# Enhancing Flow Field Performance of a Small Circulating Water Channel Based on Porous Grid Plate
## 3 Resistance Coefficient of a Porous Grid Plate  
In order to improve the uniformity of the velocity and pressure distribution of the fluid flowing to the contraction section, a porous grid plate should be placed in the rectification section to improve the flow quality [18]. The porous grid plate in the rectification section mainly includes the honeycomb and screens. In general, the honeycomb with a relatively large thickness is selected to suppress the lateral turbulence, and the screen with a little thickness is selected to suppress the axial turbulence. The screens are arranged at certain intervals, as shown in Figure 3, where \(d\) represents the spacing between the screens, and \(l\) represents the thickness of the honeycomb. When flowing through the porous grid plate, the fluid is rectified by the holes to flow along the axial direction. When the fluid flows through the hole, it will be subject to the viscous resistance and inertial resistance. In order to study the rectification characteristics of the designed circulating  
Figure 3: Local parameters of the rectification section. \(d\) represents the spacing between the screens, and \(l\) represents the thickness of the honeycomb. Figure 2: The selected contraction curve. \(R_{1}\) is the radius at the inlet of the contraction section, \(R_{2}\) is the radius at the outlet, \(L\) is the length of the contraction section, and \(R\) is the radius at a location where the distance from the inlet is \(x\). water channel based on the porous grid plate with different porosities, it is necessary to obtain the viscosity resistance coefficients and inertia resistance coefficients of the porous grid plate with different porosities. Computational fluid dynamics (CFD) is mainly used for simulating the fluid characteristics; researchers can use self-built models to achieve fast and accurate CFD calculations or take use of commercial finite element analysis software such as Fluent or CFX. [PERSON] et al. [28] built a three-phase Volume of Fluid (VOF) model to predict the sedimentation and accumulation of sediment and obtained well accuracy. The main purpose of this work is to analyze the rectification performance by a porous grid plate, and the finite element analysis software Fluent is mainly used in this work. When the fluid flows into the porous grid plate, the loss of the momentum source includes two parts: viscous loss and inertia loss, which can be described as [29]:  
\[\frac{\Delta P}{\Delta\delta}=-S=\frac{\mu}{\alpha}v+\frac{C_{2}}{2}\rho v^{2} \tag{2}\]  
where \(\Delta P\) is the pressure drop generated when the fluid flows through a porous grid plate with a thickness of \(\Delta\delta\), \(S\) is momentum, \(v\) is velocity, \(\mu\) is viscosity, \(\rho\) is density, \(1/\alpha\) is the viscosity resistance coefficient, and \(C_{2}\) is the inertia resistance coefficient. It can be seen from Formula (2) that the viscosity resistance coefficient and inertia resistance coefficient are related to the porosity of the porous grid plate but not to its thickness. A test model for obtaining the resistance coefficients is shown in Figure 4; in order to facilitate the calculating, the diameters and spacing of the holes are taken as finite decimals, which results in the porosities are infinite decimals. Generally, the porosity of a porous grid plate is between 0.5 and 0.7. The results of the velocity \(v\) and \(\Delta P/\Delta\delta\) of fluid flowing through porous grid plates with different porosities are obtained, and the corresponding viscosity resistance coefficient \(1/\alpha\) and inertia resistance coefficient \(C_{2}\) are calculated by quadratic fitting, as shown in Table 1.  
Figure 4: The test model of a porous grid plate. \(\Delta\delta\): thickness of the porous grid plate.