# Simulation Study of a New Magnetorheological Polishing Fluid Collector Based on Air Seal
## 3 Simulation Parameters of MR Polishing Liquid Collector
### Simulation Parameters  
The mixed phases used in the simulation are deionized water (DW), carbonyl iron powder (CIP), and cerium oxide (CeO\({}_{2}\)). The density, particle size, permeability, and volume fraction of each phase are shown in Table 1.  
The magnetic field distribution of the model is shown in Figure 5. Because the magnetic field intensity at the MR collector is less than that in the polishing area, the rheological properties of the polishing liquid in this area are weak, changing the viscosity properties of the material is not necessary. The MHD module built in FLUENT can be used to simulate the apparent change in the polishing liquid under the conditions of a uniform magnetic field. A magnetic induction intensity of 0.01 T [32; 33] is applied to the flow area of the polishing liquid, and the magnetic field direction is positive along the \(Y\) axis.  
Reynolds number is an infinite number that determines whether the fluid flow is laminar or turbulent. The definition is as follows:  
\[\text{Re}=\frac{\rho\text{vd}}{\mu} \tag{6}\]  
where \(\rho\) is the density of the fluid, \(\
u\) is the velocity of the fluid, \(\text{d}\) is the characteristic scale of flow field, and \(\mu\) is the viscosity coefficient of the fluid. The critical Reynolds number, \(\text{Re}_{\text{cr}}\)\(=2100\), is used as the criterion. There are multiple fluid phases in the simulation model, resulting in different Reynolds numbers in different fluid regions. The air density is 2.225 kg/m\({}^{3}\), the velocity is 30 m/s, the characteristic scale is the nozzle diameter of 0.002 m, and the aerodynamic viscosity is 1.7894 \(\times\) 10\({}^{-5}\). According to Formula (6), the Reynolds number at the airflow nozzle is 4083 \(>\) 2100, which is turbulent. MR polishing fluid at the entrance can be used as a turbulence treatment. When MR fluid is affected by the magnetic field, the viscosity of the polishing fluid changes. The polishing fluid adheres to the surface of the polishing wheel and is laminar.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** & **DW** & **CIP** & **CeO\({}_{2}\)** \\ \hline Density (g/cm\({}^{3}\)) & 1.0 & 7.8 & 7.13 \\ \hline Viscosity (Pa-s) & 0.001 & \(1.72\times 10^{-5}\) & \(1.72\times 10^{-5}\) \\ Volume fraction (\%) & 60 & 36 & 4 \\ Particle size (um) & & 3 & 3 \\ Permeability (H/m) & 1 & 1000 & 1 \\ Conductivity (S/m) & \(5.89\times 10^{-8}\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the mixed phase.  
Figure 5: Cloud map of magnetic field distribution.  
The simulation solver type is a pressure base solver, the time format is transient, the time integration scheme is implicit integration, and the interface modeling is phased local discretization. As the Reynolds number is greater than the critical number, a realizable k-epsilon turbulence model is selected. The momentum equation, kinetic energy equation, and kinetic energy dissipation rate are calculated by the first-order upwind scheme and SIMPLE algorithm. The calculation time step is 4 \(\times\) 10\({}^{-3}\), and the final simulation time is 1 s. Considering the influence of gravity, the gravity acceleration along the negative direction of the \(Y\) axis is set to 9.8 m/s. The polishing wheel surface is set as the rotating wall. The center of the rotation is the center of the curvature of the surface (0,\(-\)138.48,0). The direction of the rotation axis is counterclockwise along the \(Z\) axis, and the speed is 110 r/min. In order to make the simulation test closer to the actual situation, the linear velocity of the inlet boundary of the MR polishing liquid is applied at the same speed as that of the polishing wheel, and the non-slip wall is selected, i.e., it is assumed that the polishing liquid has no relative slip velocity with the wheel surface. The collector outlet is connected to the recovery pump, and the pressure is negative 0.2 MPa.