### 1. Introduction

### 2. Simulation Set-up

### 2.1. Governing Equations

*u*is the velocity in

*x*direction,

*v*is the velocity in

*y*direction, and

*w*is the velocity in

*z*direction.

*k-ɛ*) model is commonly employed to interpret flow properties for turbulence conditions in CFD [19]. There are two variables of turbulence kinetic energy (

*k*) and the rate of dissipation of turbulence energy (ɛ) in this model. The turbulent viscosity is assumed as isotropy that the ratio between Reynolds stress and deformation rate is the same in all directions [20]. The

*k-ɛ*equations have a lot of unknown terms. To practically approach, the standard

*k-ɛ*model is employed to minimize the unknown factors, thus applying a plenty of turbulent flow applications. The equations of turbulent kinetic energy (

*k*) and dissipation (

*ɛ*) are follows [21].

##### (2)

$$k:\frac{\partial (\rho k)}{\partial t}+\frac{\partial (\rho k{u}_{i})}{\partial {x}_{i}}=\frac{\partial}{\partial {x}_{j}}\left[\frac{\mu t}{{\sigma}_{k}}\frac{\partial k}{\partial {x}_{j}}\right]+2{\mu}_{t}{E}_{ij}{E}_{ij}-\rho \varepsilon $$##### (3)

$$\varepsilon :\frac{\partial (\rho \varepsilon )}{\partial t}+\frac{\partial (\rho \varepsilon {u}_{i})}{\partial {x}_{i}}=\frac{\partial}{\partial {x}_{j}}\left[\frac{\mu t}{{\sigma}_{\varepsilon}}\frac{\partial \varepsilon}{\partial {x}_{j}}\right]+{C}_{1\varepsilon}2{\mu}_{t}{E}_{ij}{E}_{ij}-{C}_{2\varepsilon}\rho \frac{{\varepsilon}^{2}}{k}$$*u*

*is velocity component in corresponding direction,*

_{i}*E*

*is component of deformation rate, and*

_{ij}*μ*

*is eddy viscosity.*

_{t}### 2.2. Module Structure

### 2.3. Boundary Conditions

^{2}/31,400 m

^{2}when 10,000 fibers (generally 9,000–10,000 fibers per module) were employed in the membrane. The detailed conditions of the inflow are shown in Table 1. The wall boundary conditions were applied under non-slip conditions.

### 2.4. Reynolds Number

*u*is the average velocity (m/s) on vessel,

*D*is the vessel diameter (m),

*ρ*is the water density (kg/m

^{3}), and

*μ*is the dynamic viscosity (Pa•S) of water.

### 3. Results and Discussion

### 3.1. Hydraulic Re

### 3.2. Variations of Velocity and Pressure at Cross-sectional Plane

#### 3.2.1. Cross-sectional plane contour, average, and streamline velocity

#### 3.2.2. Cross-sectional plane contour and average pressure

### 3.3. Variations of Velocity and Pressure at Outlet

### 3.4. Flow Distribution on Outlet

#### 3.4.1. Velocity variation at each section on outlet

#### 3.4.2. Pressure variation at each section on outlet

#### 3.4.3. Flowrate at each section on outlet

### 4. Conclusions

In the results of Re used to determine the flow pattern of the inflow, Re values were estimated to be under turbulent flow for Re ≫ 4,000, as a whole.

In the contour, average velocity, and pressure in the cross-sectional plane of the inflow obtained using CFD simulations, the fluid velocity of shapes 4 and 6, round-type protrusion, displayed a more uniform flow distribution than other shapes (e.g., triangle, bar, and ellipse), and the fluid pressure in shape 6 maintained the low water pressure. Overall, shape 6 displayed the best fluid flow in terms of velocity and pressure.

From the contour at outlet plane, average velocity, and pressure at the outlet, shapes 4 and 6 with round-type protrusions presented a relatively uniform fluid velocity, and the fluid pressure in shape 4 was found to have better water pressure.

In the simulations of velocity, pressure and flowrate of nine sections at 10 mm intervals on the outlet, the shape 6 was considered to be the best uniform distribution in the outlet plane, showing a high velocity and a lower standard deviation of flowrate on each section.

In summary, shape 6 showed higher average velocity on the cross-sectional and outlet plane of the module, and the standard deviation of flowrate on each section of outlet plane is lowest. Therefore, it proved that shape 6 has the most uniform flow distribution within the module.