ${\theta}_{sep}$ is the jet flow separation angle, b is the slot width, a is the radius of the curvature, and $\left({p}_{0}{p}_{\infty}\right)$ is the difference between the pressure on the wall surface and the atmospheric pressure. This shows that the flow separation angle ${\theta}_{sep}$ is a function of the pressure difference, the cylinder’s geometrical characteristics, and the fluid’s characteristics.^{[4]}
2.2 Governing equation
The ShearStress Transport (SST) kω turbulence model of the ANSYS FLUENT 16.0 was used to predict the drain performance and flow of the water flowing into the particulate separator screen and accurately predict the flow near the wall. The SST kω model combines the k  ∈ model, which can analyze the flow of a high Reynolds number appropriately and the kωmodel, which simulates the low Reynolds number area near the wall. Eqs. (4) and (5) are the transportation equations of the kinetic energ k and the specific dissipation rate ω. In Eq. (5), ${D}_{\omega}$ is a crossdiffusion term. The kω model is used to correctly predict the viscous effect near the wall and the k∈model is used in the flow’s internal area.^{[7–9]}
Here, the viscosity terms Γ_{k} and Γ_{ω} are defined by the strain rate and specific dissipation rate instead of the Reynolds number to reflect the transfer effect of the turbulent stress. Y_{k} and Y_{∈}are dissipation terms that apply the regression analysis (piecewise) method. In Eq. (4), ${\tilde{G}}_{k}$ the generation term of k, is a corrected value of G_{k}for the flow strain and the specific dissipation rate ω.^{[7~9]}
2.3 Analysis variables and boundary conditions
To verify the Coanda effect according to the shape of the particulate separator screen, analysis variables were set for each part of the screen shape to be applied to numerical analysis. Fig. 1
Fig. 2 shows the shape factors for the particulate separator screen. In total, four variable factors were given: the radius of the curvature R_{1}(030mm), that can directly influence the Coanda effect; the radius of the curvature R_{2}(020mm), that can indirectly affect the Coanda effect and affect the fluid’s main flow; h(015mm), ), which represents the height difference between the acceleration plate that increases the flow rate of water and the screen shape; and the angle θ (1040°) that influences the flow rate in the fluid entering the screen.^{[10]}
The number of screen shapes was identical at 10, the spacing between the shapes was fixed at 10 mm, and the length of the acceleration plate was 800 mm.
For the flow field and outlet, the atmospheric pressure 101.325 kPa was applied as the initial condition. Fig. 3 shows the boundary conditions and a rough system that was applied in the analysis. Water with a 100 kg/s flow rate flows into the inlet, the water that passes through the screen filter is drained through Outlet and the water that does not pass through the screen is drained through Outlet.
2.4 Evaluation of the drain performance for the particulate separator screen
Water flows into the inlet and drains through Outlet and Outlet.
The higher the screen’s drain performance, the larger the flow rate through Outlet1, which confirmed the screen’s drain performance.
The drain performance, which is determined by comparing the water flow rate into the inlet and the flow rate of the water cleaned through the screen draining through Outlet, can be expressed as Eq. (6).^{[11~12]}
3. Numerical Analysis Results
3.1 Flow analysis according to the radius of the R_{1}
In the screen shape, R_{1}is a shape factor that can directly influence the Coanda effect. The drain performance of the screen was analyzed while increasing the radius of the curvature R_{1} from 0 to 30 mm in 5 mm intervals considering the shape fabrication. Table 1 shows the flow rate and drain performance of Outlet and Outlet according to the radius of the curvature R_{1}. Fig. 4 shows the drain performance of the screen according to the radius of the curvature R_{1}.
The analysis results show that the drain performance was 0.52% when the radius of the curvature R_{1}was 0 mm. Starting from 10 mm or higher, a lowpressure zone from the Coanda effect was formed on the surface of the screen shape and the drain performance also increased greatly.
Fig. 5 shows the flow rate and pressure distribution of water according to the curvature radius. The larger the radius of the curvature R_{1}, the more the lowpressure zone develops on the curvature surface and the faster the flow rate of the water draining through the shapes. As the radius of the curvature R_{1} of the shape increased, the drain performance improved and the pattern of the lowpressure zone changed on the shape surface.
Fig. 6 shows the water speed vector when the radius of the curvature R_{1} was 30 mm. The development of the water speed vector by the Coanda effect can be seen on the surface of the screen shape.
Fig. 7 shows the pressure distribution when the radius of the curvature R_{1} was 30 mm. The development of a large lowpressure zone by the Coanda effect can be seen on the shape’s surface, which is consistent with the results of the speed vector in Fig. 6.
3.2 Flow analysis according to the radius of curvature R_{2}
The drain performance of the screen shape was analyzed according to the radius of curvature R_{2}. It is expected that R_{2}will have a small effect on the Coanda effect, but can influence the main flow of the incoming water. Since high pressure occurs at R_{2} the difference needs to be checked. For the screen shape, R_{1}=30mm was used, which showed the best performance in Section 3.1, and the value of R_{2} was increased from 0 to 20 mm in 5 mm intervals.
Table 2 shows the flow rate and drain performance of the fluid draining through Outlet and Outlet according to the radius of the curvature R_{2} The flow analysis results showed that the drain performance was the largest at the R_{2} value of 5mm, and an approximately 1–3% performance difference was observed at each different R_{2} value.
In the pressure distribution in Fig. 9, the radius of the curvature R_{2} does not significantly affect the Coanda effect. However, as the R_{2} value increases, a lowpressure zone was formed at the meeting point of R_{1} and R_{2} at top of the screen shape and the pressure rapidly became similar to the atmospheric pressure. Then, a flow separation occurs and the amount of water flowing on the shape surface decreases, lowering the drain performance.
3.3 Flow analysis according to h
A flow analysis was performed because h, which represents the acceleration plate to adjust the water speed and the top of the screen shape, can influence the shear stress and Coanda effect at the top of the screen shape. For R_{1} and R_{2}, 30 mm and 5 mm were used, respectively.
In Table 3 and Fig. 10, as the value of h increased, the drain performance tended to improve, but the drain performance dropped sharply when the value of h became 15 mm.
Fig. 11(a) and (d) show that drainage occurs from near the center of the particulate separator screen. In contrast, the drainage occurs evenly for every shape in (c) and (d) from the start to the end of the particulate separator screen.
3.4 Flow analysis according to θ
The water flow velocity accelerates as the angle θ increases. Since the flow velocity can have a large effect on the Coanda effect and pressure distribution, the effect of the flow velocity on the drain performance was observed while changing the size of angle θ .
The dimensions optimized in this study were: 30 mm for R_{1} , 10 mm for R_{2} , and 10 mm for h. Table 4 shows the flow rates of Outlet and Outlet according to θ and Fig. 12 shows the drain performance.
The smaller the angle θ , the larger the drain performance. When θ was 10°, the drain performance was 100%. Comparing the flow velocity and pressure distribution on the screen shape surface in Fig. 13 shows that a large flow velocity developed on the shape surface and the pressure of the lowpressure zone decreased further. In contrast, at a θ of 50% where the drain performance was 50%, almost no lowpressure zone formed on the shape surface.
4. Conclusion
The screen shape factors of the particulate separator that can influence the Coanda effect were determined and the drain performance was numerically analyzed while changing the sizes of factors.

For the radius of the curvature R_{1}, the Coanda effect was caused by the lowpressure zone that formed on the surface of the particulate separator screen and the development of flow velocities in the lowpressure zone, and it had the largest effect on the drain performance.

The amount of water that flowed along the shape surface due to the Coanda effect was the largest when the radius of curvature R_{1} was 30 mm.. The analysis results showed that shape factors other than R_{1} had small effects on the Coanda effect.

The size of θ mainly influenced the water flow velocity. The smaller it was, the lower the flow velocity and the higher the drain performance.

When each shape factor was analyzed from an optimum design perspective, the drain performance was highest at 96.73% when R_{1} was 30 mm, R_{2} was 5 mm, and h was 10 mm.